J. Wheeler and W. Zurek (eds.): Quantum Theory and Measurement, 1983
C. DeWitt and N. Graham: The Many Worlds Interpretation of Quantum Mechanics
H. Everett: Theory of the Universal Wavefunction
Bjorken and Drell: Relativistic Quantum Mechanics/ Relativistic Quantum Fields
10.Ryder: Quantum Field Theory, 1984
11.Guidry: Gauge Field Theories: an introduction with applications 1991
12.Messiah: Quantum Mechanics, 1961
13.Dirac:
a] Principles of QM, 4th ed., 1958
b] Lectures in QM, 1964
c] Lectures on Quantum Field Theory, 1966
14.Itzykson and Zuber: Quantum Field Theory, 1980
15.Slater: Quantum theory: Address, essays, lectures. note: Schiff, Bjorken and Drell, Fetter and Walecka, and Slater are all volumes in “International Series in pure and Applied Physics” published by McGraw-Hill.
16.Pierre Ramond: Field Theory: A Modern Primer, 2nd edition. Volume 74 in the FiP series.
17.Feynman: The Feynman Lectures, Vol. 3
18.Heitler & London: Quantum theory of molecules
19.J. Bell: Speakable and Unspeakable in Quantum Mechanics, 1987
20.Milonni: The quantum vacuum: an introduction to quantum electrodynamics 1994.
21.Holland: The Quantum Theory of Motion
22.John von Neumann: Mathematical foundations of quantum mechanics, 1955.
23.Schiff: Quantum Mechanics, 3rd ed., 1968
24.Eisberg and Resnick: Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed., 1985.
25.David Saxon: Elementary Quantum Mechanics
26.Bethe and Jackiw: Intermediate Quantum Mechanics
27.P.W.Atkins: Quanta: A Handbook of concepts
28.James Peebles: Quantum Mechanics (1993)
Statistical Mechanics and Entropy
David Chandler: Introduction to Modern Statistical Mechanics, 1987
R. Tolman: Prinicples of Statistical Mechanics. Dover
Kittel & Kroemer: Statistical Thermodynamics
Reif: Principles of statistical and thermal physics.
Felix Bloch: Fundamentals of Statistical Mechanics.
Radu Balescu: Statistical Physics
Abrikosov, Gorkov, and Dyzaloshinski: Methods of Quantum Field Theory in Statistical Physics
Huw Price: Time’s Arrow and Archimedes’ Point
Thermodynamics, by H. Callen.
10.Statistical Mechanics, by R. K. Pathria
11.Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, by D. Forster
12.Introduction to Phase Transitions and Critical Phenomena, by H. E. Stanley
13.Modern Theory of Critical Phenomena, by S. K. Ma
14.Lectures on Phase Transitions and the Renormalization Group, by N. Goldenfeld
Condensed Matter
Charles Kittel: Introduction to Solid State Physics (ISSP),
Ashcroft and Mermin: Solid State Physics,
Charles Kittel: Quantum Theory of Solids.
Solid State Theory, by W. A. Harrison
Theory of Solids, by Ziman.
Fundamentals of the Theory of Metals, by Abrikosov
Many-Particle Physics, G. Mahan.
Special Relativity
Taylor and Wheeler: Spacetime Physics Still the best introduction out there.
Relativity: Einstein’s popular exposition.
Wolfgang Rindler: Essential Relativity. Springer 1977
A.P. French: Special Relativity
Abraham Pais: Subtle is the Lord: The Science and Life of Albert Einstein
Special Relativity and its Experimental Foundations Yuan Zhong Zhang
Particle Physics
Kerson Huang: Quarks, leptons & gauge fields, World Scientific, 1982.
L. B. Okun: Leptons and quarks, translated from Russian by V. I. Kisin, North-Holland, 1982.
T. D. Lee: Particle physics and introduction to field theory.
Itzykson: Particle Physics
Bjorken & Drell: Relativistic Quantum Mechanics
Francis Halzen & Alan D. Martin: Quarks & Leptons,
Donald H. Perkins: Introduction to high energy physics
Close, Marten, and Sutton: The Particle Explosion
Christine Sutton: Spaceship Neutrino
10.Mandl, Shaw: Quantum Field Theory
11.F.Gross: Relativistic Quantum Mechanics and Field Theory
12.S. Weinberg: The Quantum Theory of Fields, Vol I,II, 1995
13.M.B. Green, J.H. Schwarz, E. Witten: Superstring Theory (2 vols)
14.M. Kaku: Strings, Conformal Fields and Topology
15.Superstrings: A Theory of Everything ed P.C.W. Davies
16.A Pais: Inward Bound
17.R.P. Crease, C.C. Mann: The Second Creation 1996
18.L. Lederman, D. Teresi: The God Particle: If the Universe Is the Answer, What Is the Question? 2006
General Relativity
Meisner, Thorne and Wheeler: Gravitation W. H. Freeman & Co., San Francisco 1973
Robert M. Wald: Space, Time, and Gravity: the Theory of the Big Bang and Black Holes.
Schutz: A First Course in General Relativity.
Weinberg: Gravitation and Cosmology
Hans Ohanian: Gravitation & Spacetime (recently back in print)
Robert Wald: General Relativity
Clifford Will: Was Einstein Right? Putting General Relativity to the Test
Kip Thorne: Black Holes and Time Warps: Einstein’s Outrageous Legacy
Mathematical Methods
Morse and Feshbach: Methods of Theoretical Physics.
Mathews and Walker: Mathematical Methods of Physics. An absolute joy for those who
Arfken: Mathematical Methods for Physicists Academic Press
Zwillinger: Handbook of Differential Equations. Academic Press
Gradshteyn and Ryzhik: Table of Integrals, Series, and Products Academic
F.W. Byron and R. Fuller: Mathematics of Classical and Quantum Physics (2 vols)
Nuclear Physics
Preston and Bhaduri: Structure of the Nucleus
Blatt and Weisskopf: Theoretical Nuclear Physics
DeShalit and Feshbach: Theoretical Nuclear Physics
Satchler: Direct Nuclear Reactions
Walecka: Theoretical Nuclear and Subnuclear Physics (1995)
Krane: Introductory nuclear physics
Cosmology
J. V. Narlikar: Introduction to Cosmology.1983 Jones & Bartlett Publ.
Hawking: A Brief History of Time
Weinberg: First Three Minutes
Timothy Ferris: Coming of Age in the Milky Way and The Whole Shebang
Kolb and Turner: The Early Universe.
Peebles: Principles of Physical Cosmology. Comprehensive, and on the whole it’s quite a
Black Holes and Warped Spacetime, by William J. Kaufmann III.
M.V. Berry: Principles of Cosmology and Gravitation
Dennis Overbye: Lonely Hearts of the Cosmos The unfinished history of converge on
10.Joseph Silk: The Big Bang
11.Bubbles, voids, and bumps in time: the new cosmology edited by James Cornell.
12.T. Padmanabhan: Structure formation in the universe
13.P.J.E. Peebles: The large-scale structure of the universe
15.Alan Lightman and Roberta Brawer: Origins: The lives and worlds of modern cosmologists, 1990
Astronomy
Hannu Karttunen et al. (eds.): Fundamental Astronomy.
Pasachoff: Contemporary Astronomy
Frank Shu: The physical universe: an introduction to astronomy
Kenneth R. Lang: Astrophysical formulae: a compendium for the physicist and astrophysicist
Plasma Physics
(See Robert Heeter’s sci.physics.fusion FAQ for details)
Numerical Methods/Simulations
Johnson and Rees: Numerical Analysis Addison Wesley
Numerical Recipes in X (X=c,fortran,pascal,etc) Tueklosky and Press
Young and Gregory: A survey of Numerical Mathematics Dover 2 volumes.
Hockney and Eastwood: Computer Simulation Using Particles Adam Hilger
Birdsall and Langdon: Plasma Physics via Computer Simulations
Tajima: Computational Plasma Physics: With Applications to Fusion and Astrophysics Addison Wesley Frontiers in physics Series.
Fluid Dynamics
D.J. Tritton: Physical Fluid Dynamics
G.K. Batchelor: Introduction to Fluid Dynamics
S. Chandrasekhar: Hydrodynamics and Hydromagnetic Stability
Segel: Mathematics Applied to Continuum Mechanics Dover.
Nonlinear Dynamics, Complexity, and Chaos
There is a FAQ posted regularly to sci.nonlinear.
Prigogine: Exploring Complexity
Guckenheimer and Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Springer
Lichtenberg, A. J. and M. A. Lieberman (1982): Regular and Stochastic Motion. New York, Springer-Verlag.
Ioos and Joseph: Elementary Stability and Bifurcation Theory. New York, Springer.
Heinz Pagels: The Dreams Of Reason
M. Mitchell Waldrop: Complexity
Optics (Classical and Quantum), Lasers
Max Born and Emil Wolf: Principles of Optics: Electromagnetic Theory of Propagation
Standard reference.
Sommerfeld: For the more classically minded.
Allen and Eberly: Optical Resonance and Two-Level Atoms.
Goodman: Introduction to Fourier Optics.
Quantum Optics and Electronics (Les Houches Summer School 1963 or 1964, but someone has claimed that Gordon and Breach, NY, are going to republish it in 1995),
Sargent, Scully, & Lamb: Laser Physics
Yariv: Quantum Electronics
Siegman: Lasers
Shen: The Principles of Nonlinear Optics
10.Meystre & Sargent: Elements of Quantum Optics
11.Cohen-Tannoudji, Dupont-Roc, & Grynberg: Photons, Atoms and Atom-Photon Interactions.
12.Hecht: Optics
13.Practical Holography by Graham Saxby, Prentice Hall: New York; 1988.
Mathematical Physics
Yvonne Choquet-Bruhat, Cecile DeWitt-Morette, and Margaret Dillard-Bleick: Analysis, manifolds, and physics (2 volumes)
Jean Dieudonne: A panorama of pure mathematics, as seen by N. Bourbaki, translated by I.G. Macdonald.
Robert Hermann: Lie groups for physicists, Benjamin-Cummings, 1966.
George Mackey: Quantum mechanics from the point of view of the theory of group representations, Mathematical Sciences Research Institute, 1984.
George Mackey: Unitary group representations in physics, probability, and number theory.
Charles Nash and S. Sen: Topology and geometry for physicists.
B. Booss and D.D. Bleecker: Topology and analysis: the Atiyah-Singer index formula and gauge-theoretic physics.
Bamberg and S. Sternberg: A Course of Mathematics for Students of Physics
Bishop & Goldberg: Tensor Analysis on Manifolds.
10.Flanders: Differential Forms with applications to the Physical Sciences.
11.Dodson & Poston: Tensor Geometry.
12.von Westenholz: Differential forms in Mathematical Physics.
13.Abraham, Marsden & Ratiu: Manifolds, Tensor Analysis and Applications.
14.M. Nakahara: Topology, Geometry and Physics.
15.Morandi: The Role of Topology in Classical and Quantum Physics
16.Singer, Thorpe: Lecture Notes on Elementary Topology and Geometry
17.L. Kauffman: Knots and Physics, World Scientific, Singapore, 1991.
18.C. Yang and M. Ge: Braid group, Knot Theory & Statistical Mechanics.
19.D. Kastler: C-algebras and their applications to Statistical Mechanics and Quantum Field Theory.
20.Courant and Hilbert: Methods of Mathematical Physics Wiley
21.Cecille Dewitt is publishing a book on manifolds that should be out soon (maybe already
22.Howard Georgi: Lie Groups for Particle Phyiscs Addison Wesley Frontiers in Physics Series.
23.Synge and Schild.
Atomic Physics
Max Born: Atomic Physics
Gerhard Herzberg: Atomic spectra and atomic structure, Translated with the co-operation
E. U. Condon and G. H. Shortley: The theory of atomic spectra, CUP 1951
G. K. Woodgate: Elementary atomic structure, 2d ed. Oxford: New York: Clarendon Press, Oxford University Press, 1983, c 1980
Alan Corney: Atomic and laser spectroscopy, Oxford, New York: Clarendon Press, 1977
Low Temperature Physics, Superconductivity
The Theory of Quantum Liquids, by D. Pines and P. Nozieres
Superconductivity of Metals and Alloys, P. G. DeGennes A classic introduction.
Theory of Superconductivity, J. R. Schrieffer
Superconductivity, M. Tinkham
Experimental techniques in low-temperature physics, by Guy K. White.
This is considered by many as a “bible” for those working in experimental low-temperature physics.
Mathematical Physics
Mechanics, Zhao, kaihua and Luo Weiyin, prepared by the new concept physics tutorial mechanics
Higher education press
Thermal, Zhao, kaihua and Luo Weiyin prepared by the thermal part of the new concept physics.
Higher education press
Electromagnetism, prepared by Zhao, kaihua and Chen Ximou of the electromagnetics, higher education press.
Optics, prepared by Zhao, kaihua and Zhong Xihua of the optics, Peking University Press
Quantum mechanics: careful, the course in quantum mechanics, the higher education press
Electrodynamics: Guo Shuohong, the electrodynamics of higher education publishing.
Theoretical mechanics: Zhou Boyan , Higher education press of the course of theoretical mechanics.
Thermodynamics and statistical physics: Wang Zhicheng, the thermodynamics and statistical physics, higher education press.
Gu chaohao , Li Daqian , Tan Yongji (?), Shen Wei Xian , Qin tiehu , Is jiahong ” Equations of mathematical physics “( The Shanghai Science and technology)
Gu chaohao , Li Daqian , Chen shuxing , Tan Yongji (?), K *,??? ” Equations of mathematical physics “( people’s education ? Higher education?)
M. Taylor “Partial Differential Equations I”(Applied Mathematical Sciences 115)
L. Hormander “Linear Partial Differential Operators, I”
Berkeley Physics or Halliday Resnick physics (Translated version).
Of course, there is the famous Feynman Feynman Lectures On Physics ,
Science Press new set of University physics textbooks, is a general and four mechanics on the side through.
HKUST four Shen Huichuan teacher of the classical mechanics in mechanics textbooks, teacher Zhang Yong-de of the quantum mechanics are similar materials in the country’s best.
Li Shumin, em
University teacher who has written a book on Physics problem-solving of interpretation,
Can go to do the physics problem code 7 Volume is sufficient for you to bite.
Fu Laji Anatoly perminov of the partial differential equation problem sets
Landau, Mechanics ( the Chinese version)
Goldstein, Classical Mechanics ( the Chinese version)
Landau, The Classical Theory of Fields ( the Chinese version)
Jackson, Classical Electrodynamics ( the Chinese version)
Landau, Statistical Physics Part1 ( Chinese version)
Kerson Huang,Statistical Mechanics
Landau, Quantum Mechanics (Non-relatisticTheory) ( Chinese version)
Greiner, Quantum Mechanics: Introduction ( Chinese version)
Huang Kun of the solid state physics
Kittel, Introduction to Solid State Physics ( Chinese version)
Feynman Feynman lectures on Physics
Born of the optical principles
Zheng Yongling mechanics, Fudan University Press
Zhang Yumin—the basic physics tutorial thermal University of science and technology of China press
Hu Youqiu of the electromagnetism of the higher education press
Guo Guangcan optics, higher education press
Xu kezhun modern physics, higher education press
Paint An Shen of the mechanics of the higher education press
Physics Department of the American physics ustc compilation of University of science and technology of China press
Chen xiru course in mathematical statistics, Shanghai Science and technology press
Chen Jiading lectures on mathematical statistics, higher education press
Lu Xuan of the statistical basis of the Tsinghua University Press
Chinese University of science and technology statistics and Department of finance problem sets of mathematical statistics, China University of science and technology lecture
Jin Shangnian of the classical mechanics of the Fudan University Press
Landau , Mechanics , Heinemann
Guo Shuohong electrodynamics, (Second Edition) by higher education press
Jackson , Classical Electrodynamics
Wang Zhicheng of the thermodynamic ? Statistical physics higher education press
Landau , Statistical Physics Part1 , Heinemann
Zhang Yong-de lectures on quantum mechanics lectures on China University of science and technology
Hilbert and Ke Lang of the methods of mathematical physics.
Liang Kunmiao, Guo d r and Wang Zhuxi’s book
On the green of the Mechanics and Thermodynamics. Under the thermal separation of the mechanical and thermal.
Zhao, kaihua of the electromagnetism.
Zhao, kaihua’s optics,
Landau of the classical mechanics.
Guo Shuohong electrodynamics, can see
JACKSON Books need very good mathematical basis, the key is to position has considerable knowledge of partial differential equations.
P.A.M DIRAC 1937 Years wrote the famous principles of quantum mechanics.
Would like to speak of the quantum mechanics I , II And the quantum mechanics problem sets .
There is a copy of the Quan-tum Physics This is discussed in detail.
Lurie of the particle and field.
If interested in condensed matter theory, statistical mechanics you can learn. Landau’s book is on.
Lady Lake’s modern course in statistical physics.
Huang Kun of the solid state physics, this book is easy to understand.
Sun Hongzhou group theory, it is enough. Briefly, group theory is a finite group and group of two consecutive parts, front part and the symmetry of the Crystal is directly related to the latter part and angular momentum theory, condensed matter people doing d or f e’s tight-binding method will be used.
Mahan of the many-particle problem (the translation) or
North of the Green’s function methods in solid state physics .
Callaway of the solid state theory.
Zhao, kaihua’s optics
Trouble boundary condition in quantum optics, General boundary quantum field theory is very simple, and quantum optics are not. A quantum optical properties of finite system is a very interesting question. Such as micro-cavity light absorption and emission and hence the photon crystals in several issues. To distinguish artificial dielectric Photonic Crystal and here. There are quantum effects in Photonic crystals, and no artificial dielectric. So a three dimensional artificial cycle working ceramic not Photonic crystals in microwave band, just artificial dielectric.
If interested in nuclear physics, then I suggest that you look more angular momentum theory or group theory book.
Real variable function theory and functional analysis, the book is the best of the REAL AND ABSTRACT ANALYSIS 》
In order to prepare for the differential geometry, to learn some topology and algebra.
Algebra : Blue’s course in advanced algebra,
Topology can be seen the basis of topology
Chen Weihuan the fundamentals of differential geometry
Shiing-Shen Chern of the differential geometry.
Of the differential forms in mathematical physics,
But I would suggest looking for a special function as a tool, introduces the book of lie groups. Read, then you know Bessel functions, such as those in the mathematical methods learned how important it is. They directly reflect the symmetry of, but when you are young and do not realize it. Learned this after you know what quantum mechanics is of real concern. Quantum mechanics is a theory about the symmetry. In the theory of group representations of wave function of the base is less important, and the group itself and on behalf of its eigenvalues are important, and these are characteristic values of physical quantities.
Fusion methods of quantum theory and general relativity,
” Advanced mathematical methods for scientists and engineers ” , The author is Bender Ozszag 。 Is a progressive learning methods (asymtotic andperturbation) good book , from the beginning to the global analysis of local analysis , very easy
The course in mathematical statistics, Chen xiru
The lectures on mathematical statistics, Chen Jiading
The fundamentals of mathematical statistics Lu Xuan
Zhao of the mathematical statistics voters
The mathematical statistic problem set Chinese University of science and technology statistics and Department of finance
《 Basic Partial Differential Equations 》 , D. Bleecker, G. Csordas The , Lee Chun kit, and higher education press, 2008.
Of the methods of mathematical physics, r.Courant, Hilbert with.
Feynman lectures on Physics
I.d.Landau theoretical physics tutorial.
