Discrete Mathematics

耿素云，离散数学，高教版
Discrete Mathematics and its Applications Kenneth H. Rosen

213《基础集合论》北师大

214《面向计算机科学的数理逻辑》陆钟万

215《图论及其算法》王树禾

216《图论及其应用》Bondy ，Murty

217《离散数学》耿素云，屈婉玲

218《具体数学》格拉厄姆，高德纳等

219《Introduction to Algorithms》 Corman

Algebraic Combinatorics & its Analysis

I.Tomescu “组合学引论” , “Problem in graph theory and combinatorics(???)” 

Lovasz “Problems in Combinatorics(?)” 

I. Anderson”Combinatorics of Finite Sets” 

Bollobas”Combinatorics” 

Ryser(赖瑟)”组合数学” 

I. Anderson “A First Course in COmbinatorial Mathematics” 

C.Berger “组合学原理”(上海科技) 

Lovasz,et al.(ed.) “Handbook of Combinatorics” 

李乔”组合数学基础” 

魏万迪 “组合论” 

C.L.Liu(刘炯朗,现新竹清华大学校长) 

220《近代组合学》王天明编著

221《组合学笔记》康庆德著

Recursion Theory & Undecidability & Model

X

Automata & Computation & Complexity Theory

Moore, Cristopher, and Stephan Mertens. The Nature of Computation. Oxford University Press, 2011. ISBN: 9780199233212.

Sipser, Michael. Introduction to the Theory of Computation. Course Technology, 2005. ISBN: 9780534950972. Covers most material from the first half of the course.

Arora, Sanjeev, and Boaz Barak. Computational Complexity: A Modern Approach. Cambridge University Press, 2009. ISBN: 9780521424264. Covers most material from the second half (as well as more advanced material that won’t be covered in this course).

Graph Theory

Graph theory and Discrete Mathematics

Hamiltonian, coloring, network flow, network algorithm, connectivity, spanning tree, connectivity testing, bipartite graphs, trees, breadth/depth first search.

Computational Number Theory

Primality, integer factorization; greatest common divisor; Chinese Remainder Theorem; modular arithmetic.

Computational geometry and discrete geometry

Convex hull, Delaunay triangulation, Voronoi diagram, arrangement, discrete curvature, discrete Ricci flow.

References:

1. A. Bondy and U. S. R. Murty: “Graph theory”, GTM, Springer, 1976.
2. T. H. Cormen, C. E. Leiserson, R. L. Rivest, & C. Stein, “Introduction to Algorithms”, MIT Press, 2009.
3. S. L. Devaloss and Joseph O’Rourke, “Discrete and Computational Geometry”, Princeton University Press, 2011.
4. Mark De Berg, “Computational Geometry: Algorithms and Applications”, Springer, 2008.
5. Xianfeng Gu and S. T. Yau, “Computational conformal geometry”, International Press, 2003.

Bondy,Murty “Graph Theoryand Applications(?)” “图论及其应用”习题解答, “图论和电路网络”

Harary(哈拉里) “Graph Theory”(图论) 

B. Bollobas “Graph Theory”(GTM 63) 

G.Chartrand,L. Lesniak”Graph and Digraphs” 

C. Berger”Graph and Hypergraph” 

Reinhard Diestel “Graph Theory”(GTM173) 

世界图书引进有GTM系列的”Modern Graph Theory”。此书确实经典！

《图论及其算法》王树禾

Appel ,Haken “Every Planar Map is Four Colorable” 

Steen(ed.) “mathematics today” 

Discrete Mathematics

Geng Suyun, discrete mathematics, and higher education
Discrete Mathematics and its Applications Kenneth H. Rosen

213 The basic set theory, Beijing Normal University

214 The Lu Zhongwan of mathematical logic in computer science

215 Wang Shuhe the graph theory and algorithms

216 Of the graph theory and its applications Bondy , Murty

217 The discrete mathematics Geng Suyun, Qu Wanling

218 The specific mathematical Graham, Knuth

219 《 Introduction to Algorithms 》 Corman

Algebraic Combinatorics & its Analysis

I.Tomescu ” An introduction to Combinatorics ” , “Problem in graph theory and combinatorics(???)”

Lovasz “Problems in Combinatorics(?)”

I. Anderson”Combinatorics of Finite Sets”

Bollobas”Combinatorics”

Ryser ( Reiso )” Combinatorial mathematics”

I. Anderson “A First Course in COmbinatorial Mathematics”

C.Berger ” Principle of combination “( The Shanghai Science and technology)

Lovasz,et al.(ed.) “Handbook of Combinatorics”

Li ” Combinatorial mathematics Foundation”

Wei Wandi ” Combinatorial theory”

C. L. Liu ( Liu Chung-lang , President of National Tsing Hua University)

220 Written by Wang tianming of the modern Combinatorics

221 Kang qng-de of the Combinatorics notebook with

Recursion Theory & Undecidability & Model

X

Automata & Computation & Complexity Theory

Moore, Cristopher, and Stephan Mertens. The Nature of Computation. Oxford University Press, 2011. ISBN: 9780199233212.

Sipser, Michael. Introduction to the Theory of Computation. Course Technology, 2005. ISBN: 9780534950972. Covers most material from the first half of the course.

Arora, Sanjeev, and Boaz Barak. Computational Complexity: A Modern Approach. Cambridge University Press, 2009. ISBN: 9780521424264. Covers most material from the second half (as well as more advanced material that won’t be covered in this course).

Graph Theory

Graph theory and Discrete Mathematics

Hamiltonian, coloring, network flow, network algorithm, connectivity, spanning tree, connectivity testing, bipartite graphs, trees, breadth/depth first search.

Computational Number Theory

Primality, integer factorization; greatest common divisor; Chinese Remainder Theorem; modular arithmetic.

Computational geometry and discrete geometry

Convex hull, Delaunay triangulation, Voronoi diagram, arrangement, discrete curvature, discrete Ricci flow.

References:

1. A. Bondy and U. S. R. Murty: “Graph theory“, GTM, Springer, 1976.

2. T. H. Cormen, C. E. Leiserson, R. L. Rivest, & C. Stein, “Introduction to Algorithms“, MIT Press, 2009.

3. S. L. Devaloss and Joseph O’Rourke, “Discrete and Computational Geometry“, Princeton University Press, 2011.

4. Mark De Berg, ” Computational Geometry: Algorithms and Applications “, Springer, 2008.

5. Xianfeng Gu and S. T. Yau, ” Computational conformal geometry “, International Press, 2003.

Bondy,Murty “Graph Theoryand Applications(?)” ” Graph theory and its applications ” Questions and problems , “Graph theory and network”

Harary ( Harare ) “Graph Theory” ( graph theory)

B. Bollobas “Graph Theory”(GTM 63)

G.Chartrand,L. Lesniak”Graph and Digraphs”

C. Berger”Graph and Hypergraph”

Reinhard Diestel “Graph Theory”(GTM173)

World Book introduction GTM Series “Modern Graph Theory” 。 This book does a classic!

The graph theory and algorithms of Wang Shuhe

Appel ,Haken “Every Planar Map is Four Colorable”

Steen(ed.) “mathematics today”