離散數學
Discrete Mathematics
學期
111-2
學分
3
學分
當期課號
515501
永久課號
CSCS10025
開課單位
資訊學院共同課程
授課教師
紀虹名
校區
光復
類別
必修
上課時間表
| 節 | 週五 |
|---|---|
3 10:10–11:00 | 離散數學 EDB27 2 節連堂 |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
概述
This course will teach students to think logically and mathematically, including logic and proofs, sets and matrices, algorithms, number theory, recursion, counting, discrete probability, relations, and graphs. Students learn this mathematical reasoning and how to apply them. Based on this course, students can learn more advanced courses in the future, such as computer architecture, data structures, and artificial intelligence.
先修科目
None
評分方式
Two homework, each 10% Midterm examination, 40% Final examination, 40%
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Proposition LogicPropositional EquivalencesPredicates and Quantifiers |
| 第 2 週 | Nested QuantifiersRules of InferenceIntroduction to Proofs |
| 第 3 週 | Proof Methods and StrategySetsSet Operations |
| 第 4 週 | FunctionsSequences and Summations |
| 第 5 週 | Algorithms Integer Representations and AlgorithmsPrimes and Greatest Common Divisors |
| 第 6 週 | Mathematical InductionStrong Induction and Well-Ordering |
| 第 7 週 | Recursive Definitions and Structural InductionRecursive Algorithms |
| 第 8 週 | Midterm Exam |
| 第 9 週 | The Basics of CountingThe Pigeonhole PrinciplePermutations and Combinations |
| 第 10 週 | Binomial Coefficients and IdentitiesGeneralized Permutations and CombinationsGenerating Permutations and Combinations |
| 第 11 週 | Applications of Recurrence RelationsSolving Linear Recurrence Relations |
| 第 12 週 | Divide-and-Conquer Algorithms and Recurrence Relations Generating Functions Inclusion-ExclusionApplications of Inclusion-Exclusion |
| 第 13 週 | Relations and Their Properties n-ary Relations and Their Applications |
| 第 14 週 | Representing Relations Closures of Relations Equivalence Relations |
| 第 15 週 | Partial Orderings Graphs and Graph ModelsGraph Terminology and Special Types of Graphs |
| 第 16 週 | Representing Graphs and Graph IsomorphismConnectivity |
| 第 17 週 | Euler and Hamilton PathsShortest-Path Problems |
| 第 18 週 | Final Exam |
教科書
K. H. Rosen, "Discrete Mathematics and Its Applications," 8th edition, 2019.
Office Hours
- 地點
- EE235A
- 時間
- d00022@nycu.edu.tw