Jiang lishang lectures on the equations of mathematical physics higher education press
Gu chaohao of the equations of mathematical physics, Li Daqian,
The equations of mathematical physics, r.Courant
The methods of mathematical physics, Liang Kunmiao
Of the equations of mathematical physics problem set fulajimiluofu
General Physics
1. M.S. Longair: Theoretical concepts in physics, 1986.
2. Arnold Sommerfeld: Lectures on Theoretical Physics
3. Richard Feynman: The Feynman lectures on Physics (3 vols)
4. Jearle Walker: The Flying Circus of Physics
5. There is the entire Landau and Lifshitz series.
6. The New Physics edited by Paul Davies.
7. Richard Feynman: The Character of Physical Law
8. David Mermin: Boojums all the way through: Communicating science in prosaic language
9. Frank Wilczek and Betsy Devine: Longing for the Harmonies: Themes and variations from modern physics
10. Greg Egan: Permutation City
Classical Mechanics
1. Herbert Goldstein: Classical Mechanics, 2nd ed, 1980.
2. Introductory: The Feynman Lectures, vol 1.
3. Keith Symon: Mechanics, 3rd ed., 1971 undergrad. level
4. H. Corbin and P. Stehle: Classical Mechanics, 2nd ed., 1960
5. V.I. Arnold: Mathematical methods of classical mechanics, translated by K. Vogtmann and A. Weinstein, 2nd ed., 1989.
6. R. Resnick and D. Halliday: Physics, vol 1, 4th Ed., 1993
7. Marion & Thornton: Classical Dynamics of Particles and Systems, 2nd ed., 1970.
8. A. Fetter and J. Walecka: Theoretical mechanics of particles and continua
9. Kiran Gupta: Classical Mechanics of Particles and Rigid Bodies (1988)
6. J. Wheeler and W. Zurek (eds.): Quantum Theory and Measurement, 1983
7.C. DeWitt and N. Graham: The Many Worlds Interpretation of Quantum Mechanics
8. H. Everett: Theory of the Universal Wavefunction
9. Bjorken and Drell: Relativistic Quantum Mechanics/ Relativistic Quantum Fields
10. Ryder: Quantum Field Theory, 1984
11. Guidry: Gauge Field Theories: an introduction with applications 1991
12. Messiah: Quantum Mechanics, 1961
13. Dirac:
a] Principles of QM, 4th ed., 1958
b] Lectures in QM, 1964
c] Lectures on Quantum Field Theory, 1966
14. Itzykson and Zuber: Quantum Field Theory, 1980
15. Slater: Quantum theory: Address, essays, lectures. note: Schiff, Bjorken and Drell, Fetter and Walecka, and Slater are all volumes in “International Series in pure and Applied Physics” published by McGraw-Hill.
16. Pierre Ramond: Field Theory: A Modern Primer, 2nd edition. Volume 74 in the FiP series.
17. Feynman: The Feynman Lectures, Vol. 3
18. Heitler & London: Quantum theory of molecules
19. J. Bell: Speakable and Unspeakable in Quantum Mechanics, 1987
20. Milonni: The quantum vacuum: an introduction to quantum electrodynamics 1994.
21. Holland: The Quantum Theory of Motion
22. John von Neumann: Mathematical foundations of quantum mechanics, 1955.
23. Schiff: Quantum Mechanics, 3rd ed., 1968
24. Eisberg and Resnick: Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed., 1985.
25. David Saxon: Elementary Quantum Mechanics
26. Bethe and Jackiw: Intermediate Quantum Mechanics
27. P.W.Atkins: Quanta: A Handbook of concepts
28. James Peebles: Quantum Mechanics (1993)
Statistical Mechanics and Entropy
1. David Chandler: Introduction to Modern Statistical Mechanics, 1987
2. R. Tolman: Prinicples of Statistical Mechanics. Dover
3. Kittel & Kroemer: Statistical Thermodynamics
4. Reif: Principles of statistical and thermal physics.
5. Felix Bloch: Fundamentals of Statistical Mechanics.
6. Radu Balescu: Statistical Physics
7. Abrikosov, Gorkov, and Dyzaloshinski: Methods of Quantum Field Theory in Statistical Physics
8. Huw Price: Time’s Arrow and Archimedes’ Point
9. Thermodynamics , by H. Callen.
10. Statistical Mechanics , by R. K. Pathria
11. Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions , by D. Forster
12. Introduction to Phase Transitions and Critical Phenomena , by H. E. Stanley
13. Modern Theory of Critical Phenomena , by S. K. Ma
14. Lectures on Phase Transitions and the Renormalization Group , by N. Goldenfeld
Condensed Matter
1. Charles Kittel: Introduction to Solid State Physics (ISSP),
2. Ashcroft and Mermin: Solid State Physics,
3. Charles Kittel: Quantum Theory of Solids.
4.Solid State Theory , by W. A. Harrison
5. Theory of Solids , by Ziman.
6.Fundamentals of the Theory of Metals , by Abrikosov
7. Many-Particle Physics , G. Mahan.
Special Relativity
1. Taylor and Wheeler: Spacetime Physics Still the best introduction out there.
2. Relativity : Einstein’s popular exposition.
3. Wolfgang Rindler: Essential Relativity . Springer 1977
4. A.P. French: Special Relativity
5. Abraham Pais: Subtle is the Lord: The Science and Life of Albert Einstein
6. Special Relativity and its Experimental Foundations Yuan Zhong Zhang
6. Francis Halzen & Alan D. Martin: Quarks & Leptons,
7. Donald H. Perkins: Introduction to high energy physics
8. Close, Marten, and Sutton: The Particle Explosion
9. Christine Sutton: Spaceship Neutrino
10. Mandl, Shaw: Quantum Field Theory
11. F.Gross: Relativistic Quantum Mechanics and Field Theory
12. S. Weinberg: The Quantum Theory of Fields, Vol I,II, 1995
13. M.B. Green, J.H. Schwarz, E. Witten: Superstring Theory (2 vols)
14. M. Kaku: Strings, Conformal Fields and Topology
15. Superstrings: A Theory of Everything ed P.C.W. Davies
16. A Pais: Inward Bound
17. R.P. Crease, C.C. Mann: The Second Creation 1996
18. L. Lederman, D. Teresi: The God Particle: If the Universe Is the Answer, What Is the Question? 2006
General Relativity
1. Meisner, Thorne and Wheeler: Gravitation W. H. Freeman & Co., San Francisco 1973
2. Robert M. Wald: Space, Time, and Gravity: the Theory of the Big Bang and Black Holes.
3. Schutz: A First Course in General Relativity.
4. Weinberg: Gravitation and Cosmology
5. Hans Ohanian: Gravitation & Spacetime (recently back in print)
6. Robert Wald: General Relativity
7. Clifford Will: Was Einstein Right? Putting General Relativity to the Test
8. Kip Thorne: Black Holes and Time Warps: Einstein’s Outrageous Legacy
Mathematical Methods
1. Morse and Feshbach: Methods of Theoretical Physics.
2. Mathews and Walker: Mathematical Methods of Physics. An absolute joy for those who
3. Arfken: Mathematical Methods for Physicists Academic Press
4. Zwillinger: Handbook of Differential Equations. Academic Press
5. Gradshteyn and Ryzhik: Table of Integrals, Series, and Products Academic
6. F.W. Byron and R. Fuller: Mathematics of Classical and Quantum Physics (2 vols)
Nuclear Physics
1. Preston and Bhaduri: Structure of the Nucleus
2. Blatt and Weisskopf: Theoretical Nuclear Physics
3. DeShalit and Feshbach: Theoretical Nuclear Physics
4. Satchler: Direct Nuclear Reactions
5. Walecka: Theoretical Nuclear and Subnuclear Physics (1995)
6. Krane: Introductory nuclear physics
Cosmology
1. J. V. Narlikar: Introduction to Cosmology.1983 Jones & Bartlett Publ.
2. Hawking: A Brief History of Time
3. Weinberg: First Three Minutes
4. Timothy Ferris: Coming of Age in the Milky Way and The Whole Shebang
5. Kolb and Turner: The Early Universe.
6. Peebles: Principles of Physical Cosmology. Comprehensive, and on the whole it’s quite a
7. Black Holes and Warped Spacetime , by William J. Kaufmann III.
8. M.V. Berry: Principles of Cosmology and Gravitation
9. Dennis Overbye: Lonely Hearts of the Cosmos The unfinished history of converge on
10. Joseph Silk: The Big Bang
11. Bubbles, voids, and bumps in time: the new cosmology edited by James Cornell.
12. T. Padmanabhan: Structure formation in the universe
13. P.J.E. Peebles: The large-scale structure of the universe
14. Andrzej Krasinski: Inhomogeneous Cosmological Models
15. Alan Lightman and Roberta Brawer: Origins: The lives and worlds of modern cosmologists, 1990
Astronomy
1. Hannu Karttunen et al. (eds.): Fundamental Astronomy.
2. Pasachoff: Contemporary Astronomy
3. Frank Shu: The physical universe: an introduction to astronomy
4. Kenneth R. Lang: Astrophysical formulae: a compendium for the physicist and astrophysicist
Plasma Physics
(See Robert Heeter’s sci.physics.fusion FAQ for details)
Numerical Methods/Simulations
1. Johnson and Rees: Numerical Analysis Addison Wesley
2. Numerical Recipes in X (X=c,fortran,pascal,etc) Tueklosky and Press
3. Young and Gregory: A survey of Numerical Mathematics Dover 2 volumes.
4. Hockney and Eastwood: Computer Simulation Using Particles Adam Hilger
5. Birdsall and Langdon: Plasma Physics via Computer Simulations
6. Tajima: Computational Plasma Physics: With Applications to Fusion and Astrophysics Addison Wesley Frontiers in physics Series.
Fluid Dynamics
1. D.J. Tritton: Physical Fluid Dynamics
2. G.K. Batchelor: Introduction to Fluid Dynamics
3. S. Chandrasekhar: Hydrodynamics and Hydromagnetic Stability
4. Segel: Mathematics Applied to Continuum Mechanics Dover.
Nonlinear Dynamics, Complexity, and Chaos
There is a FAQ posted regularly to sci.nonlinear.
1. Prigogine: Exploring Complexity
2. Guckenheimer and Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Springer
3. Lichtenberg, A. J. and M. A. Lieberman (1982): Regular and Stochastic Motion. New York, Springer-Verlag.
4. Ioos and Joseph: Elementary Stability and Bifurcation Theory. New York, Springer.
5. Heinz Pagels: The Dreams Of Reason
6. M. Mitchell Waldrop: Complexity
Optics (Classical and Quantum), Lasers
1. Max Born and Emil Wolf: Principles of Optics: Electromagnetic Theory of Propagation
Standard reference.
2. Sommerfeld: For the more classically minded.
3. Allen and Eberly: Optical Resonance and Two-Level Atoms.
4. Goodman: Introduction to Fourier Optics.
5. Quantum Optics and Electronics (Les Houches Summer School 1963 or 1964, but someone has claimed that Gordon and Breach, NY, are going to republish it in 1995),
6. Sargent, Scully, & Lamb: Laser Physics
7. Yariv: Quantum Electronics
8. Siegman: Lasers
9. Shen: The Principles of Nonlinear Optics
10. Meystre & Sargent: Elements of Quantum Optics
11. Cohen-Tannoudji, Dupont-Roc, & Grynberg: Photons, Atoms and Atom-Photon Interactions.
12. Hecht: Optics
13. Practical Holography by Graham Saxby, Prentice Hall: New York; 1988.
Mathematical Physics
1. Yvonne Choquet-Bruhat, Cecile DeWitt-Morette, and Margaret Dillard-Bleick: Analysis, manifolds, and physics (2 volumes)
2. Jean Dieudonne: A panorama of pure mathematics, as seen by N. Bourbaki, translated by I.G. Macdonald.
3. Robert Hermann: Lie groups for physicists, Benjamin-Cummings, 1966.
4. George Mackey: Quantum mechanics from the point of view of the theory of group representations, Mathematical Sciences Research Institute, 1984.
5. George Mackey: Unitary group representations in physics, probability, and number theory.
6. Charles Nash and S. Sen: Topology and geometry for physicists.
7. B. Booss and D.D. Bleecker: Topology and analysis: the Atiyah-Singer index formula and gauge-theoretic physics.
8. Bamberg and S. Sternberg: A Course of Mathematics for Students of Physics
9. Bishop & Goldberg: Tensor Analysis on Manifolds.
10. Flanders: Differential Forms with applications to the Physical Sciences.
11. Dodson & Poston: Tensor Geometry.
12. von Westenholz: Differential forms in Mathematical Physics.
13. Abraham, Marsden & Ratiu: Manifolds, Tensor Analysis and Applications.
14. M. Nakahara: Topology, Geometry and Physics.
15. Morandi: The Role of Topology in Classical and Quantum Physics
16. Singer, Thorpe: Lecture Notes on Elementary Topology and Geometry
17. L. Kauffman: Knots and Physics, World Scientific, Singapore, 1991.
18. C. Yang and M. Ge: Braid group, Knot Theory & Statistical Mechanics.
19. D. Kastler: C-algebras and their applications to Statistical Mechanics and Quantum Field Theory.
20. Courant and Hilbert: Methods of Mathematical Physics Wiley
21. Cecille Dewitt is publishing a book on manifolds that should be out soon (maybe already
22. Howard Georgi: Lie Groups for Particle Phyiscs Addison Wesley Frontiers in Physics Series.
23. Synge and Schild.
Atomic Physics
1. Max Born: Atomic Physics
2. Gerhard Herzberg: Atomic spectra and atomic structure, Translated with the co-operation
3. E. U. Condon and G. H. Shortley: The theory of atomic spectra, CUP 1951
4. G. K. Woodgate: Elementary atomic structure, 2d ed. Oxford: New York: Clarendon Press, Oxford University Press, 1983, c 1980
5. Alan Corney: Atomic and laser spectroscopy, Oxford, New York: Clarendon Press, 1977
Low Temperature Physics, Superconductivity
1. The Theory of Quantum Liquids , by D. Pines and P. Nozieres
2. Superconductivity of Metals and Alloys , P. G. DeGennes A classic introduction.
3. Theory of Superconductivity , J. R. Schrieffer
4. Superconductivity , M. Tinkham
5. Experimental techniques in low-temperature physics , by Guy K. White.
This is considered by many as a “bible” for those working in experimental low-temperature physics.
★Frazier，An Introduction to Wavelets Throughout Linear Algebra Hernandez，
《时间序列的小波方法》Percival
★Pinsky，Introduction to Fourier Analysis and Wavelets
Weiss，A First Course on Wavelets
Wojtaszczyk，An Mathematical Introduction to Wavelets Analysis
●微分方程（期权定价、动态分析）
○常微分方程和偏微分方程（微分方程稳定性，最优消费组合）
V. I. Arnold, Ordinary Differential Equations，常微分方程（英文版）（现代化，较难）
★W. F. Boyce, R. C. Diprima, Elementary Differential Equations and Boundary Value Problems
《数学物理方程》陈恕行，复旦
E. A. Coddington, Theory of ordinary differential equations
A. A. Dezin, Partial differential equations
L. C. Evans, Partial Differential Equations
丁同仁《常微分方程教程》高教
《常微分方程习题集》菲利波夫，上海科技社
★G. B. Folland, Introduction to Partial Differential Equations
Fritz John, Partial Differential Equations
《常微分方程》李勇
☆The Laplace Transform: Theory and Applications，Joel L. Schiff（适合自学）
G. Simmons, Differntial Equations With Applications and Historecal Notes
索托梅约尔《微分方程定义的曲线》
《常微分方程》王高雄，中山大学社
《微分方程与边界值问题》Zill
○偏微分方程的有限差分方法（期权定价）
福西斯，偏微分方程的有限差分方法
★Kwok，Mathematical Models of Financial Derivatives（有限差分方法美式期权定价）
★Wilmott，Dewynne，Howison，The Mathematics of Financial Derivatives （有限差分方法美式期权定价）
○统计模拟方法、蒙特卡洛方法Monte Carlo method in finance（美式期权定价）
★D. Dacunha-Castelle, M. Duflo， Probabilités et Statistiques II
☆Fisherman，Monte Carlo Glasserman，Monte Carlo Mathods in Financial Engineering（金融蒙特卡洛方法的经典书，汇集了各类金融产品）
☆Peter Jaeckel，Monte Carlo Methods in Finance（金融数学好，没Glasserman的好）
★D. P. Heyman and M. J. Sobel, editors，Stochastic Models, volume 2 of Handbooks in O. R. and M. S., pages 331-434. Elsevier Science Publishers B.V. (North Holland)
Jouini，Option Pricing，Interest Rates and Risk Management
★D. Lamberton, B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance（连续时间）
★N. Newton，Variance reduction methods for diffusion process :
★H. Niederreiter，Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conference Series in Appl. Math. SIAM
★W.H. Press and al.，Numerical recepies.
★B.D. Ripley. Stochastic Simulation
★L.C.G. Rogers et D. Talay, editors， Numerical Methods in Finance. Publications of the Newton Institute.
★D. Talay，Simulation and numerical analysis of stochastic differential systems, a review. In P. Krée and W. Wedig, editors, Probabilistic Methods in Applied Physics, volume 451 of Lecture Notes in Physics, chapter 3, pages 54-96.
★P.Wilmott and al.，Option Pricing (Mathematical models and computation).
Benninga，Czaczkes，Financial Modeling
○数值方法 、数值实现方法
Numerical Linear Algebra and Its Applications，科学社
K. E. Atkinson, An Introduction to Numerical Analysis
R. Burden, J. Faires, Numerical Methods
《逼近论教程》Cheney
P. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation, Cambridge Texts in Applied Mathematics
A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge Texts in Applied Mathematics
《数值逼近》蒋尔雄
《数值分析》李庆杨，清华
《数值计算方法》林成森
J. Stoer, R. Bulirsch, An Introduction to Numerical Analysis
J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations
L. Trefethen, D. Bau, Numerical Linear Algebra
《数值线性代数》徐树芳，北大
其他（不必）
《数学建模》Giordano
《离散数学及其应用》Rosen
《组合数学教程》Van Lint
◎几何学和拓扑学 （凸集、凹集）
●拓扑学
○点集拓扑学
★Munkres，Topology：A First Course《拓扑学》James R.Munkres
Spivak，Calculus on Manifolds
◎代数学（深于数学系高等代数）（静态均衡分析）
○线性代数、矩阵论（资产组合的价值）
M. Artin，Algebra
Axler, Linear Algebra Done Right
★Curtis，Linear Algeria：An Introductory Approach
W. Fleming, Functions of Several Variables
Friedberg, Linear Algebra Hoffman & Kunz, Linear Algebra
★Protter，Stochastic Integration and Differential Equations（文笔优美）
★D. Revuz, M. Yor, Continuous martingales and Brownian motion（连续鞅）
Ross，Introduction to probability model（适合入门）
★Steel，Stochastic Calculus and Financial Application（与Oksendal的水平相当，侧重金融，叙述有趣味而削弱了学术性，随机微分、鞅）
☆《随机过程通论》王梓坤，北师大
○概率论、随机微积分应用（连续时间金融）
Arnold，Stochastic Differential Equations
☆《概率论及其在投资、保险、工程中的应用》Bean
Damien Lamberton,Bernard Lapeyre. Introduction to stochastic calculus applied to finance.
David Freedman.Browian motion and diffusion.
Dykin E. B. Markov Processes.
Gihman I.I., Skorohod A. V.The theory of Stochastic processes基赫曼，随机过程论，科学
Lipster R. ,Shiryaev A.N. Statistics of random processes.
