離散數學(英文授課)
Discrete Mathematics
| 節 | 週二 | 週五 |
|---|---|---|
3 10:10–11:00 | 離散數學(英文授課) EC016（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 離散數學(英文授課) EC016（光復） |
* 根據陽明交大上課時間表所列
1. Students are expected to use mathematical reasoning to comprehend mathematical arguments and learn basic concepts of mathematical logic and proof 2. Students will learn to use counting to perform combinatorial analysis 3. Students will learn basic concepts of sets, permutations, relations, graphs, and tree discrete structures
basic high school mathematics
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https://people.cs.nctu.edu.tw/~ttyeh/course/2021_Spring/DCP1244/outline.html
Coursework assignment: 8 homework Exam: 8 Quizzes Evaluation: (tentative) There will be 8 quizzes (70%) and 8 homework (30%)
Chap1: Logic and Proofs
Proposition Logic Proposition Equivalences Predicates and Quantifiers Nested Quantifiers Rules of Inference Introduction to Proofs Proof Methods and Strategy
Chap 2: Sets, Functions, Sequences, and Sums
Sets Set Operations Functions Sequences and Summations
Chap 3,4: Algorithms and the Integers
The Integers and Division Primes and Greatest Common Divisors Integers and Algorithms Applications of Number Theory
Chap 5: Induction and Recursion
Mathematical Induction Strong Induction and Well-Ordering Recursive Definitions and Structural Induction Recursive Algorithms
Chap 6: Counting
The Basics of Counting The Pigeonhole Principle Permutations and Combinations Binomial Coefficients Generalized Permutations and Combinations Generating Permutations and Combinations
Chap 8: Advanced Counting Techniques
Recurrence Relations Solving Linear Recurrence Relations Divide-and-Conquer Algorithms and Recurrence Relations Generating Functions Inclusion-Exclusion Applications of Inclusion-Exclusion
Chap 9: Relations
Relations and Their Properties n-ary Relations and Their Applications Representing Relations Closures of Relations Equivalence Relations Partial Orderings
Chap 10: Graphs
Graph Models Graph Isomorphism Connectivity Euler and Hamilton Paths Shortest-Path Problems Graph Coloring
Chap 11: Trees
Introduction to Trees Tree Traversal Spanning Trees Minimum Spanning Trees
Chap 12: Boolean Algebra
Boolean Functions Logic Gates Minimization of Circuit
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1.1 Proposition Logic 1.2 Proposition Equivalences 1.3 Predicates and Quantifiers |
| 第 2 週 | 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs |
| 第 3 週 | 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations |
| 第 4 週 | 2.3 Functions 2.4 Sequences and Summations 4.1 Divisibility and Modular Arithmetic |
| 第 5 週 | 4.2 Integer Representations and Algorithms 4.3 Primes and Greatest Common Divisors 4.4 Solving Congruences |
| 第 6 週 | 5.1 Mathematical Induction 5.2 Strong Induction and Well-Ordering |
| 第 7 週 | 5.3 Recursive Definitions and Structural Induction 5.4 Recursive Algorithms |
| 第 8 週 | 6.1 The Basics of Counting 6.2 The Pigeonhole Principle 6.3 Permutations and Combinations 6.4 Binomial Coefficients |
| 第 9 週 | 6.5 Generalized Permutations and Combinations 6.6 Generating Permutations and Combinations |
| 第 10 週 | 8.1 Recurrence Relations 8.2 Solving Linear Recurrence Relations |
| 第 11 週 | 8.3 Divide-and-Conquer Algorithms and Recurrence Relations 8.4 Generating Functions 8.5 Applications of Inclusion-Exclusion |
| 第 12 週 | 9.1 Relations and Their Properties 9.2 n-ary Relations and Their Applications 9.3 Representing Relations |
| 第 13 週 | 9.4 Closures of Relations 9.5 Equivalence Relations 9.6 Partial Orderings |
| 第 14 週 | 10.1 Graphs and Graph Models 10.2 Graph Terminology and Special Types of Graphs 10.3 Representing Graphs and Graph Isomorphism |
| 第 15 週 | 10.4 Connectivity 10.5 Euler and Hamilton Paths 10.6 Shortest Path Problems |
| 第 16 週 | 10.8 Graph Coloring 11.3 Tree Traversal 11.4 Spanning Trees |
| 第 17 週 | 11.5 Minimum Spanning Trees 12.1 Boolean Functions 12.3 Logic Gates |
| 第 18 週 | Bonus Exams |
Kenneth H. Rosen, Discrete Mathematics and Its Applications, 8th ed., 2018, McGraw-Hill Inc.
- 地點
- TBA
- 時間
- TBA
- 聯絡方式
- ttyeh@cs.nctu.edu.tw