南京大学：《计算机问题求解》课程教学资源（课件讲稿）集合论 II 关系 Relation（简版）

南京大学：《计算机问题求解》课程教学资源（课件讲稿）集合论 II 关系 Relation

南京大学：《计算机问题求解》课程教学资源（课件讲稿）集合论 I 公理与操作（简版）

南京大学：《计算机问题求解》课程教学资源（课件讲稿）集合论 I 公理与操作

The first three chapters cover the standard material on sets, relations, and functions and algorithms. Next come chapters on logic, counting, and probability. We then have three chapters on graph theory: graphs, directed graphs, and binary trees. Finally there are individual chapters on properties of the integers, languages, machines, ordered sets and lattices, and Boolean algebra, and appendices on vectors and matrices, and algebraic systems. The chapter on functions and algorithms includes a discussion of cardinality and countable sets, and complexity. The chapters on graph theory include discussions on planarity, traversability, minimal paths, and Warshall’s and Huffman’s algorithms. We emphasize that the chapters have been written so that the order can be changed without difficulty and without loss of continuity

1 Fundamentals 2 Collections 3 Counting and Relations 4 More Proof 5 Functions 6 Probability 7 Number Theory 8 Algebra 9 Graphs 10 Partially Ordered Sets

1 The How, When, and Why of Mathematics Spotlight: George Polya Tips on Doing Homework 2 Logically Speaking 3 Introducing the Contrapositive and Converse 4 Set Notation and Quantifiers Tips on Quantification 5 Proof Techniques Tips on Definitions …… 10 Relations Tips on Reading Mathematics 11 Partitions Tips on Putting It All Together 12 Order in the Reals 13 Consequences of the Completeness of R Tips: You Solved ItNow What? 14 Functions, Domain, and Range Spotlight: The Definition of Function 15 Functions, One-to-One, and Onto 16 Inverses 17 Images and Inverse Images Spotlight: Minimum or Infimum? 18 Mathematical Induction 19 Sequences 20 Convergence of Sequences of Real Numbers 21 Equivalent Sets 22 Finite Sets and an Infinite Set 23 Countable and Uncountable Sets 24 The Cantor–Schroder–Bernstein Theorem Spotlight: The Continuum Hypothesis ……

《计算机问题求解》课程教学资源（参考教材）Computer Algorithms - Introduction to Design and Analysis

《计算机问题求解》课程教学资源（阅读材料）Computational Thinking：What and Why?

Part I. Preliminaries Part II. Methods and Analysis Part III. Limitations and Robustness Part IV. Relaxing the Rules Part V. The Bigger Picture