★Malliaris，Brock，Stochastic Methods in Economics and Finance
★Merton，Continuous-time Finance
Salih N. Neftci，Introduction to the Mathematics of Financial Derivatives
☆Steven E. Shreve ，Stochastic Calculus for Finance I: The Binomial Asset Pricing Model；II: Continuous-Time Models（最佳的随机微积分金融（定价理论）入门书，易读的金融工程书，没有测度论基础最初几章会难些，离散时间模型，比Naftci的清晰，Shreve的网上教程也很优秀）
Sheryayev A. N. Ottimal stopping rules.
Wilmott p., J.Dewynne,S. Howison. Option Pricing: Mathematical Models and Computations.
Stokey，Lucas，Recursive Methods in Economic Dynamics
Wentzell A. D. A Course in the Theory of Stochastic Processes.
Ziemba，Vickson，Stochastic Optimization Models in Finance
○概率论、随机微积分应用（高级）
Nielsen，Pricing and Hedging of Derivative Securities
Ross，《数理金融初步》An Introduction to Mathematical Finance：Options and other Topics
Shimko，Finance in Continuous Time：A Primer
○概率论、鞅论
★P. Billingsley，Probability and Measure
K. L. Chung & R. J. Williams，Introduction to Stochastic Integration
Doob，Stochastic Processes
严加安，随机分析选讲，科学
○概率论、鞅论Stochastic processes and derivative products（高级）
★J. Cox et M. Rubinstein : Options Market
★Ioannis Karatzas and Steven E. Shreve，Brownian Motion and Stochastic Calculus（难读的重要的高级随机过程教材，若没有相当数学功底，还是先读Oksendal的吧，结合Rogers & Williams的书读会好些，期权定价，鞅）
★M. Musiela – M. Rutkowski : (1998) Martingales Methods in Financial Modelling
★Rogers & Williams，Diffusions, Markov Processes, and Martingales: Volume 1, Foundations；Volume 2, Ito Calculus （深入浅出，要会实复分析、马尔可夫链、拉普拉斯转换，特别要读第1卷）
★David Williams，Probability with Martingales（易读，测度论的鞅论方法入门书，概率论高级教材）
○鞅论、随机过程应用
Duffie，Rahi，Financial Market Innovation and Security Design：An Introduction，Journal of Economic Theory
Kallianpur，Karandikar，Introduction to Option Pricing Theory
★Dothan，Prices in Financial Markets （离散时间模型）
Hunt，Kennedy，Financial Derivatives in Theory and Practice
何声武，汪家冈，严加安，半鞅与随机分析，科学社
★Ingersoll，Theory of Financial Decision Making
★Elliott Kopp，Mathematics of Financial Markets（连续时间）
☆Marek Musiela，Rutkowski，Martingale Methods in Financial Modeling（资产定价的鞅论方法最佳入门书，读完Hull书后的首选，先读Rogers & Williams、Karatzas and Shreve以及Bjork打好基础）
○弱收敛与随机过程收敛
★Billingsley，Convergence of Probability Measure
Davidson，Stochastic Limit Theorem
★Ethier，Kurtz，Markov Process：Characterization and Convergence Hall，Martingale Limit Theorems
★Jocod，Shereve，Limited Theorems for Stochastic Process
Van der Vart，Weller，Weak Convergence and Empirical Process
◎运筹学
●最优化、博弈论、数学规划
○随机控制、最优控制（资产组合构建）
Borkar，Optimal control of diffusion processes
Bensoussan，Lions，Controle Impulsionnel et Inequations Variationnelles
Chiang，Elements of Dynamic Optimization
Dixit，Pindyck，Investment under Uncertainty
Fleming，Rishel，Deterministic and Stochastic Optimal Control
Harrison，Brownian Motion and Stochastic Flow Systems
Kamien，Schwartz，Dynamic Optimization
Krylov，Controlled diffusion processes
○控制论（最优化问题）
●数理统计（资产组合决策、风险管理）
○基础数理统计（非基于测度论）
★R. L. Berger, Cassell, Statistical Inference
Bickel，Dokosum，Mathematical Stasistics：Basic Ideas and Selected Topics
★Birrens，Introdution to the Mathematical and Statistical Foundation of Econometrics
数理统计学讲义，陈家鼎，高教
★Gallant，An Introduction to Econometric Theory
R. Larsen, M. Mars, An Introduction to Mathematical Statistics
☆《概率论及数理统计》李贤平，复旦社
☆Papoulis，Probability，random vaiables，and stochastic process
☆Stone，《概率统计》
★《概率论及数理统计》中山大学统计系，高教社
○基于测度论的数理统计(计量理论研究)
Berger，Statistical Decision Theory and Bayesian Analysis
陈希儒，高等数理统计
★Shao Jun，Mathematical Statistics
★Lehmann，Casella，Theory of Piont Estimation
★Lehmann，Romano，Testing Statistical Hypotheses
《数理统计与数据分析》Rice
○渐近统计
★Van der Vart，Asymptotic Statistics
○现代统计理论、参数估计方法、非参数统计方法
参数计量经济学、半参数计量经济学、自助法计量经济学、经验似然
统计学基础部分
1、《统计学》《探索性数据分析》 David Freedman等，中国统计 （统计思想讲得好）
2、Mind on statistics 机械工业 （只需高中数学水平）
3、Mathematical Statistics and Data Analysis 机械工业 （这本书理念很好，讲了很多新东西）
4、Business Statistics a decision making approach 中国统计 （实用）
5、Understanding Statistics in the behavioral science 中国统计
John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, and Andrew Y. Lo ，The Econometrics of Financial Markets（金融经济学简明教材，不涉及宏观金融（宏观和货币经济学），不好读，需要一定经济学和金融学基础，水平没有Duffie和Cochrane的高）
★John H. Cochrane，Asset Pricing（易读，写法现代，需要必要金融经济学基础，读后可以看懂该领域论文，想学金融数学还是读Duffie的吧）
☆Russell Davidson，Econometric Theory and Methods （讲得最清晰的中级书，比格林的好读得多，虽然没林文夫的经典）
Helmut Lütkepohl，Markus Krātzig，Applied Time Series Econometrics，《应用时间序列计量经济学》
Ian Jacques，Mathematics for Economics and Business，《商务与经济数学》
B. Jerkins，Time Series Analysis：Forecasting & Control
☆Peter Kennedy, A Guide to Econometrics（绝佳初级教材，通俗易懂，不次于伍德里奇的《现代方法》） 皮特，《计量经济学指南》
☆平狄克《计量经济模型与经济预测》Econometric Models and Economic Forecasts
平狄克《不确定性下的投资》
Roger Myerson, Curt Hinrichs, Probability Models for Economic Decision，《经济决策的概率模型》
★J. H. Stock, M. W. Watson, Introduction to Econometrics
A. H. Studenmund，Introductory Econometrics with Applications，《应用计量经济学》（基础性）
T. J. Watsham, K. Parramore《金融数量方法》
★Jeffrey Wooldridge，Introductory Econometrics: A Modern Approach （初级，不侧重数学推理，可自学，适合经济类专业，不适合统计专业，Kennedy的书不次于它，古扎拉底的书比它深一些）
☆Wooldridge 伍德里奇，Econometric Analysis of Cross Section and Panel Data 《横截面与面板数据的计量经济学分析》（微观计量理论的经典，Green和Hayashi两本书的补充，需要初级或中级基础，易读）
邵宇《微观金融学及其数学基础》清华社
○时间序列建模、时间序列分析及其算法研究
McKenzie，Research Design Issues in Time-Series Modeling of Financial Market Volatility
Watsham，Parramore，Quantitative Methods in Finance
○数理金融学Econometrics of Finance
Abramowitz，Stegun，Handbook of Mathematical Functions
Briys，Options，Futures and Exotic Derivatives
★Brockwell, P. and Davis, Time series : theory and methods
☆《金融计量经济学导论》克里斯•布鲁克斯（Chris Brooks）
★Campbell, J.Y., A.W. Lo and A.C. MacKinlay, The econometrics of financial markets（消费的资本资产定价模型）
Cox，Huang，Option Pricing and Application，Frontiers of Financial Theory
Dempster，Pliska，Mathematics of Derivative Securities
☆Walter Enders, Applied Econometric Time Series（时间序列分析绝佳入门书，比汉密尔顿的经典易读得多）
★Gourieroux, G., ARCH models and financial applications
★James Douglas Hamilton, Time series analysis《时间序列分析》汉密尔顿（时间序列经典，侧重理论技术，不适合初学，需要一定基础，统计和经济都可用）
★Hamilton, J. and B. Raj, (Eds), Advances in markov switching models
Karatzas，Lectures on the Mathematics of Finance
★Lardic S., V. Mignon, Econométrie des séries temporelles macroéconomiques et financières. Economica.
★《连续时间金融》罗伯特•莫顿（Robert Merton）Continuous time finance
★Mills, T.C., The econometric modelling of financial time series
★Muselia，Rutkowski，Martingale Models in Financial Modeling（连续时间、期权定价）
★Pliska，Introduction to Mathematical Finance：Discrete Time Models（离散时间模型高级教材） 数理金融学引论——离散时间模型
★Reinsel, G., Elements of multivariate time series analysis
《金融数学》Stampfli
☆Ross，An Introduction to Mathematical Finance：Options and other Topics, Ross S. M., 《数理金融初步》罗斯(Sheldon M.Ross)（投资组合）
Schachermayer，Introduction to the Mathematics of Financial Markets
★Tsay, R.S., Analysis of financial time series《金融时间序列分析》蔡瑞胸(Ruey S.Tsay)（美）
软件：
1、EViews
2、SAS
◎微观经济学
★马斯•科莱尔《微观经济学》Andreu Mas-Colell Green, Microeconomic Theory （高级顶尖，微观的百科全书。一般均衡讲得好，适合学完微分方程、实分析和线性代数的经济系学生，商科学生能大部分领会就很可以啦。博弈论部分要结合Kreps书和Tirole《产业组织理论》来看）
☆《高级微观经济理论》Advanced Microeconomic Theory杰里/瑞尼 Geoffrey A. Jehle / Philip J. Reny （高级入门，前半部分写得好，仅次于范里安，博弈论一般但简洁。没有马斯科莱尔的全面和艰深，简洁准确易懂，两书相得益彰。比范里安和尼科尔森的分析深入，不想复杂地学高微就用它吧）
☆A Course in Microeconomic，David M. Kreps（高级，侧重博弈论方法，其他一般，写法轻松而严谨欠缺，马斯科莱尔的补充）
★曼昆《经济学原理》(初级)
☆Walter Nicholson etl，Microeconomic Theory: Basic Principles and Extensions（让你很容易地掌握和爱上微观，中级平狄克向高级马斯科莱尔的过渡，博弈论薄弱些）
Valuation：Measuring and Managing the Value of Companies
1.理论金融
资产定价:
★Duffie，Futures Markets（远期合约和期货合约）
Duffie: security market
★《金融经济学基础》黄奇辅（Chi-fu Huang），罗伯特•鲍勃•李兹森伯格（Robert H. Litzenberger）Foundation for financial economics
★Ingersoll: Theorey of financial decision making
Ross: Neoclassical Finance
证券承销：
公司并购：
2.入门和综合类
Amman: Credit risk valuation
★Baxter M., Rennie A., Financial Calculus : An Introduction to Derivative Pricing（金融工程必读书，循序渐进地介绍随机微积分，金融偏微分方程还是看Willmott吧，侧重理论，仅需基本的微积分和概率论基础）《金融数学衍生产品定价导论》
Bielecki, Rutkowski: Credit Risk : Modeling , Valuation and Hedging
★Tomas Bjork: Arbitrage theory in continuous time（Hull的后续中级书，连续时间、期权定价）
Cvitanic, Zapatero: Introduction to the economics and mathematics of financial markets
★Dana，Jeanblanc，Financial Markets in Continuous Time（连续时间）
Duffie Singleton: Credit Risk
★Elliott, Kopp: Mathematics of Financial markets
★Fouque，Papanicolau，Derivatives in Financial Markets with Stochastic Volatility（随机波动率）
★Gourieroux，ARCH Models and Financial Applications（ARCH模型和GARCH模型）
★Harris:Trading and Exchanges: Market Microstructure for Practitioners（详述不同类型证券交易）
★Options, Futures, and Other Derivatives《期权、期货和其他衍生品》约翰•赫尔(John C.Hull） （衍生品和数理金融初级经典教材，期货和期权市场组织、远期合约和期货合约、期权定价、期权交易）
Hull，J. C.，Risk Management and Financial Insititutions《风险管理与金融机构》
★Karatzas Shreve: Methods of mathematical finance（美式期权、随机微分、连续时间动态规划、鞅、连续时间模型高级教材）
☆Lawrence G. McMillan，Options as a Strategic Investment
Rrederic S. Mishkin, Financial Markets and Institutions《金融市场与金融机构》
Option Pricing: Mathematical Models and Computation, by P. Wilmott, J.N. Dewynne, S.D. Howison
Pricing Financial Instruments: The Finite Difference Method, by Domingo Tavella, Curt Randall
Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach by Daniel Duffy
MONTE CARLO
Monte Carlo Methods in Finance, by Peter Jäcke (errata available at jaeckel.org)
Monte Carlo Methodologies and Applications for Pricing and Risk Management , by Bruno Dupire (Editor)
Monte Carlo Methods in Financial Engineering, by Paul Glasserman
Monte Carlo Frameworks in C++: Building Customisable and High-performance Applications by Daniel J. Duffy and Joerg Kienitz
STOCHASTIC CALCULUS
Stochastic Calculus and Finance by Steven Shreve (errata attached)
Stochastic Differential Equations: An Introduction with Applications by Bernt Oksendal
VOLATILITY
Volatility and Correlation, by Riccardo Rebonato
Volatility, by Robert Jarrow (Editor)
Volatility Trading by Euan Sinclair
INTEREST RATE
Interest Rate Models – Theory and Practice, by D. Brigo, F. Mercurio updates available on-line Professional Area of Damiano Brigo’s web site
Modern Pricing of Interest Rate Derivatives, by Riccardo Rebonato
Interest-Rate Option Models, by Riccardo Rebonato
Efficient Methods for Valuing Interest Rate Derivatives, by Antoon Pelsser
Interest Rate Modelling, by Nick Webber, Jessica James
FX
Foreign Exchange Risk, by Jurgen Hakala, Uwe Wystup
Mathematical Methods For Foreign Exchange, by Alexander Lipton
STRUCTURED FINANCE
The Analysis of Structured Securities: Precise Risk Measurement and Capital Allocation (Hardcover) by Sylvain Raynes and Ann Rutledge
Salomon Smith Barney Guide to MBS & ABS, Lakhbir Hayre, Editor
Securitization Markets Handbook, Structures and Dynamics of Mortgage- and Asset-backed securities by Stone & Zissu
Securitization, by Vinod Kothari
Modeling Structured Finance Cash Flows with Microsoft Excel: A Step-by-Step Guide (good for understanding the basics)
Structured Finance Modeling with Object-Oriented VBA (a bit more detailed and advanced than the step by step book)
STRUCTURED CREDIT
Collateralized Debt Obligations, by Arturo Cifuentes
An Introduction to Credit Risk Modeling by Bluhm, Overbeck and Wagner (really good read, especially on how to model correlated default events & times)
Credit Derivatives Pricing Models: Model, Pricing and Implementation by Philipp J. Schönbucher
Credit Derivatives: A Guide to Instruments and Applications by Janet M. Tavakoli
Structured Credit Portfolio Analysis, Baskets and CDOs by Christian Bluhm and Ludger Overbeck
RISK MANAGEMENT/VAR
VAR Understanding and Applying Value at Risk, by various authors
Value at Risk, by Philippe Jorion
RiskMetrics Technical Document RiskMetrics Group
Risk and Asset Allocation by Attilio Meucci
SAS/S/S-PLUS
The Little SAS Book: A Primer, Fourth Edition by Lora D. Delwiche and Susan J. Slaughter
Modeling Financial Time Series with S-PLUS
Statistical Analysis of Financial Data in S-PLUS
Modern Applied Statistics with S
HANDS ON
Implementing Derivative Models, by Les Clewlow, Chris Strickland
The Complete Guide to Option Pricing Formulas, by Espen Gaarder Haug
NOT ENOUGH YET?
Energy Derivatives: Pricing and Risk Management, by Les Clewlow, Chris Strickland
Hull-White on Derivatives, by John Hull, Alan White 1899332456
Exotic Options: The State of the Art, by Les Clewlow (Editor), Chris Strickland (Editor)
Market Models, by C.O. Alexander
Pricing, Hedging, and Trading Exotic Options, by Israel Nelken
Modelling Fixed Income Securities and Interest Rate Options, by Robert A. Jarrow
Black-Scholes and Beyond, by Neil A. Chriss
Risk Management and Analysis: Measuring and Modelling Financial Risk, by Carol Alexander
Mastering Risk: Volume 2 – Applications: Your Single-Source Guide to Becoming a Master of Risk, by Carol Alexander
Financial Mathematics
Micro-finance including financial markets and financial institutions, investment financial engineering and financial economics, corporate finance and financial management aspects of macro-finance including monetary economics, money and banking, international finance, empirical and quantitative methods include mathematical finance and financial econometrics, following the bibliography focus on mathematical foundations of economic theory and mathematical finance section.
