Discrete Mathematics for Computer Science, Some Notes

These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural deduction system ``a la Prawitz''. The rest of the material is more or less traditional but I emphasize partial functions more than usual (after all, programs may not terminate for all input) and I provide a fairly complete account of the basic concepts of graph theory.

[1]  R. Stanley What Is Enumerative Combinatorics , 1986 .

[2]  Jonathan L. Gross,et al.  Topological Graph Theory , 1987, Handbook of Graph Theory.

[3]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[4]  P. Cameron Combinatorics: Topics, Techniques, Algorithms , 1995 .

[5]  D. Prawitz Ideas and Results in Proof Theory , 1971 .

[6]  H. Enderton Elements of Set Theory , 1977 .

[7]  Gerhard Gentzen,et al.  Investigations into Logical Deduction , 1970 .

[8]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[9]  Jean Gallier,et al.  Constructive Logics Part I: A Tutorial on Proof Systems and Typed gamma-Calculi , 1993, Theor. Comput. Sci..

[10]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[11]  Jean Gallier,et al.  Geometric Methods and Applications: For Computer Science and Engineering , 2000 .

[12]  Frank Harary,et al.  Graph Theory , 2016 .

[13]  Peter B. Andrews An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[14]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[15]  Jean H. Gallier,et al.  What's So Special About Kruskal's Theorem and the Ordinal Gamma0? A Survey of Some Results in Proof Theory , 1991, Ann. Pure Appl. Log..

[16]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[17]  Éva Tardos,et al.  Algorithm design , 2005 .

[18]  D. Prawitz Natural Deduction: A Proof-Theoretical Study , 1965 .

[19]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[20]  Patrick Suppes,et al.  Axiomatic set theory , 1969 .