離散數學
Discrete Mathematics
| 節 | 週二 | 週五 |
|---|---|---|
3 10:10–11:00 | 離散數學 EC022（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 離散數學 EC022（光復） |
* 根據陽明交大上課時間表所列
1. To demonstrate to students how mathematics can be applied to solve nontrivial real-life problems 2. To gain more experience with mathematical thinking, arguments and proof techniques, which are essential in reasoning about computation 3. To learn about a number of different discrete structures (e.g., sets, relations, graphs, trees, etc.) that provide the mathematical formalizations for many computational problems 4. To hope that students will not only learn some powerful mathematical tools but also develop their ability to perceive, to formulate, and to solve mathematical problems 5. To provide a gateway to more advanced courses in any computer science courses, including data structures, algorithm, database automata theory, computer security, etc.
basic high school mathematics
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Midterm 35% Final 35% Homework 30%
Chap1: Logic and Proofs Proposition
Proposition Logic Proposition Equivalences Predicates and Quantifiers Nested Quantifiers Rules of Inference Introduction to Proofs Proof Methods and Strategy
- 講授：
- 11
Chap 2: Sets, Functions, Sequences, and Sums
Sets Set Operations Functions Sequences and Summations
- 講授：
- 7
Chap 3: Algorithms
Algorithms Growth of Functions Complexity of Algorithms
- 講授：
- 6
Chap.4 Number Theory and Cryptography
Divisibility and Modular Arithmetic Integer Representations and Algorithms Primes and Greatest Common Divisors Solving Congruences Applications of Congruences Cryptography
- 講授：
- 6
Chap 5: Induction and Recursion
Mathematical Induction Strong Induction and Well- Ordering Recursive Definitions and Structural Induction Recursive Algorithms
- 講授：
- 4
Chap 6: Counting
The Basics of Counting The Pigeonhole Principle Permutations and Combinations Binomial Coefficients Generalized Permutations and Combinations Generating Permutations and Combinations
- 講授：
- 4
Chap 9: Relations
Relations and Their Properties n-ary Relations and Their Applications Representing Relations Closures of Relations Equivalence Relations Partial Orderings
- 講授：
- 4
Chap 10: Graphs
Graphs and Graph Models Graph Terminology and Special Types of Graphs Representing Graphs and Graph Isomorphism Connectivity Euler and Hamilton Paths Shortest-Path Problems
- 講授：
- 6
| 週次 | 主題 |
|---|---|
| 第 1 週 | Proposition Logic Proposition Equivalences |
| 第 2 週 | Predicates and Quantifiers Nested Quantifiers |
| 第 3 週 | Rules of Inference |
| 第 4 週 | Introduction to Proofs Proof Methods and Strategy Sets Set Operations |
| 第 5 週 | Functions Sequences and Summations |
| 第 6 週 | Cardinality of Sets |
| 第 7 週 | Algorithms Growth of Functions |
| 第 8 週 | Complexity of Algorithms |
| 第 9 週 | Midterm Exam |
| 第 10 週 | Divisibility and Modular Arithmetic Integer Representations and Algorithms Primes and Greatest Common Divisors |
| 第 11 週 | Solving Congruences Applications of Congruences Cryptography |
| 第 12 週 | Mathematical Induction Strong Induction and Well- Ordering Recursive Definitions and Structural Induction |
| 第 13 週 | Recursive Algorithms The Basics of Counting The Pigeonhole Principle |
| 第 14 週 | Permutations and Combinations Binomial Coefficients Generalized Permutations and Combinations |
| 第 15 週 | Generating Permutations and Combinations Relations and Their Properties n-ary Relations and Their Applications Representing Relations |
| 第 16 週 | Closures of Relations Equivalence Relations Partial Orderings Graphs and Graph Models Graph Terminology and Special Types of Graphs |
| 第 17 週 | Representing Graphs and Graph Isomorphism Connectivity Euler and Hamilton Paths Shortest-Path Problems |
| 第 18 週 | Final Exam |
Kenneth H. Rosen, Discrete Mathematics and Its Applications, 8th ed., McGraw-Hill Inc.
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