Analysis of functions and
What is mathematics, Oxford books
Set theory
☆ Paul R. Halmos , Naive Set Theory Naive set theory (u) Hammons (great book, profound but simple)
Set theory ( English version ) Thomas Jech (Depth)
Moschovakis , Notes on Set Theory
On the basis of the collection (English version)-the original Turing Mathematics Statistics series (u) Ende Teng
Mathematical analysis
0 Calculus
☆ Tom M. Apostol, Calculus vol Ⅰ & II (classic advanced calculus textbook written by mathematicians / The reference books written in precise, 40Years, Second Edition, is committed to a more profound understanding of removal interval calculus and mathematical analysis, link analysis, differential equations, linear algebra, differential geometry and probability theory, learning, the prelude to real analysis, linear algebra and Multivariable calculus book best, practice was great, hard to read and difficult to understand for beginners, but with the advantages that other materials cannot have. Stewart ‘s book the same, is relatively simple. ）
Carol and Robert Ash , The Calculus Tutoring Book (Good calculus resource materials)
★ R.Courant,F.John,IntroductiontoCalculusandAnalysisvol I&II (suitable for engineering, physics and applications)
Morris Kline , Calculus, an intuitive approach
Ron LarsonCalculus (With Analytic Geometry(introduction to calculus textbooks, rare clear and simplified, and Stewart with popular textbooks)
Of the advanced calculus Lynn H.Loomis / Shlomo Stermberg
Morris Kline , Calculus: An Intuitive and Physical Approach (Clear the resource materials)
Richard Silverman , Modern Calculus with Analytic Geometry
Michael , Spivak , Calculus (Interesting, for mathematics, read it or Stewart You can read Rudin Principles of Mathematical Analysis Or MarsdenElementary Classical Analysis , Then read Royden Real Analysis The Lebesgue integral and measure theory, or Rudin Functional Analysis Learning s.Banach and and spectral theory of operators on a Hilbert space)
James Stewart , Calculus (Popular textbooks for science and Mathematics Department, you can use Larson Book supplement, but slightly better than it, if you find it difficult to use Larson Bar)
Earl W. Swokowski , Cengage Advantage Books: Calculus: The Classic Edition (For engineering)
Silvanus P. Thompson , Calculus Made Easy (For Calculus for beginners, easy to read and understand)
0 in real analysis (math undergraduate level consolidation analysis) (static analysis)
Understanding Analysis , Stephen Abbott , (Introduction to real analysis book, although it is not meant to be exhaustive, but clear and concise, Rudin, Bartle, Browder Who, after all, not good at writing book, multi spoke less)
★ T. M. Apostol, Mathematical Analysis
Problems in Real Analysis Real analysis problem set ( United States ) Alipulansi, (United States), Prof Birkinshaw
☆ Of the mathematical analysis of the enterprise, the North
Hu Shi Geng, of real variable function
Of the analysis of the Elliott H. Lieb / Michael Loss
★ H. L. Royden, Real Analysis
W. Rudin, Principles of Mathematical Analysis
Elias M.Stein , Rami Shakarchi, Real Analysis : Measure Theory , Integration and Hilbert Spaces , Real analysis ( English version)
The mathematical analysis of eight told khinchine
☆ The new mathematical analysis about building of Peking University Zhou Min, and theory of functions of a real variable, Peking University
☆ Shanghai, Zhou Min intensity of the mathematical analysis of the science and technology Club
0 measure theory (overlapping with the consolidation analysis)
Probability and measure theory (English) (United States) Ashe ( Ash.R.B. ), ( United States ) Multi-lang – Dade ( Doleans-Dade,C.A. )
☆ Halmos , Measure Theory And measure theory ( English version ) (De) Holmes
0 Fourier Analysis (half of the real variable analysis and Wavelet analysis)
An introduction to Wavelets (u) Cui Jintai
H. Davis, Fourier Series and Orthogonal Functions
★ Folland , Real Analysis : Modern Techniques and Their Applications
★ Folland , Fourier Analysis and its Applications Mathematical physics equations: Fourier analysis and its applications (English version)-era .Featured excellent teaching materials in colleges and universities in foreign countries (U) Fu Lande
Fourier Analysis (English version)-age education • featured excellent teaching materials in colleges and universities in foreign countries (U) gelafakesi
B. B. Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the Making
Katanelson , An Introduction to Harmonic Analysis
R. T. Seeley, An Introduction to Fourier Series and Integrals
★ Stein , Shakarchi , Fourier Analysis : An Introduction
0 of complex analysis (math undergraduate level of functions of a complex variable)
L. V. Ahlfors, Complex Analysis , Mathematical translation of complex analysis – a fragment bundle (u) Ahlfors ( Ahlfors,L.V. )
★ Brown , Churchill , Complex Variables and Applications Convey, Functions of One Complex Variable Ⅰ & Ⅱ
Concise complex analysis of Gong Sheng , North
Greene , Krantz , Function Theory of One Complex Variable
Marsden , Hoffman , Basic Complex Analysis
Palka , An Introduction to Complex Function Theory
★ W. Rudin, Real and Complex Analysis of the real analysis and complex analysis of the Nasruddin (standard textbooks, preferably with measure theory)
Siegels , Complex Variables
Stein , Shakarchi , Complex Analysis The complex functions of Zhuang Chetai
Functional analysis (portfolio value)
0 basic functional analysis (functions of a real variable, operator theory and Wavelet analysis)
Foundations of real analysis and functional analysis, drive their envelope, higher education
★ Friedman , Foundations of Modern Analysis
Hu Shi of the consolidation and functional no-tillage
The introduction of functional analysis and its applications kelizige Functional analysis of problem sets (printed) s. Radhakrishnan
Problems and methods in analysis , Krysicki
Xia Daoxing, functional analysis, a second course in higher education
★ Xia Daoxing, functions of real variable & functional analysis
The mathematical analysis problem set Huimin Xie, higher education
The lectures on functional analysis, Zhang Gongqing, Peking University
0 high-functional analysis (operator theory)
J.B.Conway, A Course in Functional Analysis And functional analysis tutorial ( English version)
★ Lax , Functional Analysis
★ Rudin , Functional Analysis And functional analysis (English) [ United States ] Nasruddin (Distribution and Fourier transform classic, to a topological base)
Zimmer , Essential Results of Functional Analysis
0 Wavelet analysis
Daubeches , Ten Lectures on Wavelets
★ Frazier , An Introduction to Wavelets Throughout Linear Algebra Hernandez ,
Of the wavelet methods for time series Percival
★ Pinsky , Introduction to Fourier Analysis and Wavelets
Weiss , A First Course on Wavelets
Wojtaszczyk , An Mathematical Introduction to Wavelets Analysis
Differential equations (and dynamic analysis of option pricing)
0 of ordinary differential equations and partial differential equations (differential equation stability, optimal consumption and portfolio)
★ W. F. Boyce, R. C. Diprima, Elementary Differential Equations and Boundary Value Problems
The equations of mathematical physics Chen shuxing, Fudan University
E. A. Coddington, Theory of ordinary differential equations
A. A. Dezin, Partial differential equations
L. C. Evans, Partial Differential Equations
Ding Tongren of the higher education course in ordinary differential equations
The ordinary differential equation problem sets Filipov, Shanghai Science and technology Club
★ G. B. Folland, Introduction to Partial Differential Equations
Fritz John, Partial Differential Equations
Of the ordinary differential equations Li Yong
☆ The Laplace Transform: Theory and Applications , Joel L. Schiff (Suitable for self-study)
G. Simmons, Differntial Equations With Applications and Historecal Notes
Sotomayor of the differential equations of curves that are defined
King of the ordinary differential equation in Kaohsiung, Sun Yat-sen University
Of the differential equations and boundary value problems Zill
0 partial differential equation by finite difference method (option)
Fuxisi, finite difference methods for partial differential equations
★ Kwok , Mathematical Models of Financial Derivatives (Finite difference method for American option pricing)
★ Wilmott , Dewynne , Howison , The Mathematics of Financial Derivatives (Finite difference method for American option pricing)
0 statistical simulation methods, Monte Carlo methods Monte Carlo method in finance (American option pricing)
★ D. Dacunha-Castelle, M. Duflo, Probabilités et Statistiques II
☆ Fisherman , Monte Carlo Glasserman , Monte Carlo Mathods in Financial Engineering (The classic Monte Carlo method for financial books, brings together a variety of financial products)
☆ Peter Jaeckel , Monte Carlo Methods in Finance (Financial mathematics good, no Glasserman Good)
★ D. P. Heyman and M. J. Sobel, editors,Stochastic Models, volume 2 of Handbooks in O. R. and M. S., pages 331-434. Elsevier Science Publishers B.V. (North Holland)
Jouini , Option Pricing , Interest Rates and Risk Management
★ D. Talay,Simulation and numerical analysis of stochastic differential systems, a review. In P. Krée and W. Wedig, editors, Probabilistic Methods in Applied Physics, volume 451 of Lecture Notes in Physics, chapter 3, pages 54-96.
★ P.Wilmott and al. , Option Pricing (Mathematical models and computation).
Benninga , Czaczkes , Financial Modeling
0 numerical methods And numerical methods
Numerical Linear Algebra and Its Applications , The science society
K. E. Atkinson, An Introduction to Numerical Analysis
R. Burden, J. Faires, Numerical Methods
Of the course in approximation theory Cheney
P. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation, Cambridge Texts in Applied Mathematics
A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge Texts in Applied Mathematics
The numerical approximation of Jiang erxiong
The numerical analysis of Li Qingyang, Tsinghua University
Of the numerical method of the forest forest
J. Stoer, R. Bulirsch, An Introduction to Numerical Analysis
J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations
L. Trefethen, D. Bau, Numerical Linear Algebra
The numerical linear algebra Xu Shufang, Peking University
Other (not necessarily)
Of the mathematical modeling Giordano
Discrete mathematics and its applications Rosen
The course in Combinatorial mathematics Van Lint
Geometry and topology (Convex, concave set)
Topology
0 point set topology
★ Munkres , Topology : A First Course Of the topology of the James R.Munkres
Spivak , Calculus on Manifolds
Algebra (deep in the Department of mathematics, algebra) (static analysis)
0 linear algebra, matrix theory (portfolio value)
M. Artin,Algebra
Axler, Linear Algebra Done Right
★ Curtis , Linear Algeria : An Introductory Approach
W. Fleming, Functions of Several Variables
Friedberg, Linear Algebra Hoffman & Kunz, Linear Algebra
P.R. Halmos , Finite-Dimensional Vector Spaces (The classic textbook, mathematics linear algebra, note about abstract algebraic structures rather than matrix, hard to read)
J. Hubbard, B. Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
N. Jacobson,Basic Algebra Ⅰ&Ⅱ
☆ Jain Of the linear algebra
Lang , Undergraduate Algeria
Peter D. Lax , Linear Algebra and Its Applications (For mathematics)
G. Strang, Linear Algebra and its Applications(for science and engineering, clearest teaching materials of linear algebra, speak a lot, his online lecture is important)
★ Magill , Quinzii , Theory of Incomplete Markets (Incomplete market equilibrium)
★ Mas-Dollel , Whinston , Microeconomic Theory (General equilibrium)
★ Stokey , Lucas , Recursive Methods in Economic Dynamics (Macroscopic equilibrium)
Probability and statistics
Probability theory (financial products revenue estimation, decision making under conditions of uncertainty, options)
0 basic probability theory (Department of mathematics, theory of probability level)
★ The theory of probability (in three volumes), Fudan University
Davidson , Stochastic Limit Theory
Durrett , The Essential of Probability That probability theory 3 Edition (English version)
★ W. Feller,An Introduction to Probability Theory and its Applications of probability theory and its application (part 3 )-Turing Mathematics • Statistics series
Of the probability theory Foundation of the Li Xianping, higher education
G. R. Grimmett, D. R. Stirzaker, Probability and Random Processes
☆ Ross , S. a first couse in probabilityand statistics print version in China; probability based tutorials ( 7 version)-books-Turing mathematics • statistics (example)
☆ To the theory of probability Wang ren, Peking University
Wang Shouren, probability theory and stochastic processes, science society
☆ To the theory of probability Yang Zhenming, Nankai, the science society
0 theory of probability based on measure theory,
Measure theory and probability theory, programming macros, Peking University
★ D. L. Cohn, Measure Theory
Dudley , Real Analysis and Probability
★ Durrett , Probability : Theory and Examples
Jacod , Protter , Probability Essentials Resnick , A Probability Path
★ Shirayev , Probability
Strictly, measure theory, lecture notes, science society
★ Zhong Kailai, A Course in Probability Theory
0 random calculus Introduction of diffusion processes ( option pricing)
K. L. Chung, Elementary Probability Theory with Stochastic Processes
Cox , Miller , The Theory of Stochastic
★ R. Durrett, Stochastic calculus
★ Huang Zhi Yuan, introduction to stochastic analysis
Huang Zhi Yuan The scientific fundamentals of stochastic analysis
Jiang lishang, mathematical models and methods in option pricing, higher education
An introduction to stochastic processes Kao
Karlin , Taylor , A First Course in Stochastic Prosses (For graduate students)
Karlin , Taylor , A Second Course in Stochastic Prosses (For graduate students)
Stochastic process, laws, China
☆ J.R.Norris,MarkovChains(needs a basis)
★ Bernt Oksendal, Stochastic differential equations (An excellent introduction to stochastic differential equations book, focus on Brownian motion,Karatsas Shreve Book short read, preferably with probability theory, reading the book can read financial literature, the financial part Shreve Good)
★ Protter , Stochastic Integration and Differential Equations (Well-written)
☆ To the theory of probability and its applications in investment, insurance, engineering Bean
Damien Lamberton,Bernard Lapeyre. Introduction to stochastic calculus applied to finance.
David Freedman.Browian motion and diffusion.
Dykin E. B. Markov Processes.
Gihman I.I., Skorohod A. V.The theory of Stochastic processes Jiheman, theory of stochastic processes, the scientific
Lipster R. ,Shiryaev A.N. Statistics of random processes.
★ Malliaris , Brock , Stochastic Methods in Economics and Finance
★ Merton , Continuous-time Finance
Salih N. Neftci , Introduction to the Mathematics of Financial Derivatives
☆ Steven E. Shreve , Stochastic Calculus for Finance I: The Binomial Asset Pricing Model ; II: Continuous-Time Models (The best stochastic calculus and financial (price theory) book, easy to read books in financial engineering, no measure on the basis of the first few chapters will be difficult, discrete-time model Naftci Clear, Shreve Online tutorial is also very good)
Sheryayev A. N. Ottimal stopping rules.
Wilmott p., J.Dewynne,S. Howison. Option Pricing: Mathematical Models and Computations.
Stokey , Lucas , Recursive Methods in Economic Dynamics
Wentzell A. D. A Course in the Theory of Stochastic Processes.
Ziemba , Vickson , Stochastic Optimization Models in Finance
Nielsen , Pricing and Hedging of Derivative Securities
Ross , Of the mathematical finance preliminary An Introduction to Mathematical Finance : Options and other Topics
Shimko , Finance in Continuous Time : A Primer
0 probability theory and martingale theory
★ P. Billingsley,Probability and Measure
K. L. Chung & R. J. Williams,Introduction to Stochastic Integration
Doob , Stochastic Processes
Strictly, selected topics in stochastic analysis, scientific
0 probability theory and martingale theory Stochastic processes and derivative products (Advanced)
★ J. Cox et M. Rubinstein : Options Market
★ Ioannis Karatzas and Steven E. Shreve , Brownian Motion and Stochastic Calculus (Hard to read advanced stochastic processes for important textbooks, if not quite a mathematical skills, or to read Oksendal , Combined with Rogers & Williams Read the book is better, option pricing, martingale)
★ M. Musiela – M. Rutkowski : (1998) Martingales Methods in Financial Modelling
★ Rogers & Williams , Diffusions, Markov Processes, and Martingales: Volume 1, Foundations ; Volume 2, Ito Calculus (Simple and implements complex analysis, Laplace transformations, Markov chains, in particular, to read 1 Volume)
★ David Williams , Probability with Martingales (Easier to read, measure theory, the martingale method book, high probability theory teaching materials)
0 martingales theory and stochastic processes
Duffie , Rahi , Financial Market Innovation and Security Design : An Introduction , Journal of Economic Theory
Kallianpur , Karandikar , Introduction to Option Pricing Theory
★ Dothan , Prices in Financial Markets (A discrete-time model)
Hunt , Kennedy , Financial Derivatives in Theory and Practice
He Sheng Wu, Wang Jiagang, strict, half martingales and stochastic analysis, the science society
★ Ingersoll , Theory of Financial Decision Making
★ Elliott Kopp , Mathematics of Financial Markets (Continuous-time)
☆ Marek Musiela , Rutkowski , Martingale Methods in Financial Modeling (Asset pricing theory of martingale methods best book read Hull Book of choice, read first Rogers & Williams 、 Karatzas and Shreve Bjork Lay a good foundation)
0 to weak convergence and convergence of stochastic processes
★ Billingsley , Convergence of Probability Measure
Davidson , Stochastic Limit Theorem
★ Ethier , Kurtz , Markov Process : Characterization and Convergence Hall , Martingale Limit Theorems
★ Jocod , Shereve , Limited Theorems for Stochastic Process
Van der Vart , Weller , Weak Convergence and Empirical Process
Operational research
Optimization, game theory, mathematical programming
Stochastic control, optimal control 0 (portfolio construction)
Borkar , Optimal control of diffusion processes
Bensoussan , Lions , Controle Impulsionnel et Inequations Variationnelles
Chiang , Elements of Dynamic Optimization
Dixit , Pindyck , Investment under Uncertainty
Fleming , Rishel , Deterministic and Stochastic Optimal Control
Harrison , Brownian Motion and Stochastic Flow Systems
★ Birrens , Introdution to the Mathematical and Statistical Foundation of Econometrics
Lectures on mathematical statistics, Chen Jiading, higher education
★ Gallant , An Introduction to Econometric Theory
R. Larsen, M. Mars, An Introduction to Mathematical Statistics
☆ The probability theory and mathematical statistics, Li Xianping, Fudan University
☆ Papoulis , Probability , random vaiables , and stochastic process
☆ Stone , Of the probability and statistics
★ The Sun Yat-sen University Department of statistics, probability theory and mathematical statistics, higher education
0 based on the theory of mathematical statistics ( Measure theory)
Berger , Statistical Decision Theory and Bayesian Analysis
Chen Xiru, advanced mathematical statistics
★ Shao Jun , Mathematical Statistics
★ Lehmann , Casella , Theory of Piont Estimation
★ Lehmann , Romano , Testing Statistical Hypotheses
Of the mathematical statistics and data analysis Rice
0 asymptotic statistics
★ Van der Vart , Asymptotic Statistics
0, parameter estimation method of modern statistical theory, non-parametric statistical methods
Parameters Econometrics, Semiparametric econometric, self-help method to econometrics, empirical likelihood
Statistics section
1 , The statistics, exploratory data analysis David Freedman China’s statistics (The statistics speak well)
2 、 Mind on statistics Machinery industry (Only high school level)
3 、 Mathematical Statistics and Data Analysis Machinery industry (This book is very good ideas about a lot of new things)
4 、 Business Statistics a decision making approach China statistics (Utility)
5 、 Understanding Statistics in the behavioral science China statistics
Return to section
1 And the application of the linear regression China statistics (blue book series, there is a certain depth, very good)
2 、 Regression Analysis by example , (Attractive, less derived)
3 、《 Logistics Regression model-methods and applications Wang Jichuan Guo Zhigang higher education (not much domestic classical statistical packages)
Multi-
1 And the application of multivariate analysis Wang Xuemin Shanghai University of Finance (domestic good statistical textbooks)
2 、 Analyzing Multivariate Data , Lattin Machinery industry (Visual, math requirements are not high)
3 、 Applied Multivariate Statistical Analysis , Johnson & Wichem China statistics (very high)
The journal of applied regression analysis and other Multivariable methods Kleinbaum
The multivariate data analysis Lattin
Time sequence
1 And the business and economic forecasting, time series models Francis (of focus on application, classic)
2 、 Forecasting and Time Series an applied approach , Bowerman & Connell (By Box-Jenkins(ARIMA) Method, attach the SAS Minitab Program)
3 , The time series analysis: forecasting and control Box , Jenkins China statistics
Of the forecasting and time series Bowerman
Sample
1 And the sampling technique Cochrane (of authority in this field, the classic book. Difficult to understand-even understand each formula may not be able to understand its meaning)
2 、 Sampling: Design and Analysis , Lohr China statistics (spoke in a lot of new, hard to understand)
Software and other
1 、《 SAS Statistical analysis software and applications Wang Jili Zhang yaoxue Chambers Editor (books)
2 、《 SAS V8 Basic tutorial Wang Jiagang series statistics, China (focus on programming, not what statistics)
4 And the statistical analysis of financial markets Zhang Yaoting with Guangxi Normal University (short)
Economics and financial mathematics
Econometrics, time series analysis (regression analysis (analysis of hedging) and multivariate analysis (factor analysis and principal components analysis (risk management)))
John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, and Andrew Y. Lo , The Econometrics of Financial Markets (Concise financial economics textbooks, not related to macro-financial (macro and Monetary Economics), well read, requires some basic economics and finance, without DuffieCochrane High)
★ John H. Cochrane , Asset Pricing (Easier to read, and writing modern, necessary financial economics, reading can read papers in the field, to study financial mathematics or reading Duffie Bar)
☆ Russell Davidson , Econometric Theory and Methods (Intermediate books spoke most clearly, Biglin reads much better, although not Lin Wenfu classic)
★ Darrell Duffie , Dynamic Asset Pricing Theory (Continuous-time dynamic programming, although easy to read is the best functional analysis, measure theory, stochastic calculus and vector space optimization knowledge base, there is no Hull Good reads)
★ Golderberg , A Course in Econometrics
☆ William H. Greene , Econometric Analysis (Intermediate Econometrics, classic, hard to read, the focus is not prominent, suited for reference books)
☆ Gujarati And Econometrics (junior classic, easy to read but a bit old)
☆ Lin Wenfu Fumio Hayashi , Econometrics (Intermediate, classical theory of econometrics, and first two chapters of important to certain mathematical Foundation and teacher guidance, Biglin books easier to read)
Helmut Lütkepohl , Markus Krātzig , Applied Time Series Econometrics , The journal of applied econometrics time series
Ian Jacques , Mathematics for Economics and Business , Of the business and economic mathematics
B. Jerkins,Time Series Analysis:Forecasting & Control
☆ Peter Kennedy, A Guide to Econometrics (An excellent primary materials, easy to understand, and Woodridge-not of the modern method) Peter, the Guide to econometrics
☆ Robert s. pindyck of the econometric models and economic forecasts Econometric Models and Economic Forecasts
Robert s. pindyck of the investment under uncertainty
Roger Myerson, Curt Hinrichs, Probability Models for Economic Decision , Of the probability model of economic decision making
★ J. H. Stock, M. W. Watson, Introduction to Econometrics
A.H.Studenmund,IntroductoryEconometricswithApplications, the journal of applied econometrics (Basic)
T.J.Watsham,K.Parramorethe quantitative methods in finance
★ Jeffrey Wooldridge , Introductory Econometrics: A Modern Approach (Beginner, not on mathematical reasoning, learning, and for economic majors, not suitable for statistics, Kennedy Books from it, guzhaladi’s book is deeper than it)
☆ Wooldridge Woodridge, Econometric Analysis of Cross Section and Panel Data The econometric analysis of cross section and panel data (the classic micro-econometric theory, Green Hayashi Two books supplement, require primary or secondary basis, easier to read)
Shao Yu of the micro-finance and mathematical basis of the Tsinghua University
0 time series modeling, time series analysis and its algorithm
McKenzie , Research Design Issues in Time-Series Modeling of Financial Market Volatility
Watsham , Parramore , Quantitative Methods in Finance
0 mathematical finance Econometrics of Finance
Abramowitz , Stegun , Handbook of Mathematical Functions
Briys , Options , Futures and Exotic Derivatives
★ Brockwell, P. and Davis, Time series : theory and methods
☆ The introduction of financial econometrics Chris Brooks ( Chris Brooks )
★ Campbell, J.Y., A.W. Lo and A.C. MacKinlay, The econometrics of financial markets (Consumption of capital asset pricing model)
Cox , Huang , Option Pricing and Application , Frontiers of Financial Theory
Dempster , Pliska , Mathematics of Derivative Securities
☆ Walter Enders, Applied Econometric Time Series (Great book of time series analysis, much easier to read than Hamilton’s classic)
★ Gourieroux, G., ARCH models and financial applications
★ James Douglas Hamilton, Time series analysis The time series analysis Hamilton (classics of the time series, focusing on the theory and technology, not suitable for the beginner, need a basis, available statistics and economic)
★ Hamilton, J. and B. Raj, (Eds), Advances in markov switching models
Karatzas , Lectures on the Mathematics of Finance
★ Lardic S., V. Mignon, Econom é trie des s é ries temporelles macro é conomiques et financi è res. Economica.
