培養學生對於基礎數學(離散、組數)的認知與解題能力，而著重於基本原理的理解及其引申應用題目之解決方法與模式的訓練，借以增進學生的理解、分析、組織、推理、應用等能力，更進而培養學生獨立思考、解決問題的能力，包括：
Chap.1 Fundamental Principles of Counting
Chap.2 Fundamentals of Logic
Chap.4 Properties of the Integers
Chap.5 Relations and Functions
Chap.9 Generating Functions
Chap.10 Recurrence RelationsCultivate students' cognition and problem-solving ability of basic mathematics (discrete, group numbers), and focus on the understanding of basic principles and the training of solutions and models for extended application problems, so as to enhance students' understanding, analysis, organization, reasoning, and application and other abilities, and further cultivate students’ ability to think independently and solve problems, including:
Chap.1 Fundamental Principles of Counting
Chap.2 Fundamentals of Logic
Chap.4 Properties of the Integers
Chap.5 Relations and Functions
Chap.9 Generating Functions
Chap.10 Recurrence Relations
本課程為大學部三年級之必修課程，本課程除了教授學生們已知的數學外還教導學生們如何利用數理邏輯方法進行分析，建立出適當的模式，再發展出一個有效率的演算法來解決相關的問題。
本課程共有四個主要教學主題，分別為(一)教學推論(含基本運算和證明建構方法)、(二)組合學分析、(三)離散結構(含圖論)、(四)演算法
本課程教授上述四個主題之外，也強調相關的應用，例如使用基本整數論和知識，發展出和模算數相關演算法(如超大整數的四則運算)，在進行RSA譯碼學分析。
學生們順利修讀本課程後，除了可以學習到一些數學的知識外，更重要的是建立符合邏輯的數理分析與推論態度與方法，碰到實務問題時，可以順利解析問題的重點，再運用或發展合宜的模式與演算法解決問題。
This course is a required course for third-year undergraduate students. In addition to teaching students the mathematics they already know, this course also teaches students how to use mathematical logic methods to analyze, establish appropriate models, and then develop an efficient algorithm. Solve related problems.
This course has four main teaching themes, namely (1) teaching inference (including basic operations and proof construction methods), (2) combinatorics analysis, (3) discrete structure (including graph theory), and (4) algorithm
In addition to teaching the above four topics, this course also emphasizes related applications, such as using basic integer theory and knowledge to develop algorithms related to modular arithmetic (such as the four arithmetic operations of very large integers), and conducting RSA decoding analysis.
After students successfully complete this course, in addition to learning some mathematical knowledge, more importantly, they can establish logical attitudes and methods of mathematical analysis and inference. When encountering practical problems, they can successfully analyze the key points of the problem and then apply it. Or develop appropriate models and algorithms to solve problems.
教科書 : Discrete and Combinatorial Mathematics ; Grimaldi ; 新月圖書。
參考書 :
1. Introduction to Combinatorial Mathematics ; C. L. Liu。
2. 離散與組合數學；劉涵初；華泰書局。
Textbooks: Discrete and Combinatorial Mathematics; Grimaldi; Crescent Books.
Reference books:
1. Introduction to Combinatorial Mathematics; C. L. Liu.
2. Discrete and Combinatorial Mathematics; Liu Hanchu; Huatai Book Company.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 小考二次小考二次 Quiz twice |
30 | 平時成績：+ 0 ~ 8 |
| 期中考期中考 midterm exam |
30 | |
| 期末考期末考 final exam |
40 |