★ The continuous-time finance Robert k. Merton ( Robert Merton ) Continuous time finance
★ Mills, T.C., The econometric modelling of financial time series
★ Pliska , Introduction to Mathematical Finance : Discrete Time Models (Discrete-time model of advanced materials) An introduction to mathematical finance – a discrete-time model
★ Reinsel, G., Elements of multivariate time series analysis
Of the financial mathematics Stampfli
☆ Ross , An Introduction to Mathematical Finance : Options and other Topics, Ross S. M., The mathematical finance preliminary Ross (Sheldon M.Ross) (Portfolio)
Schachermayer , Introduction to the Mathematics of Financial Markets
★ Tsay, R.S., Analysis of financial time series Ruey s. Tsay in the analysis of financial time series (Ruey S.Tsay) (U)
Software:
1 、 EViews
2 、 SAS
Micro-economics
★ Masi·kelaier of microeconomics Andreu Mas-Colell Green, Microeconomic Theory (High top, micro-encyclopedia. General equilibrium speaks well suited to learn differential equations and real analysis and linear algebra Department of economics students, business students can most understand it’s okay. Part of game theory in conjunction with Kreps and Tirolethe theory of industrial organization)
☆ Of the advanced microeconomic theory Advanced Microeconomic Theory Jerry / Swiss-Nepal Geoffrey A. Jehle / Philip J. Reny (Advanced Start, the first half well written, second only to HAL Varian, game theory in general but concise. No masikelaier comprehensive and complicated, simple and accurate and easy to understand, the two books complement each other. Analysis of bifanlian and Nicholson, and want to use it without complex geo-high)
☆ A Course in Microeconomic , David M. Kreps (Advanced, focused on game theory, other generally written in easily and lack of rigorous, masikelaier supplement)
★ Gregory Mankiw’s principles of Economics ( Primary)
☆ Walter Nicholson etl , Microeconomic Theory: Basic Principles and Extensions (Let you easily grasp and falls in love with micro, intermediate to senior masikelaier Robert s. pindyck transition, weak in game theory)
★ Robert s. pindyck Robert Pindyck Of the micro-economics Microeconomics (Intermediate, easy simple, covering different aspects of micro, such as game theory and the pricing strategy. Suitable for beginners, focusing on applications, mathematics and theoretical analysis on less people know but don’t know the why. As a weak secondary, for intermediate)
★ Paul Samuelson Economics (Basic, but mathematical reasoning)
★ Stiglitz Economics (first class)
★ HAL Varian microeconomics: a modern perspective Intermediate Microeconomics: A Modern Approach (Intermediate, too little math)
★ HAL Varian microeconomics advanced course (Advanced base, too short, instead of mathematics to explain the concept in words, the first half well, suitable for learning, by looking at meaningless, to HAL Varian Kreps Claire) Hal R. Varian , Microeconomic Analysis
☆ Five: selling the Orange statement (getting started)
Macroeconomics
Aobosifaerde, and ruogefu: the advanced course in international finance Foundations of International Macroeconomics by Maurice Obstfeld and Kenneth S. Rogoff (Writing can also be improved, senior, well-known authors, applications and practice a lot, harder than Krugman)
★ Robert J. Barro, Economic Growth
★ Olivier Blanchard Blanchard of the macro-economics Macroeconomics (For major in finance or economics, maths is harder than Greg Mankiw, there’s a Intermediate Algebra, trigonometry and calculus and statistics, the exercise did not answer, other professional and Mankiw. As intermediate seems difficult (of course more difficult for advanced mathematical), the system clearly)
Blanchard Olivier Jean Blanchard The lectures on Macroeconomics Lectures on Macroeconomics (Advanced) (macro and Monetary Economics, as a senior is too easy)
Dennis R. Appleyard , Alfred J. Field , International economics
★ Rudiger Dornbusch of the macro-economics (intermediate)
☆ Krugman of the International Economics (intermediate)
☆ The recursive method of economic dynamics Lucas (GAO Hong’s top teaching) recursive method in economics dynamics by Robert e. Lucas
★ Greg Mankiw N. Gregory MankiwmacroeconomicsMacroeconomics(intermediate, clear and concise, as his principle of simplifying as far as possible, but no how get paid? Or Blanchard and Rudiger Dornbusch, a professional and deep was Romer. ）
¡Ï advanced macroeconomics David . Romer (Advanced Start) Advanced Macroeconomics by David Romer(wide, macro models, analysis of high quality, less mathematics to explain mathematics can be more concise, easy to cause confusion, open macroeconomics this is not enough, not suitable for core intermediate books)
★ International Economics in El Salvador
☆ Of the dynamic macroeconomic theory Sargent (basic textbook Gao Hong) Recursive Macroeconomic Theory by Lars Ljungqvist Thomas I. Sargent
Sachs macroeconomics in the global perspective
Of the financial economics
Economic history / The history of economic thought
Of the financial history of Western Europe
The American economic history of Cambridge
The history of economic analysis
Aikelunde, and Herbert: the history of economic theory and methods
Roger E. Backhouse , The History of Economic
Stanley L. Brue , The Evolution of Economic Thought And the history of economic thought
Spiegel: the growth of economic thought
Of the methods of analysis in economics Akira Takayama
Michael Todaro , Stephen Smith , Economic Development , Of the development economics
Finance
Allen , Santomero , The Theory of Financial Intermediation , Journal of Banking and Finance
★ Of the finance Zvi bodioe (Zvi Bodie), Robert k. Merton (Robert Merton)
★ The investments Zvi bodioe ( Zvi bodie ), Yalikesi·Kaien ( Alex Kane ), Alan Marcus ( Alan Marcus ) Investments (Capital, interest rates and the discount)
Bodie , Essentials of Investments
Dubofsky , Options and Financial Futures : Valuation and Uses
Dunbar , Invent Money : The Story of Long-Term Capital Management and the Legend behind it
★ Erichberger , Harper , Financial Economics
Fabozzi , Foundations of Financial Markets and Institutions
James , Webber , Interest Rate Modiling
★ Jarrow , Finance Theory
★ LeRoy , Werner , Principals of Financial Economics (Mean-variance method)
★ Madura of the structure of financial markets and
Malkiel , A Random Walk Down Wall Street
Mayer , Money , Banking and the Economy Meyer of the monetary, banking and economic
McMillan , McMillan on Options
Mel’nikov , Financial Market-Stochastic Analysis and the Pricing of Derivative Securities
The money and banking Mishkin
Naftci , Investment Banking , and Securities Trading
Nassim , Taleb , Dynamic Hedging
Pelsser , Efficient Methods for Valuing Internet Rate Derivatives
Ritchken , Theory , Strategy and Applications
Santomero , Financial Markets , Instruments and Institutions
Saunders , Financial Institutions Management : A Modern Perspective
★ William of the investment F• Sharp ( William F.Sharpe ), Gordon J• Alexander ( Gordon J.Alexander ), Jeffrey V• Bailey ( Jeffery V.Bailey )Investments (Capital, interest rates and the discount)
Shefrin , Behavioral Finance
Of the monetary theory and policy Carl E. Walsh
Willmott , Dewynne , Howison , The Mathematics of Financial Deribatives
Zhang , Exotic Options
Corporate finance
Bernstein , Capital Idea : The Improbable Origins of Modern Wall Street
Scott Besley, Eugene F. Brigham, Essentials of Managerial Finance Of the essentials of financial management
Richard A. Brealey, Stewart C. Myers, Principles of Corporate Finance The principle of corporate finance
Brennan , The Theory of Corperate Finance
Burroughs , Helyar , Barbarians in the Gate : The Fall of RJR Nabisco
Copeland , Financial Theory and Corporate Policy
Damodaran , Applied Corporate Finance : A User’s Manual
Damodaran , Corporate Finance : Theory and Practice
Emery , Finnerty , Corporate Financial Management
☆ Corporate finance, Stephen A. Ross ( Stephen A.Ross ), Luodeerfu W. Weisitefeierde ( Radolph W.Wdsterfield ), Jiefuli F. Jiefu ( Jeffrey F.Jaffe )
☆ To the theory of corporate finance • ladder Jordan ( Jean Tirole )
Valuation : Measuring and Managing the Value of Companies
1. the theory of finance
Asset pricing:
★ Duffie , Futures Markets (Forward contracts and futures contracts)
Duffie: security market
★ The fundamentals of financial economics Huang Qifu ( Chi-fu Huang ), Luobote·baobo·lizisenboge ( Robert H. Litzenberger ) Foundation for financial economics
★ Ingersoll: Theorey of financial decision making
Ross: Neoclassical Finance
Underwriting:
Company mergers and acquisitions:
2. Introduction and General
Amman: Credit risk valuation
★ Baxter M., Rennie A., Financial Calculus : An Introduction to Derivative Pricing (Financial engineering required reading step by step introduction to stochastic calculus and financial partial differential equation is Willmott Focus on theory, only elementary calculus and probability theory) of the mathematical finance an introduction to derivative pricing
Bielecki, Rutkowski: Credit Risk : Modeling , Valuation and Hedging
★ Tomas Bjork: Arbitrage theory in continuous time ( Hull Follow-on intermediate book, continuous-time pricing, options)
Cvitanic, Zapatero: Introduction to the economics and mathematics of financial markets
★ Dana , Jeanblanc , Financial Markets in Continuous Time (Continuous-time)
Duffie Singleton: Credit Risk
★ Elliott, Kopp: Mathematics of Financial markets
★ Fouque , Papanicolau , Derivatives in Financial Markets with Stochastic Volatility (Stochastic volatility)
★ Gourieroux , ARCH Models and Financial Applications ( ARCH Model and GARCH Model)
★ Harris:Trading and Exchanges: Market Microstructure for Practitioners (Detailing various types of securities transactions)
★ Options, Futures, and Other Derivatives Yuehan·Heer the options, futures and other derivatives (John c. Hull) (derivatives and mathematical finance primary classical materials, Organization for futures and options markets, forward contracts, option pricing, options trading and futures contracts)
Hull , J. C. , Risk Management and Financial Insititutions Of the risk management and financial institutions
★ Karatzas Shreve: Methods of mathematical finance (American-style option, stochastic differential, continuous-time dynamic programming, martingale, continuous-time model of advanced materials)
☆ Lawrence G. McMillan , Options as a Strategic Investment
Rrederic S. Mishkin, Financial Markets and Institutions Of the financial markets and financial institutions
★ Mishkin the economics of money banking and financial markets
Edgar A. Norton , Introduction to Finance : Markets , Investments and Financial Management Introduction to the financial markets, investment and financial management of
★ Lewis , Option Valuation under Stochastic Volatility : with Mathemetical Code (Stochastic volatility)
Principles of financial engineering by ☆ Saleh . Neifusi (Salih N.Neftci)
Peter Rose, Sylvia C. Hudgins, Commercial Bank Management The management of commercial banks
Peter S. Rose, Money and Capital Markets Of the financial markets
Shreve:Stochastic Calculus Models for Finance vol 1 & 2
Taleb:Dynamic Hedging
Lloyd B. Thomas, Money, Banking, and Financial Markets Money, banking and gold Of the financial markets
☆ Of the financial economics Wang
Robert E. Whaley, Derivatives: Markets, Baluation, and Risk Management Of the derivative
Paul Wilmott, Paul Wilmott introduces quantitative finance Of the financial econometrics
Wilmott P.: quantitative finance (Interest rate)
★ Wilmott P. , Derivatives : The Theory and Practice of Financial Engineering (Option pricing, good use of partial differential equations)
★ Sundaresan , Fixed Income Markets and Their Derivaties (Fixed-income bonds, interest rate derivatives) Senda sang of the fixed income securities market and its derivatives
Tavakoli: Collateralized Debt Obligations and Structured Finance
Tavakoli: Credit Derivatives & Synthetic Structures: A Guide to Instruments and Applications
Tuckman: Fixed Income Securities: Tools for Today’s Markets
Fabozzi Fabozzi Books:
★ Bond Markets : Analysis and Strategies (Fixed-income bonds, interest rate derivatives)
★ Capital Markets , Institutions and Instruments (Organization)
Collateralized Debt Obligations: Structures and Analysis
Fixed Income Mathematics
Fixed Income Securities
Handbook of Mortgage Backed Securities
Interest Rate, Term Structure, and Valuation Modeling
The Handbook of Fixed Income Securities,
Investment management
4: Other classes Rebonato :
Volatility and Correlation : The Perfect Hedger and the Fox
Modern Pricing of Interest-Rate Derivatives : The LIBOR Market Model and
Beyond
Interest-Rate Option Models : Understanding, Analysing and Using Models
for Exotic Interest-Rate Options
GENCAY: An Introduction to High-Frequency Finance
O’Hara:Market Microstructure Theory
Important book (does not have to. Now few will go throughout the study 18, and19 all these magnificent works of the century. ):
☆ The economic table fulangsiwa • Quesnay
Thomas of the British wealth derived from foreign trade
The selected works of Hume’s economic theory of David Hume
☆ The wealth of the theory of moral sentiments by Adam Smith
The principle of population Thomas Robert Malthus
Introduction to political economy Rang·badisite·Sayi
The principles of political economy McCulloch
☆ To the theory of taxation of the political arithmetic ofthe currency on the William petty
☆ Guanzi
Principles of political economy and taxation by ☆ David Ricardo
☆ New principles of political economy, Ximeng·de·xisi cover
Of the national system of political economy Fulidelixi·lisite
The principles of political economy John Stuart Mill
☆ Das Karl Marx
☆ The Anti-Dühring, Engels
☆ The complete works of Marx and Engels
The theory of political economy Weilian·sitanli·jiewensi
The principle of national economy of Carl Menger
The essence of pure economics Liang·waerlasi
The capital and interest of the positive theory of capital Ougen·Feng·pangbaweike
The dynamics of luoyi·fubusi·haluode
Principles of Economics by ☆ afulide·maxieer
☆ The Federal Communications Commission, the problem of social cost, the company, the market and the nature of the Corporation, the property rights of the legal and institutional changes R• Kos
The economic system of capitalism Oliver Williamson
Social choice and individual values, ARO
☆ The economic interpretation of the theory of share tenancy, Steven Cheung
The comparative institutional analysis of Aoki
☆ The Ricardian Theory of Production and Distribution, The risk, uncertainty and profit, Frank Knight
☆ To the theory of monopolistic competition Chamberlain
☆ To the theory of Fisher
☆ The price theory of the consumption function theory of the quantity theory of money and the other saying the Marshallian demand curve, capitalism and freedom Milton Friedman
☆ Friedman of the monetary history of the United States, Schwartz
☆ Of the uncertainty, evolution and economic theory Some Economics of Property Rights, A• A. alchain
☆ Of the University of Economics A• A. alchain, Ellen
The property right and system changes-the collected works of property right theory and the translation of new system school R• Kos, A• A. alchain, road gelasi·nuosi
The contractual economics of Coase, Hart, Stiglitz
☆ The structure and change in economic history, the road of the rise of the Western world gelasi·nuosi
☆ The development of utility theory, industrial organization, George Stigler
Of the interest and price kenute·weikesaier
Conditions of the distribution of wealth and the economic progress of the John Bates Clark Medal
The theory of the distribution of wealth qiaozhi·Lamu game
The theory of the leisure class Tuoersitan·bende·fanbolun
Of the boom from the competition ludeweixi·aihade
History of the theory of economic development, economic analysis, capitalism, socialism and democracy, Joseph Alois schhumpeter
The economics of shortage of yanuoshi·keneier
☆ ASE·saixier of the welfare economics Pigou
☆ The economics of imperfect competition and the introduction of modern economics Joan Robinson
The economic analysis of human behavior in the family of Nations and · S• Becker
The economic growth theory of Lewis
The theory of democratic finance Buchanan
The conflict strategy of Schelling
The economic development strategy of aibote·heximan
The comparative financial analysis of Richard A• Musgrave
☆ The general theory of employment, interest and money, monetary theory of John Maynard Keynes
The value and capital of the theory of economic history John Richard Hicks
The road to serfdom Hayek
An introduction to the theory of socialist economic growth mihaer·kalaisiji
The economic cycle theory of Lucas
The economic growth of the countries of the modern growth of the Kuznets
The stages of economic growth Rostow
The theory of monetary equilibrium Myrdal
Kang Mang of the institutional economics
Money and capital in economic development, Ronald I• McKinnon
The economics and public goals of the affluent society Yuehan·kennisi·jiaerbuleisi
The transformation of traditional agriculture and the human capital investment of Theodore · W• Schultz
The development concept in the general theory of economic activities in the new position F• Perroux
Of the capital formation in the developed countries R• Knox
Of the theory of economic growth of the solo
The stages of economic growth Woerte·luosituo
The competitive advantage of Nations Porter
Schumacher of the small is beautiful
The poverty and famine, collective choice and social welfare, rereading Adam Smith, Economist
Of the nature and significance of economic science
Principles of Economics by Yang xiaokai
Of the human capital investment Xiaoduo·weilian·shuerci
Of the methodology of Economics mark blaug
Other reference books:
Andeson O. D. Editor, Time Series Analysis: Theory and Practice
Bingham N. H., Kiesel R., Risk-Nertral Valuation Pricing and Hedging of Financial Derivatives
Buchan M. J., Convertible Bond Pricing: Theory and Evidence
John Y. Campell , Andrew W. Lo, The Econometrics of Financial Markets
Chen J., Gupta A. K., Parametric Statistical Change Point Analysis
Chow Y. S., Teicher H., Probability Theory: Independence, Interchangeability, Martingales
Christian P. R., George C., Monte Carlo Statistical Methods
Thomas E. Copeland, Finance Theory and Corporate Policy
Csòrgǒ M., Horváth L., Limit Theorems in Change-Point Analysis
R. V. Norbert Haug, A. T. Mr Clegg, an introduction to mathematical statistics
Harrison J. M., Brownian Motion and Stochastic Flow System
Hsiao C., Analysis of Panel Data
Jorion P., Value at Risk: the New Benchmark for Managing Financial Risk
Edward P. C. Kao, An Introduction to Stochastic Processes
Takeaki Kariya, Quantitunive Methods for Portfolio Analysis (Portfolio)
Korn R., Optimal Portfolio
Kwok Y. K., Mathematical Models of Financial Derivatives
Levy H., Stochastic Dominance: Investment Decision Making under Uncertainly (Portfolio)
Lin X. S., Introductory Stochastic Analysis for Finance
Markowitz H. , Mean-Variance Analysis in Portfolio Choice and Capital Markets (Transaction costs, portfolio)
Markowitz H. , Portfolio Selection: Efficient Diversification of Investment
Percival D. B., Walden A. T., Wavelet Methods for Time Analysis (Wavelet)
Peters E. E., Fractal Market Analysis: Applying Chaos Theory to Investment and Economics
Rosen L. R., The McGraw-Hill Handbook of Interest Yield and Returns
Willmott P., Dewynne J., Option Pricing: Nathematical Model and Computation
Game theory
☆ Theory of games Zhu·fudengboge Jordan • ladder (top of game theory textbooks) Game Theory by Drew Fudenberg Jean Tirole
☆ Gibbons of the basic game theory (Game theory) a Primer in Game Theory by Roerbt Gibbons
Jack Hirshleifer, John G. Riley, The Analysis of Uncertainly and Information
Inez Macho-stadler , David Perez-Castrillo J., An Introduction to the Economics of Information: Incentives and Contracts
Laffort Jean-Jacques, The Economics of Uncertainly and Information
Myerson: game theory: analysis of conflict (Advanced)
☆ A course in game theory, Martin . J. Osborne Alier·lubinsitan (an introduction to game theory), An Introduction to Game Theory by Martin j. Osborne Ariel Rubinstein
Richard Watt, An Introduction to the Economics of Information
Zhang weiying, game theory and information economics (Intermediate)
The theory of industrial organization / Industrial economics
Morris, sea: Business Economics and organization
Clarkson, Miller: the industrial organization: theory, evidence and public policy
☆ Ladder Jordan: of the theory of industrial organization The Theory of Industrial Organization , Jean Tirole (Classics of industrial organization theory, Department of Economics, for students, not suitable for schools, requires some basic algebra and game theory, first read Martin Advanced Industrial Organisation As the transition)
Incentive theory / The economics of information
Laffon, and laffontand martimort: the motivation theory (volume I): principal-agent model
Laffon, ladder Jordan: the theory of incentives in procurement and regulation of Government
Marco Ines macho-Stadler: an introduction to the economics of information: incentives and contracts
★ Joshi , The Concepts and Practice of Mathematical Finance
★ Joshi , C++ Design Patterns and Derivatives Pricing
London , Modeling Derivatives in C++
Meyer Books:
Effective C++
More Effective C++
Effective STL
Saul , Numerical Recipes in C++
Accounting
Basic accounting, financial accounting, cost accounting, management accounting, auditing, financial management, accounting, law and tax law
Anthony, accounting: text and cases 》
Hayes, the auditing: based on the perspective of the international auditing standards
Whittington, of the audit and other assurance services
Garrison, of the management accounting
Weygandt, of the financial accounting
Williams, the accounting: the basis for business decisions
Warren, of the accounting
Institutional economics
The system of Economics
Thrainn eggertsson: System of the economic behavior and
Feilvboteng: of the new institutional economics
★ Jean Tirole The theory of industrial organization
Of the modern institutional economics, Sheng Hong Editor
Evolutive economics
Gillis, Romer: the economics of development
Public economics / Public finance
Brown, Jackson: the economics of the public sector
☆ Harvey s. Rosen: of the finance
Joseph Stiglitz: the economics of the public sector
Other (language, computer, literature)
★ Douglas . R. Douglas r.Emery of the company’s financial management
S.CharlesMaurice,ChristopherR.Thomas,ManagerialEconomics, management in the boardroom
Michael R. Czinkota , Illkka A. Ronkainen And of the international business
Patrick A Garghan , Of the mergers, acquisitions and corporate restructuring Mergers , Acquisitions , and Corporate Restructurings
★ Philip Kotler Marketing Management
Technical analysis of stock trends (USA) Beverly Magee, (u) Basetti
Technical analysis of the futures market (U) Murphy
★ Robbins of the management
Technical analysis of futures trading (USA) Peter schwieger ( Schwager,J.D. )
(Not required)
Gann on Wall Street 45 Year (u) Gann
How to profit from the commodities futures trading (USA) Gann
Crowe talking about investment strategy–the magic of Murphy’s law (u) Crowe ( Krol,S. )
… …
Paul Wilmott Introduces Quantitative Finance, Paul Wilmott, Wiley, 2007
Paul Wilmott on Quantitative Finance, Paul Wilmott, Wiley, 2006
Frequently Asked Questions in Quantitative Finance, Paul Wilmott, Wiley, 2007
The Complete Guide to Option Pricing Formulas, Espen Gaardner Haug, McGraw-Hill, 1997
Derivatives: Models on Models, Espen Gaardner Haug, Wiley, 2007
Monte Carlo Methods in Finance, Peter Jackel, Wiley, 2002
Bootstrap Method A guid for practioners and reseachers MICHAEL R. CHERNICK.pdf
C++ Primer[ Chinese non-scan version ]Stanley b Lippman. PDF
C++ Getting started with classic ( 3 ) Ivor Horton. PDF
C++ Programming _ Tan haoqiang · Tsinghua University .pdf
Convergence Of Probability Measures Billingsley.pdf
C Programming languages ( 2 · New version) Dennis M Ritchie.pdf
Data Abstraction and Problem Solving with C++ 3Ed frank m carrano.pdf
Data Analysis Using Regression and Multilevel 、 Hierarchical Models ANDREW GELMAN.pdf
Data Structures and Algorithms Alfred. Aho.pdf
Design and Modeling for Computer Experiments Kai-Tai Fang Runze Li.pdf
Ergodicity And Stability Of Stochastic Processes a a Borovkov.pdf
Excel 2007 Formulas John Walkenbach.chm
Excel 2007 VBA Programmer Reference john green stephen bullen rob bovey.pdf
Excel 2010 Formulas John Walkenbach.pdf
Excel 2010 Power Programming with VBA John Walkenbach.pdf
excel hacks david raina hawley.pdf
Excel2003 Application tips . CHM
fifty challenging problems in probability with solutions frederick mosteller.pdf
Functional Analysis Lax.pdf
Functional Analysis Rudin.pdf
Functional Analysis Spectral Theory v.s. Sunder.pdf
Functional Ito calculus and stochastic integral representation of martingales Rama Cont Functional Ito Calculus and martingales stochastic integral representation (English version) .pdf
Geometric Probability Herbert Solomon.pdf
gnu autoconf David MacKenzie.pdf
Graphical models Probability graphic .pdf
GTM001 Introduction to Axiomatic set theory G. Takeuti w M Zaring.djvu
GTM002 Measure and Category-A Survey of the Analogies between Topological and Measure Spaces . John c Oxtoby measure and category: a summary of the report on the topological space and measure space is similar . DjVu
GTM004 A Course in Homological Algebra P.J. Hilton U.Stammbach.djvu
GTM005 Categories for the Working Math Saunders Mac Lane .djvu
GTM016 The Structure of Fields David Winter .djvu
GTM016 The Structure of Fields David Winter.djvu
GTM018 Measure Theory Paul R. Halmos .djvu
GTM027 General topology John L. Kelley .djvu
Handbook of computational statistics-Concepts and methods J.E.Gentle.pdf
Handbook Of Measure Theory Pap.pdf
Handbook Of Stochastic Methods c w Gardiner.pdf
Intro to Data Management and Programming in SAS Harvard School of Public Health.pdf
Introduction to Cybernetics W. ROSS ASHBY.pdf
Introduction To Functional Analysis Taylor.pdf
Introduction To Martingale Methods In Option Pricing Home Martingale used in option pricing . PDF
Introduction to Nonparametric Regression Kunio Takezawa.djvu
Introduction To Stochastic Analysis Z. Qian and J. G. Ying.pdf
Introduction to Stochastic Integration Hui-Hsiung Kuo.pdf
Large deviations and stochastic calculus Large deviations and stochastic analysis of large random matrices Alice Gnionnet.pdf
Large Random Matrices Lectures On Macroscopic Asymptotics Guionnet.pdf
Latex A Document Preparation System Lamport.pdf
latex in 90 mins Tobias Oetiker.pdf
Latex Notes Alpha Huang.pdf
Latex2e Technology publishing Guide Deng Jiansong . PDF
Latex Get started and improve Chan Chi Kit . PDF
Lectures on Stochastic Analysis Lectures on stochastic analysis University of Wisconsin, Thomas g. Kurtz. PDF
letex Layout tips Li Dongfeng . PDF
Levy Processes And Infinitely Divisible Distributions ken iti Sato.pdf
Lie Theory And Special Functions willard Miller.pdf
Limit Theorems Of Probability Theory Petrov.pdf
Lindo User manual .pdf
LINDO Package introduction .pdf
linear Regression Analysis george a e seber alan a lee.pdf
LINGO Quick start .pdf
Local Polynomial Modelling and Its Applications j fan.pdf
Long-Memory Time Series-Theory And Methods Wilfred0 Palma.pdf
Markov Processes Feller Semigroups And Evolution Equations Jan A van Casteren.pdf
martingale limit theory and its applications hall.pdf
Mathematical Principles Of Natural Philosophy Newton.pdf
\
mathematical statistics keith knight.pdf
Mathematical Statistics with Applications Kandethody M.Ramachandran.pdf
Mathematical Statistics-Basic Ideas and Selected Topics bickel & Dokosum.djvu
Measure Theory j l Doob.pdf
Microeconomic Theory A Mathematical Approach james e henderson.pdf
Microsoft Office Excel 2007 Visual Basic for Applications Step by Step Reed Jacobson.chm
model-oriented data analysis V. Fedorov H. Lauter.pdf
Monte Carlo Strategies in Scientific Computing jun s liu harvard.pdf
Monte Carlo Strategies in Scientific Computing jun s liu.pdf
More Math Into Latex 7ed George Gratzer.pdf
MS OFFICE Complete the formula little key.pdf
Multirate and wavelet signal processing Bruce W. Suter.pdf
Multiscale Wavelet Methods for Partial Differential Equations Wolfgang Dahmen, Andrew J. Kurdila and Peter Oswald.pdf
Neural networks and pattern recognition Omid Omidvar and Judith Dayhoff.pdf
nonparamatrics economitrics Adrian Pagan, Aman Ullah.pdf
Nonparametric and Semiparametric Models-An Introduction Wolfgang H¨ardle, Marlene M¨ uller, Stefan.pdf
Nonparametric Functional Data Analysis Theory and Practice Frédéric Ferraty Philippe Vieu.pdf
Numerical Solution Of Stochastic Differential Equations P E Kloeden & E Platen.pdf
Numerical Solution Of Stochastic Differential Equations With Jumps In Finance Eckhard Platen.pdf
open source development with cvs Moshe Bar Karl Fogel 3ed.pdf
Partial Identification Of Probability Distributions Charles F. Manski.pdf
Practical Time-Frequency Analysis-Gabor and Wavelet Transforms with an Implementation in S Ren& Ingrid Daubechies.pdf
Probabilities And Potential CLAUDE DELLACHERIE.pdf
Probability And Information a m Yaglom.pdf
Probability Inequalities Probability inequalities Zhengyan Lin Zhidong Bai.pdf
Probability Theory The Logic of Science E. T. Jaynes Meditations of probability theory .pdf
Ordinary differential equations and dynamical systems
ODE and dynamical systems, critical points, phase space & stability analysis; Hamiltonian dynamical systems; ODE system with gradient structure, conservative ODE’s.
Partial differential equations and applications
Basic theory for elliptic, parabolic, and hyperbolic PDEs; calculus of variations: Euler-Lagrange equations; shock waves and rarefaction waves in scale conservation laws; method of characterization, weak formulation, energy estimates, maximum principle; Hamilton-Jacobi equations, Lax-Milgram, Fredholm operator.
Mathematical modeling, simulation, and applied analysis
原名《A First Course in Mathematical Modeling》，是很好的书。
230《数学建模与数学实验.第3版》赵静, 但琦主编
231《数学建模及其基础知识详解》王文波编著
232《数学建模方法及其应用》韩中庚编著
233《数学建模》Maurice D. Weir, (美) William P. Fox著
Modeling
Ordinary differential equations and dynamical systems
ODE and dynamical systems, critical points, phase space & stability analysis; Hamiltonian dynamical systems; ODE system with gradient structure, conservative ODE’s.
Partial differential equations and applications
Basic theory for elliptic, parabolic, and hyperbolic PDEs; calculus of variations: Euler-Lagrange equations; shock waves and rarefaction waves in scale conservation laws; method of characterization, weak formulation, energy estimates, maximum principle; Hamilton-Jacobi equations, Lax-Milgram, Fredholm operator.
Mathematical modeling, simulation, and applied analysis
Rick Durrett, Probability: Theory and Examples, Cambridge University Press, 2010
Kai-Lai Chung , A Course in Probability Theory, New York, 1968, 有中译本(钟开莱：概率论教程， 机械工业出版社， 2010）
Syllabus on Statistics
Distribution Theory and Basic Statistics
Families of continuous distributions: normal, chi-sq, t, F, gamma, beta; Families of discrete distributions: multinomial, Poisson, negative binomial; Basic statistics: sample mean, variance, median and quantiles.
Testing
Neyman-Pearson paradigm, null and alternative hypotheses, simple and composite hypotheses, type I and type II errors, power, most powerful test, likelihood ratio test, Neyman-Pearson Theorem, generalized likelihood ratio test.
Estimation
Parameter estimation, method of moments, maximum likelihood estimation, criteria for evaluation of estimators, Fisher information and its use, confidence interval.
Consistency, asymptotic normality, chi-sq approximation to likelihood ratio statistic.
References:
Casella, G. and Berger, R.L. (2002). Statistical Inference (2nd Ed.) Duxbury Press.
茆诗松，程依明，濮晓龙，概率论与数理统计教程（第二版），高等教育出版社，2008.
陈家鼎，孙山泽，李东风，刘力平，数理统计学讲义，高等教育出版社，2006.
郑明，陈子毅，汪嘉冈，数理统计讲义，复旦大学出版社，2006.
陈希孺，倪国熙，数理统计学教程，中国科学技术大学出版社，2009.
Sheldon M. Ross, Introduction to Probability Models
R. Larsen and M. Marx: An Introduction to Mathematical Statistics, Prentice-Hall, 1986。
Foundations of Modern Probability by Olav Kallenberg
汪仁官，《概率论引论》，北大版
程士宏，《高等概率论》，北大版
严士健，《概率论基础》，北大版
陈希孺，高等数理统计，科大版
王(辛/梓)坤《概率论基础及其应用》《概率论及其应用》科学出版社
苏淳《概率论》中国科学技术大学讲义
杨振明《概率论》科学出版社
《概率论基础》李贤平
《概率论与数理统计》（上、下）中山大学数学力学系编
82《概率论基础》李贤平
84《概率与统计》陈家鼎, 郑忠国编著
85《概率论与数理统计》盛骤，谢式千，潘承义编
【习题集】
【提高】
88《测度论与概率论基础》程士宏编著
90《现代概率论基础》汪嘉冈编著
91《分析概率论》拉普拉斯著
《决疑数学》（伽罗威著），
92《概率论及其应用》威廉•费勒著
93《概率， 随机变量， 与随机过程》 帕普里斯著
94《概率论与数理统计讲义•提高篇》姚孟臣编著
95《概率论思维论》张德然著
96《概率论思想方法的历史研究》朱春浩编著
97《概率论的思想与方法》运怀立著
补充：《逻辑代数》沈小丰, 喻兰, 沈钰编著
Random Walk & Random Variables
Hughes, B. Random Walks and Random Environments. Vol. 1. Oxford, UK: Clarendon Press, 1996. ISBN: 0198537883.
Buy at Amazon Redner, S. A Guide to First Passage Processes. Cambridge, UK: Cambridge University Press, 2001. ISBN: 0521652480.
Buy at Amazon Risken, H. The Fokker-Planck Equation. 2nd ed. New York, NY: Springer-Verlag, 1989. ISBN: 0387504982.
Further Readings
Buy at Amazon Bouchaud, J. P., and M. Potters. Theory of Financial Risks. Cambridge, UK: Cambridge University Press, 2000. ISBN: 0521782325.
Buy at Amazon Crank, J. Mathematics of Diffusion. 2nd ed. Oxford, UK: Clarendon Press, 1975. ISBN: 0198533446.
Buy at Amazon Rudnick, J., and G. Gaspari. Elements of the Random Walk. Cambridge, UK: Cambridge University Press, 2004. ISBN: 0521828910.
Buy at Amazon Spitzer, F. Principles of the Random Walk. 2nd ed. New York, NY: Springer-Verlag, 2001. ISBN: 0387951547.
Stochastic Calculus & Stochastic Process
S.M. Ross, Stochastic Processes, John Wiley & Sons, 1983
A First Course in Stochastic Processes by Samuel Karlin, Howard Taylor
A Second Course in Stochastic Processes by Samuel Karlin, Howard Taylor
The Theory of Stochastic Processes I &II Gikhman, I.I., Skorokhod, A.V
《随机过程及应用》陆大金
《随机过程》孙洪祥
《随机过程论》钱敏平，龚鲁光
钱敏平，龚光鲁，随机过程，北京大学出版社
钱敏平，龚光鲁，随机微分方程，北京大学出版社
Probabilistic Methods in Combinatorics
The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008.
Probability and Statistical Reference
Syllabus on Probability Theory
Random variable, Expectation, Independence
Variance and covariance, correlation, moment
Various distribution functions
Multivariate distribution
Characteristic function, Generating function
Various modes of convergence of random variables
Law of large numbers
Random series
Central limit theorem
Bayes formula, Conditional probability
Conditional expectation given a sigma-field
Markov chains
References:
1.Rick Durrett, Probability: Theory and Examples, Cambridge University Press, 2010
2.Kai-Lai Chung , A Course in Probability Theory, New York, 1968, Chinese translation ( Zhong Kailai: course in probability theory,mechanical industry publishing house, 2010)
Syllabus on Statistics
Distribution Theory and Basic Statistics
Families of continuous distributions: normal, chi-sq, t, F, gamma, beta; Families of discrete distributions: multinomial, Poisson, negative binomial; Basic statistics: sample mean, variance, median and quantiles.
Testing
Neyman-Pearson paradigm, null and alternative hypotheses, simple and composite hypotheses, type I and type II errors, power, most powerful test, likelihood ratio test, Neyman-Pearson Theorem , generalized likelihood ratio test.
Estimation
Parameter estimation, method of moments, maximum likelihood estimation, criteria for evaluation of estimators, Fisher information and its use, confidence interval.
Consistency, asymptotic normality, chi-sq approximation to likelihood ratio statistic.
References:
3.Casella, G. and Berger, R.L. (2002). Statistical Inference (2nd Ed.) Duxbury Press.
4.Mao poem song, Cheng Yiming, Pu Xiaolong, probability theory and mathematical statistics course (Second Edition), higher education press2008.
5.Chen Jiading, Sun Shanze, Li Dongfeng and Liu Liping, lectures on mathematical statistics, higher education press 2006.
6.Cheng, Chen Ziyi, Wang Jiagang, mathematical statistics, handouts, Fudan University Press 2006.
7.Chen xiru, Ni Guoxi, course in mathematical statistics, China University of science and technology press, 2009.
Sheldon M. Ross, Introduction to Probability Models
R. Larsen and M. Marx: An Introduction to Mathematical Statistics, Prentice-Hall, 1986。
Foundations of Modern Probability by Olav Kallenberg
Wang ren, an introduction to probability theory, North Edition
CHENG Shihong, the high probability of Peking University
Yan Shijian, of the probability theory Foundation of the North version
Chen xiru, higher mathematics and statistics, University
Wang ( Xin / Zi ) Kun of the Foundation and its application to probability theory, probability theory and its applications, science press
Su Chun of the probability of the China Science and Technology University lecture notes
Yang Zhenming probability theory science press
Of the probability theory Foundation of the Li Xianping
Probability theory and mathematical statistics (upper and lower) of Sun Yat-sen University Department of mathematics and mechanics of knitting
82 Of the probability theory Foundation of the Li Xianping
84 Chen Jiading of the probability and statistics , Written by Zheng Zhongguo
85 Sudden sheng of the probability theory and mathematical statistics, Xie shiqian, Pan Chengyi series
“Onward”
“Increase”
88 Written by CHENG Shihong of the measure theory and probability theory
90 Of the basis of modern probability theory written by Wang Jiagang
91 The analysis of probability theory, Laplacian of the
Solve math (Galen Lowe with),
92 Weilian·feile of the probability theory and its applications
93 The probability, Random variables, and stochastic processes papulisi the
94 Lectures on probability theory and mathematical statistics: lower post Yao Mengchen authoring
95 Probability theory thinking of the theory of Zhang Deran with
96 The probability theory thinking history study written by Zhu Chunhao
97 Shipped huaili of probability theory and method of the
Added: the logical algebra Shen Xiaofeng , Yu Lan , Written by Shen Yu
Random Walk & Random Variables
Hughes, B. Random Walks and Random Environments. Vol. 1. Oxford, UK: Clarendon Press, 1996. ISBN: 0198537883.
Buy at Amazon Redner, S. A Guide to First Passage Processes. Cambridge, UK: Cambridge University Press, 2001. ISBN: 0521652480.
Buy at Amazon Risken, H. The Fokker-Planck Equation. 2nd ed. New York, NY: Springer-Verlag, 1989. ISBN: 0387504982.
Further Readings
Buy at Amazon Bouchaud, J. P., and M. Potters. Theory of Financial Risks. Cambridge, UK: Cambridge University Press, 2000. ISBN: 0521782325.
Buy at Amazon Crank, J. Mathematics of Diffusion. 2nd ed. Oxford, UK: Clarendon Press, 1975. ISBN: 0198533446.
Buy at Amazon Rudnick, J., and G. Gaspari. Elements of the Random Walk. Cambridge, UK: Cambridge University Press, 2004. ISBN: 0521828910.
Buy at Amazon Spitzer, F. Principles of the Random Walk. 2nd ed. New York, NY: Springer-Verlag, 2001. ISBN: 0387951547.
Stochastic Calculus & Stochastic Process
S.M. Ross, Stochastic Processes, John Wiley & Sons, 1983
A First Course in Stochastic Processes by Samuel Karlin, Howard Taylor
A Second Course in Stochastic Processes by Samuel Karlin, Howard Taylor
The Theory of Stochastic Processes I &II Gikhman, I.I., Skorokhod, A.V
The stochastic processes and applications of Lu Dajin
Of the random process of the Sun
Qian Minping of the theory of stochastic processes, Gong Luguang
Qian Minping, Gong Guanglu, a stochastic process, Peking University Press
Qian Minping, Gong Guanglu, stochastic differential equations, Peking University Press
Probabilistic Methods in Combinatorics
The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008.
[Ha2] R. Hartshorne. Residues and duality. Springer LNM 20, 1966.
[Ke] G. Kempf. Cohomology and convexity. // G.Kempf, F. Knudsen, D. Mumford, B. Saint-Donat. Toroidal Embeddings I. Springer LNM 339, Chap. I, \S 3, 49–52 (1973).
[Ke2] G. Kempf, A. Ramanathan. Multi-cones over Schubert Varieties. // Inv. Math. 87, 353–363 (1987).
[Ko] S. Kov\’acs. A Characterization of Rational Singularities. // Duke Math. J. 102(2), 187–191 (2000).
[V] E. Viehweg. Rational singularities of higher dimensional schemes. // Proc. Am. Math. Soc. 63, 6-8 (1977).
[Ha2] R. Hartshorne. Residues and duality. Springer LNM 20, 1966.
[Ke] G. Kempf. Cohomology and convexity. G.Kempf, F. Knudsen, D. Mumford, B. Saint-Donat. Toroidal Embeddings I. Springer LNM 339, Chap. I, \S 3, 49–52 (1973).
[Ke2] G. Kempf, A. Ramanathan. Multi-cones over Schubert Varieties. Inv. Math. 87, 353–363 (1987).
[Ko] S. Kov\’acs. A Characterization of Rational Singularities. Duke Math. J. 102(2), 187–191 (2000).
[V] E. Viehweg. Rational singularities of higher dimensional schemes. Proc. Am. Math. Soc. 63, 6-8 (1977).
A.T.Fomenko Differential geometry and topology，Consultants Bureau
Dubrovin, Fomenko, Novikov “Modern geometry-methods and applications”Vol 1—3
A Comprehensive Introduction to Differential Geometry vol 1-5 ,by Michael Spivak
Differential Geometry of Curves and Surfaces by Manfredo Do Carmo
M. Postnikov，Linear algebra and differential geometry，Mir Publishers
W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry Academic Press, Inc., Orlando, FL, 1986
Chen Qing and Chia Kuai Peng, Differential Geometry
Eisenhart的”Diffenrential Geometry(?)”
N. Hicks, Notes on differential geometry, Van Nostrand.
Hilbert ,foundations of geometry；
T. Frenkel, Geometry of Physics
Peter Petersen, Riemannian Geometry：
Riemannian Manifolds: An Introduction to Curvature by John M. Lee：
Bott, Raoul, R. Bott, and Loring W. Tu. Differential Forms in Algebraic Topology (Graduate Texts in Mathematics; 82). Reprint edition. New York: Springer-Verlag, June 1, 1995. ISBN: 0387906134.
Buy at Amazon Abraham, Ralph, Jerrold E. Marsden, and Tudor Ratiu. “Manifolds, Tensor Analysis, and Applications.” Applied Mathematical Sciences. Vol. 75. New York: Springer Verlag, May 1, 1998. ISBN: 3540967907.
Buy at Amazon Hirsch, Morris W. “Differential Topology.” Graduate Texts in Mathematics. Vol. 33. Reprint edition. New York: Springer-Verlag, November 1, 1988. ISBN: 0387901485.
3 。 The coordinates of a surface, coordinate curves, smooth surface geometry, the tangent vector, intrinsic coordinates.
4 。 The mapping between the surfaces, coordinate transformations, diffeomorphisms, the concept of local coordinate basis transformation of Jacobian matrix.
5 。 Tangent plane equations, the distance between the cutting plane.
6 。 The arc length of curves, natural parameter.
7 。 The curvature of a curve, close and the osculating circle, gentle curvature of the curve.
2 , Regular curves and Frenet triangle and Frenet flexible curves , with constant curvature of plane curves, plane curves, space curve, the relationship between curvature and torsion.
3 , Frenet equations,Frenet formulas.
9 。 Torsion theorem,Frenet triangle reversed.
Fundamental theorem of the theory of local curve, Minkowski Space, Minkowski Space on the Frenet Equation, the number of closed curves, winding, rotation, four-vertex theorem, convex curve and its classification.
10 。 Calculation formulas of curvature and torsion.
11 。 Surfaces and natural parameter equation of a space curve.
12 。 The first fundamental form of a surface, tangent vector length and angle, surface area of intrinsic coordinates, classification of surfaces of different methods
13 。 The curvature of curves on the surface and curved Green Center,Meusnier theorem.
4 , Special relativity mathematics model and thePoincare Group,Lorenz transformations, surface, surface of the first fundamental form and surface orientation, the induced metric on the surface.
14 。 The center of curvature and the curvature of the surface, the principal curvatures and directions, the second fundamental form of a surface.
5 , Gauss map,Weingarten map, surface, the second and the third fundamental form,
15 。 As the second basic form non-variable curvature and direction, Euler’s formula, Gaussian curvature and its geometrical significance.
Principal curvature, Formula for calculating the principal curvatures and principal directions. Rotating surface,Beltrami-Enneper theorem, ruled.
17 。 Curvilinear coordinates in the Euclidean space of smooth curves and tangent vectors, coordinate transformations, diffeomorphisms, invariance of dimension, the local Jacobian matrix of the coordinate basis transformation.
18 。 Activity coordinates of a surface in Euclidean space, coordinate transformations and local base, invariance of dimension, local continuous equations of the active coordinate system.
19 。 Curvilinear coordinates in the Euclidean metric, arc length, angles between curves, volumes, polar, cylindrical, spherical coordinates mapping.
20 。 Riemannian metrics and examples, arc length, the angle between curves, volumes, isometries, equivalent to the Euclidean metric.
7 , Weierstrass representation,Minkowski space on the surface, hypersurface, spherical measure on.
21 。 Pseudo-Euclidean space of orthogonal complete, orthogonal basis.
22 。 Pseudo-orthogonal basis transform.
23 。 Pseudo orthogonal plane, analytic expression for angle of pseudo orthogonal vectors in the plane.
24 。 Orthogonal groups on the Euclidean space, structure of pseudo orthogonal group.
25 。 Two-dimensional sphere and pseudosphere geometry, the triangle inequality.
26 。 The uniqueness of the sphere and pseudosphere, sphere and pseudosphere under transformation groups.
27 。 As Lobachevsky plane, pseudosphere, Gloria of the Lobachevsky plane models and transformation group, Euclid’s five postulates of independence, Euclid, Riemannian and lobachevskian geometry concepts.
28 。 Measurement on the Lobachevsky plane in polar coordinates with the ball closed curve of length and area.
29 。 Measurement on the Lobachevsky plane projective coordinates with the ball.
30 。 Rotating the coordinates and the principal curvatures of the surface, and rotation on the surface of luobaqiefusijiping curves and curvatures of the surface.
31 。 Conformal Euclidean metric and raster coordinates, the sum of the Interior angles of a triangle on a sphere and luobaqiefusijiping estimated that equivalent measures.
8 , Lobachevsky metric,Lobachevsky geometry of the Poincare metric model and the Klein model of measurement, Minkowskispace curvature of spacelike surfaces, complex transformations, complex analytic functions,Riemann surfaces, Conformal coordinate.
9 , Beltrami equation, spherical measure and Lobachevsky metric, a space of constant curvature, matrix, matrices, the exponential map of the surface in space.
32 。 Derivative of a vector-valued functions, differentiable vector fields on affine space and its basic properties.
10 , Four-element number, the Conformal metric, Conformal transformations,Liouville theorem, differentiability of a vector field, directional derivative and the covariant derivative and the covariant differential and intrinsic differential and its basic properties.
Liaison, Surface intrinsic differential operators on the coordinates, Christoffel Symbols,
35 。 Christoffel symbol symmetry,Christoffel identity.
Gauss Formulas, Weingarten Equation.
11 , Parallel vector fields, the GEODESIC curvature of the curve on a surface, GEODESIC, and
37 。 GEODESIC equations, existence and uniqueness of geodesics and geodesics on the luobaqiefusijiping.
38 。 Through two points of GEODESIC, GEODESIC RADIUS.
39 。 GEODESIC distance, in Compact sets limits on the relationship.
40 。 Half-GEODESIC coordinates on a two-dimensional surface.
41 。 As shortest geodesics on two-dimensional surfaces.
In parallel moves,
42 。 Offset curves parallel moves, the determinant of the derivative of a vector field.
43 。 Offset curves on surfaces, speed and angle of rotation of a vector field.
44 。 Bounded surfaces parallel to the angle between the vectors and moving, rotation of a vector field and measure the sum of the Interior angles of a triangle.
45 。 Bounded surfaces of vector angles and parallel relationship between curvature and movement.
Shortest path theorem, Gaussian curvature invariant Gauss Great theorem, Gauss Equation, Codazzi-Mainardi Curvature tensor, equation, theorem, the local surface theory Gauss Parallel to the curvature, GEODESIC coordinates.
12 , Surface of isomorphism,Maurer-Cartan equations, GEODESIC curvature,Gauss-Bonnet theorem. The Interior angles of a triangle on a sphere and luobaqiefusijiping.
13 , Widespread nature of surfaces,Riemann and pseudo- Riemann space of tensors and fake a one-parameter group of diffeomorphisms, indices of a vector field maps.
47 。 Surface of sphere mapping.
48 。 Complex structures on the surface, spherical complex structures and complex form of Conformal Euclidean metric.
Differential Geometry
1 , B.A.Dubrovin 、 A.T.Fomenko 、 S.P.Novikov Modern geometry.
2 , P.K.Rachevsky , Differential geometry tutorials 13-58 (In addition to 23 、 29 、 30 、 33 、 43 Section) and 86-88Sections.
3 , S.P.Novikov 、 A.T.Fomenko And preliminary differential geometry and topology, the first part.
A? C? Feijinke differential geometry problem set, Beijing Normal University Press
In the differential geometry theory and exercises puxici
A.T.Fomenko Differential geometry and topology ,Consultants Bureau
Dubrovin, Fomenko, Novikov “Modern geometry-methods and applications”Vol 1—3
A Comprehensive Introduction to Differential Geometry vol 1-5 ,by Michael Spivak
Differential Geometry of Curves and Surfaces by Manfredo Do Carmo
M. Postnikov, Linear algebra and differential geometry ,Mir Publishers
W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry Academic Press, Inc., Orlando, FL, 1986
Chen Qing and Chia Kuai Peng, Differential Geometry
Eisenhart “Diffenrential Geometry(?)”
N. Hicks, Notes on differential geometry, Van Nostrand.
Hilbert ,foundations of geometry ;
T. Frenkel, Geometry of Physics
Peter Petersen, Riemannian Geometry :
Riemannian Manifolds: An Introduction to Curvature by John M. Lee :
kobayashi/nomizu, Foundations of Differential Geometry :
Riemannian Geometry I.Chavel :
Darboux “Lecons sur la theorie generale des surfaces” 。
Gauss “Disquisitiones generales circa superficies curvas” 。
P.Dombrowski “150 years after Gauss’ ‘Disquisitiones generales circa superficies curvas’ “
R.Osserman “Lectures of Minimal Surfaces”
J.C.C.Nitsche “Lectures on Minimal Surfaces”(Vol.1)
Shiing-Shen Chern, lectures on differential geometry, North Edition
Chen Weihuan, the differentiable manifold of the preliminary higher education version
Su buqing , Of the differential geometry of the higher education version
Wu Daren ” Differential geometry (?)”, Lectures on differential geometry of the higher education press
Su Jingcun ” The topology of manifolds “. This book was a large , The informative , And there are many authors and , Interesting . There is a book , May not import expert discernment , But I think it is very good,
Bott, Raoul, R. Bott, and Loring W. Tu. Differential Forms in Algebraic Topology (Graduate Texts in Mathematics; 82). Reprint edition. New York: Springer-Verlag, June 1, 1995. ISBN: 0387906134.
Buy at Amazon Abraham, Ralph, Jerrold E. Marsden, and Tudor Ratiu. “Manifolds, Tensor Analysis, and Applications.” Applied Mathematical Sciences. Vol. 75. New York: Springer Verlag, May 1, 1998. ISBN: 3540967907.
Buy at Amazon Hirsch, Morris W. “Differential Topology.” Graduate Texts in Mathematics. Vol. 33. Reprint edition. New York: Springer-Verlag, November 1, 1988. ISBN: 0387901485.
Geometric Analysis
Peter Li
Yau
Differential geometry and topology
4 。 Tangent vector with hypersurface tangent, curvature tensor of differentiable functions.
5 。 Smooth maps on differentiable manifolds.
1 , Vector field, the integral curves of the vector field and his smooth, flow, tubular neighborhood,
8 。 Regular map dirty form inverse mapping of the structure.
9 。 Canonical mapping is a compact inverse mapping of vector bundles on a smooth manifold.
10 。 The commutator of vector fields, and its nature.
11 。 Holomorphic vector bundle its properties.
Fiber bundles and vector bundles, the sphere bundle, topological groups, track space.
2 , Lens spaces, homotopy, homology of map, homotopy, fundamental group, the basic group of operations, path lifting lemma, homotopy lifting lemma, the orbit space of fundamental groups, basic groups of product space.
16 。 Symmetric and skew-symmetric tensor, staggered symmetric operators.
19 。 Basic information of the skew-symmetric tensor space, differential forms the base and coordinate.
20 。 Differential form under the coordinate transformations and coordinate transformations of base maps.
21 。 To the manifold, to books, to differential forms.
22 。 Exterior derivative, exterior differential operation that coordinates.
23 。 Three dimensional space vector field of differential operation.
24 。 De Rham cohomology,de Rham theorem.
25 。 De Rham cohomology of differential forms on a manifold of smooth maps.
26 。 De Rham cohomology of homotopy properties.
27 。 De Rham cohomology of the homotopy invariance ofPoincare theorem.
6 , Riemann metric,Riemann manifolds, and Riemann metric of a smooth manifold. Riemann product manifold,Riemann manifolds, andRiemann immersion, complex projective space, homogeneous Riemann space, Steenrod Theorem, contact, Levi-CivitaLiaison, Riemann Submanifolds in contact.
28 。 Manifold and the integration of differential forms on a manifold.
29 。 Riemann integral of a function on a manifold and its comparison with the differential form of integral, and three dimensional space curved surface and curve integral of a vector field on.
30 。 Stokes formula, special forms and results (three dimensional space of vector fields and thede Rham cohomology).
31 。 Euclid space derivative of a vector field, and its basic properties.
32 。 Affine contact absolute derivative of a vector field, coordinate,Christoffel symbols, equivalent contact contact the affine equivalence.
33 。 Symmetric affine connection.
34 。 Vector differential and moving parallel to the vertical curve, tangent space transformation properties of differential operators on a vector field.
35 。 Curve moves along the vectors with arbitrary tensors, tensor products and curl.
36 。 Tensor’s covariant derivative.
37 。 Number of vector and tensor coordinates of differential forms, parallel condition, the gradient of a tensor, vector field of fork.
38 。 Riemann coordination condition of the affine connection on a manifold.
39 。 Riemann affine connection on a manifold and uniqueness of the Levi-Civita theorem.
40 。 Euclidean space, pseudo-Euclidean space and Riemann manifold of submanifolds of covariant derivative and affine connection.
41 。 And its equation of GEODESIC, GEODESIC equations of existence, specify the direction of a point on the existence and uniqueness of geodesics.
42 。 Riemann curvature of manifolds andRiemann manifold of the GEODESIC curvature of the curve on the manifold, ball and Lobachevsky plane of curvature.
7 , Covariant derivative along a curve, parallel move, GEODESIC, GEODESIC local existence and uniqueness, exponential map,Gauss ‘s lemma, complete Riemann manifolds and theHopf-Rinow theorem.
43 。 Elementary calculus: extreme value of Lagrange and Euler equations.
44 。 As action and extreme value for the functional length of the GEODESIC.
45 。 GEODESIC nature of the neighborhood, and extensibility, GEODESIC completeness of geodesics on a manifold of infinite extension.
46 。 Connectivity on a closed set and geodesics, normal coordinates, measuring the Earth’s surface, measuring the radius of the Earth’s surface, their orthogonality and Geodesy extrema.
47 。 Riemann curvature tensor of the manifold.
48 。 Properties of curvature and its coordinates.
49 。 Riemann metric symbols.
50 。 Two-dimensional Riemann curvature of the manifold, as a locally Euclidean space of zero curvature.
51 。 Sectional curvature, as measured the total curvature of a surface.
53 。 Two-dimensional Riemann manifolds the rotation tensor field along the closed road.
54 。 Around the closed curve on a two-dimensional manifold a vector measure the sum of the Interior angles of a triangle.
55 。 Geometric mean curvature tensor (a closed curve surrounding the relationship between the vector and bivector).
56 。 Two-dimensional geometric curvature of the manifold along a given direction.
8 , Cut locus, the second covariant derivative, the curvature tensor algebra properties, calculation of curvature,Ricci curvature, the scalar curvature, the second variation of the first variational forms, forms,Jacobifield, level.
9 , O ‘ Neill formula, formal homogeneity metric,Gauss ‘s lemma, conjugate, with constant sectional curvature of space and theMyers theorem,Hadamard theorem, a differentiable manifold on the measurable sets, Volume estimates, exponential growth of finite groups, andMilnor-Wolf theorem.
10 , Fundamental groups of compact manifolds of negative curvature growth, andMilnor theorem,Gauss-Bonnetformula,Gromov theorem, theCheeger theorem, Conformally flat manifolds, the second Bianchi identity, simple
3 , P.K.Rachevsky , Riemannian Geometry, and tensor analysis, technology and literature Publishing House, 1953 。
4 , A.S.Mishchenko 、 A.T.Fomenko , Course in differential geometry and topology, faketeliya Publishing House, 2000 。
5 , S.P.Novikov 、 I.A.Taimanov Modern geometry and field theory, independent of Moscow University Press, 2004 。
6 , J.Milnor , Morse Theory of Moscow book publishers in the world, 1985 。
Chen Weihuan, an introduction to Riemannian Geometry (upper and lower), Peking University
Wu Hongxi, of the initial Riemannian Geometry, North Edition
Application of geometric problems
1 。 Configuration space, examples of non-trivial structure space, planar pendulum with three-dimensional, and secondary compound pendulum movement of the rigid body around a fixed point.
2 。 Phase space, for example.
3 。 Manifold.
4 。 Variational problems, Euler’s equation.
5 。 Symplectic manifolds and symplectic space is defined.
6 。 The symplectic form on the symplectic space and its nature.
7 。 Hamilton functionHamilton equations.
8 。 Oblique derivative function,Poisson brackets.
9 。 Score for the first time.
10 。 Vector fields and their distribution.
11 。 Frobenius theorem of complex forms.
12 。 Symplectic form into standard form,Darboux theorem.
13 。 Exchange and the Diffeomorphism Group of a vector field.
14 。 Symplectic manifolds on the Diffeomorphism Group of finite algebras.
15 。 And symmetric integrals for the first time the Netter theorem.
16 。 Completely integrable Hamilton System Liouville theorem.
2 , R.Thom And some general properties of differentiable manifolds, loading ” Fiber spaces and its applications ” A book, Moscow, foreign languages Publishing House, 1958 。
3 , V.V.Trofimov 、 A.T.Fomenko , Differential equation of integrable Hamiltonian of algebra and geometry, faketeliya Publishing House, 1995 。
4 , V.I.Arnold 、 V.V.Kozlov 、 A.I.Neyshtadt , Mathematical topics in classical mechanics and celestial mechanics, science and technology information Research Institute of the Soviet Union, 1985 。
5 , A.S.Mishchenko Fiber bundle and its application, science press, 1984 。
Curves and Parametrization, Regular Surfaces; Inverse Images of Regular Values. Gauss Map and Fundamental Properties; Isometries; Conformal Maps; Rigidity of the Sphere.
Topological space
Space, maps, compactness and connectedness, quotients; Paths and Homotopy. The Fundamental Group of the Circle. Induced Homomorphisms. Free Products of Groups. The van Kampen Theorem. Covering Spaces and Lifting Properties; Simplex and complexes. Triangulations. Surfaces and its classification.
Differential Manifolds
Differentiable Manifolds and Submanifolds, Differentiable Functions and Mappings; The Tangent Space, Vector Field and Covector Fields. Tensors and Tensor Fields and differential forms. The Riemannian Metrics as examples, Orientation and Volume Element; Exterior Differentiation and Frobenius’s Theorem; Integration on manifolds, Manifolds with Boundary and Stokes’ Theorem.
Homology and cohomology
Simplicial and Singular Homology. Homotopy Invariance. Exact Sequences and Excision. Degree. Cellular Homology. Mayer-Vietoris Sequences. Homology with Coefficients. The Universal Coefficient Theorem. Cohomology of Spaces. The Cohomology Ring. A Kunneth Formula. Spaces with Polynomial Cohomology. Orientations and Homology. Cup Product and Duality.
Riemannian Manifolds
Differentiation and connection, Constant Vector Fields and Parallel Displacement
Riemann Curvatures and the Equations of Structure Manifolds of Constant Curvature,
Spaces of Positive Curvature, Spaces of Zero Curvature, Spaces of Constant Negative Curvature
References:
M. do Carmo , Differentia geometry of curves and surfaces.
Prentice- Hall, 1976 (25th printing)
Chen Qing and Chia Kuai Peng, Differential Geometry
M. Armstrong, Basic Topology Undergraduate texts in mathematics
W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry Academic Press, Inc., Orlando, FL, 1986
M. Spivak, A comprehensive introduction to differential geometry
N. Hicks, Notes on differential geometry, Van Nostrand.
Curves and Parametriz ation , Regular Surfaces; Inverse Images of Regular Values. Gauss Map and Fundamental Properties;Isometries; Conformal Maps; Rigidity of the Sphere.
Topological space
Space, maps, compactness and connectedness, quotients; Paths and Homotopy. The Fundamental Group of the Circle. Induced Homomorphisms. Free Products of Groups. The van Kampen Theorem. Covering Spaces and Lifting Properties; Simplex and complexes. Triangulations. Surfaces and its classification.
Differential Manifolds
Differentiable Manifolds and Submanifolds, Differentiable Functions and Mappings; The Tangent Space, Vector Field and Covector Fields. Tensors and Tensor Fields and differential forms. The Riemannian Metrics as examples, Orientation and Volume Element; Exterior Differentiation and Frobenius’s Theorem; Integration on manifolds, Manifolds with Boundary and Stokes’ Theorem.
Homology and cohomology
Simplicial and Singular Homology. Homotopy Invariance. Exact Sequences and Excision. Degree. Cellular Homology. Mayer-Vietoris Sequences. Homology with Coefficients. The Universal Coefficient Theorem. Cohomology of Spaces. The Cohomology Ring. A Kunneth Formula. Spaces with Polynomial Cohomology. Orientations and Homology. Cup Product and Duality.
Riemannian Manifolds
Differentiation and connection , Constant Vector Fields and Parallel Displacement
Riemann Curvature s and the Equations of Structure Manifolds of Constant Curvature,
Spaces of Positive Curvature, Spaces of Zero Curvature, Spaces of Constant Negative Curvature
References:
1.M. do Carmo , Differentia geometry of curves and surfaces.
2.Prentice- Hall, 1976 (25th printing)
3.Chen Qing and Chia Kuai Peng, Differential Geometry
4.M. Armstrong, Basic Topology Undergraduate texts in mathematics
5.W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry Academic Press, Inc., Orlando, FL, 1986
6.M. Spivak, A comprehensive introduction to differential geometry
7.N. Hicks, Notes on differential geometry, Van Nostrand.
I.M.Singer, J.A.Thorp “Lecture notes on elementary topology and geometry
Greenberg “Lectures on Algebraic Topology”
Glen Bredon ‘s ” Topology and Geometry”(GMT139) is praised as the successor of Spanier’s great book.
Introduction to Topological Manifolds by John M. Lee :
From calculus to cohomology by Madsen :
Fomenko,Differential geometry and topology
Aleksandrov’s ” Combinatorial Topology ” is very good for beginner.
J. Milnor, Morse Theory
J. Milnor, Topology from the differentiable viewpoint
You Chengye, lectures on the basic topology, Peking University
Xiong Jincheng, lectures on the point set topology, higher education
Zhang Zhu, the new talk of differential topology, Peking University
Li Yuanxi , Zhang Guoli ( Wood ) ” Topology”
Kodama macro theory of topological space science press
Chen Zhaojiang of the point set topology , Solution to the point set topology and anti-Nanjing University Press
3，N.Bourbaki, Groupes et Algèbres de Lie，Chapitres 4-6，Hermann，1968。
Elliptic Curve
X Washington, Lawrence C. Elliptic Curves: Number Theory and Cryptography. Chapman & Hall / CRC, 2008. ISBN: 9781420071467. (This resource may not render correctly in a screen reader.errata (PDF)) [Preview with Google Books]
Buy at Amazon Milne, J. S. Elliptic Curves. BookSurge Publishing, 2006. ISBN: 9781419652578. (This book is also available online at the author’s website, along with This resource may not render correctly in a screen reader.addendum / erratum (PDF).)
Buy at Amazon Silverman, Joseph H. The Arithmetic of Elliptic Curves. Springer-Verlag, 2009. ISBN: 9780387094939. (This resource may not render correctly in a screen reader.errata (PDF)) [Preview with Google Books]
Buy at Amazon ———. Advanced Topics in the Arithmetic of Elliptic Curves. Springer-Verlag, 1994. ISBN: 9780387943251. (This resource may not render correctly in a screen reader.errata (PDF))
Buy at Amazon Cox, David A. Primes of the Form X2 + Ny2: Fermat, Class Field Theory, and Complex Multiplication. Wiley-Interscience, 1989. ISBN: 9780471506546.
The following two books give quite accessible introductions to elliptic curves from very different perspectives. You may find them useful as supplemental reading, but we will not use them in the course.
Buy at Amazon Blake, Ian F., G. Seroussi, and Nigel P. Smart. Elliptic Curves in Cryptography. Cambridge University Press, 1999. ISBN: 9780521653749. [Preview with Google Books]
Buy at Amazon Silverman, Joseph H., and John Torrence Tate. Rational Points on Elliptic Curves. Springer-Verlag, 1994. ISBN: 9780387978253. [Preview with Google Books]
The following references provide introductions to algebraic number theory, which is not part of this course per se, but may be useful background for those who are interested.
Algebraic Number Theory Course Notes by J. S. Milne.
Buy at Amazon Stewart, Ian, and David Orme Tall. Algebraic Number Theory and Fermat’s Last Theorem. A. K. Peters / CRC Press, 2001. ISBN: 9781568811192.
The book by Stewart and Tall also includes some introductory material on elliptic curves and the proof of Fermat’s last theorem, which are topics we will cover, but in greater depth.
3 , V.A.Ufnarovskii , Algebra -6 ( ” Modern mathematics and its application ” Series 57 Volumes), all-Russian Institute of scientific and technical information.
11 , Central simple algebra, with the exception of algebra.
12 , Hilbert A zero-point theorem, theorem of Zeng Jiong.
Algebraic groups and invariant theory
1 。 Algebraic group concept algebra homomorphism of groups.
2 。 Lie algebra.
3 。 Algebraic groups, track of partial closure, algebra of regular functions.
4 。 Imitation of Ray’s role in affine algebraic groups and clusters.
5 。 Homogeneous spaces,Chevalley theorem.
6 。 Jordan decomposition of algebraic torus,Engel theorem of unipotent group.
7 。 Commutators of algebraic groups, solvable groups, fixed point of Borel theorem,Lie-Kolchina theorem.
8 。 Reductive group, fully yuezi group.
9 。 Invariant Hilbert theorem of affine clusters under reductive group functor categories, factorization theorem for morphisms.
10 。 Invariants of finite groups,Chevalley theorem.
11 。 Rational invariant. Invariants of orbital separation of Rozenlikhta theorem.
12 。 Closed orbits, Matsumura criterion between China and Britain, stability,Popov criterion index branch of a family of sufficient conditions of stability.
13 。 Nilpotent orbits,Hilbert-Mumford criterion.
14 。 Reductive group connect ideals, his track and is not variable.
15 。 Tensor invariant quantum systems of classical theory.
16 。 Under the projective semi-stability and stability,Mumford functor.
1 , E.M.Andreev 、 E.B.Vinberg 、 A.G.Elashvili Maximum linear semisimple Lie Group tracks ” Functional analysis and its applications ” Magazine, 1967 , Vol.1 , No.4 , pp.3-7 。
2 。 E. b. Vinberg, anda. l. Onishchik, lie groups and algebraic groups, science press,1988.
3 。 E. B. Vinberg, andv. L. Popov, invariant theory (mathematics and its applications series 55 volumes), all-Russian Institute of scientific and technical information.
5 。 H.Kraft,Geometrische Methoden in der Invariantentheorie,Vieweg-Verlag,1985。
6 。 V. Popov, about clusters of semisimple groups under the stability criterion,” the National Academy of Sciences of the Soviet Union – mathematics “,1970, Vol.34, No.3 , pp.523-531 。
1 。 Reflection, roots, and root, in combination with the roots, single reflection builds.
2 。 The length function, reduced conditions and Exchange conditions and a maximum length.
3 。 Reflection groups of generators and relations.
4 。 Parabolic subgroups and the related class minimum.
5 。 Poincare polynomials, inducing formulas.
6 。 Weyl conjugate base domain.
7 。 Parabolic subgroup,$ w $ reflexes.
8 。 Coxeter complex irreducible components.
9 。 Combination of quadratic, non-negative definite and Coxeter graph classification.
10 。 SubgraphPerron-Frobenius theorem.
11 。 Crystal root and the Weyl Group,Dynkin diagrams, root, root on the right.
12 。 Root structure, the calculation of the order of the reflection group, exception of Weyl groups,$H_3$ and $H_4$ groups.
13 。 $ R ^ n $ real division of the polyhedron,Shlefli-Coxeter symbols and charts.
14 。 Polynomial of finite groups is not edge,Hilbert theorem andNoether theorem.
15 。 Chevalley theorem, the fundamental invariants.
16 。 $W$ number of group and its uniqueness.
17 。 Free mode and common mode.
18 。 And the product of the number of theorems.
19 。 Algebraic independence of Jacobi criterion.
20 。 Pseudo reflection, complex pseudo reflection group, the free algebra of invariants of the Shepard-Todd theorem.
21 。 With polynomials.
22 。 Coxeter element,Coxeter number.
23 。 $ W $ group component and number of compute clusters $ E_i, \i = 6, 7, 8 $ times.
1 , J.Humphreys , Reflection Groups and Coxeter Groups , Cambridge University Press , 1990 。
2 , E.B.Vinberg 、 O.B.Schwartzman , A space of constant curvature motion of a discrete group (books of modern mathematics and its application 29 Volume, P147-264 ), All-Russian scientific and technical information publishing house.
3 , E.B.Vinberg 、 A.L.Onishchik , Lie groups and algebraic groups, science press, 1988 。
4 , N.Bourbaki, Groupes et Alg è bres de Lie , Chapitres 4-6 , Hermann , 1968 。
Affine Weyl Group and Coxeter Group
1 。 Affine reflections, the affine Weyl Group of $W_a$. (Using roots of crystal structures)
2 。 Alcoves, single, count hyperplaneAlcoves of single pass in Exchange for.
3 。 Coxeter graph and expand the Dynkin diagram.
4 。 The base field,$ w $ first-order formula.
5 。 The affine Weyl Group of affine axiom of reflection generated by a set of discrete groups of definitions.
6 。 Coxeter and Coxeter groups, example: reflection group, an affine Weyl Group, General Coxeter Group,$ PGL_2 (Z) $ The group, the length function.
7 。 Coxeter Group of geometric representations, positive and complex roots.
8 。 Parabolic subgroup, length functions of geometric interpretation and reflection, strong Exchange.
9 。 Bruhat order,Bruhat order expression group,Bruhat order interval.
10 。 Poincare series and formula.
11 。 Foundations and geometric representation of a quadratic invariant subspace of finite Coxeter groups.
12 。 Crystal Coxeter Group.
13 。 Third-order Coxeter Group.
14 。 Hyperbolic Coxeter groups.
1 , J.Humphreys , Reflection Groups and Coxeter Groups , Cambridge University Press , 1990 。
2 , E.B.Vinberg 、 O.B.Schwartzman , A space of constant curvature motion of a discrete group (books of modern mathematics and its application 29 Volume, P147-264 ), The all-Russian Institute of scientific and technical information.
3 , N.Bourbaki, Groupes et Alg è bres de Lie , Chapitres 4-6 , Hermann , 1968 。
Elliptic Curve
X Washington, Lawrence C. Elliptic Curves: Number Theory and Cryptography. Chapman & Hall / CRC, 2008. ISBN: 9781420071467. (This resource may not render correctly in a screen reader.errata (PDF)) [Preview with Google Books]
Buy at Amazon Milne, J. S. Elliptic Curves. BookSurge Publishing, 2006. ISBN: 9781419652578. (This book is also available online at the author’s website, along with This resource may not render correctly in a screen reader.addendum / erratum (PDF).)
Buy at Amazon Silverman, Joseph H. The Arithmetic of Elliptic Curves. Springer-Verlag, 2009. ISBN: 9780387094939. (This resource may not render correctly in a screen reader.errata (PDF)) [Preview with Google Books]
Buy at Amazon ———. Advanced Topics in the Arithmetic of Elliptic Curves. Springer-Verlag, 1994. ISBN: 9780387943251. (This resource may not render correctly in a screen reader.errata (PDF))
Buy at Amazon Cox, David A. Primes of the Form X2 + Ny2: Fermat, Class Field Theory, and Complex Multiplication. Wiley-Interscience, 1989. ISBN: 9780471506546.
The following two books give quite accessible introductions to elliptic curves from very different perspectives. You may find them useful as supplemental reading, but we will not use them in the course.
Buy at Amazon Blake, Ian F., G. Seroussi, and Nigel P. Smart. Elliptic Curves in Cryptography. Cambridge University Press, 1999. ISBN: 9780521653749. [Preview with Google Books]
Buy at Amazon Silverman, Joseph H., and John Torrence Tate. Rational Points on Elliptic Curves. Springer-Verlag, 1994. ISBN: 9780387978253. [Preview with Google Books]
The following references provide introductions to algebraic number theory, which is not part of this course per se, but may be useful background for those who are interested.
Algebraic Number Theory Course Notes by J. S. Milne.
Buy at Amazon Stewart, Ian, and David Orme Tall. Algebraic Number Theory and Fermat’s Last Theorem. A. K. Peters / CRC Press, 2001. ISBN: 9781568811192.
The book by Stewart and Tall also includes some introductory material on elliptic curves and the proof of Fermat’s last theorem, which are topics we will cover, but in greater depth.
Serendipities 