教學大綱表 (100學年度 第1學期)
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課程名稱
Course Title		 (中文) 數學導論
(英文) Introduction To Mathematics 		開課單位
Departments		 應用數學系
課程代碼
Course No.		 A1070A
授課教師
Instructor		 張薰文
學分數
Credit		 3.0 必/選修
core required/optional		 必修 開課年級
Level		 大一
先修科目或先備能力(Course Pre-requisites)：高中數學
課程概述與目標(Course Overview and Goals)：1. Logic and Proofs
2. Sets, Functions, Sequences, and Sums
3. Algorithms and the Integers
4. Induction and Recursion
5. Counting
教科書(Textbook) Kenneth H. Rosen
Discrete Mathematics and Its Applications (6th edition)
McGraw Hill, 2007
參考教材(Reference) 1. R. P. Grimaldi, Discrete and Combinatorial Mathematics (5th edition), Addison-Wesley, 2003.
2. E. G. Goodaire & M. M. Parmenter, Discrete Mathematics with Graph Theory
(3rd edition), Prentice Hall, 2005.
課程大綱 Syllabus 分配時數 (小時) 備註
Notes
單元主題
Unit topic		 內容綱要
Content summary		 講授 示範 習作 其他
Basic Structures: Sets, Functions, Sequences and Sums 1. Sets
2. Set Operations
3. Functions
4. Sequences and Summations 		5 2 3 0  
The Foundations: Logic and Proofs 1. Propositional Logic
2. Propositional Equivalences
3. Predicates and Quantifiers
4. Nested Quantifiers
5. Rules of Inference
6. Introduction to Proofs
7. Proof Methods and Strategy 		10 3 5 0  
The Fundamentals: Algorithms, the Integers, and Matrices 1. The Integers and Division
2. Primes and Greatest Common Divisors
3. Integers and Algorithms
4. Applications of Number Theory
5. Algorithms 		5 2 3 0  
Induction and Recursion 1. Mathematical Induction
2. Strong Induction and Well-Ordering
3. Recursive Definitions & Structural Induction
4. Recursive Algorithms 		10 3 5 0  
Counting 1. The Basics of Counting
2. The Pigeonhole Principle
3. Permutations and Combinations
4. Binomial Coefficients
5. Generalized Permutations and Combinations
6. Generating Permutations and Combinations 		10 2 4 0  


教學要點概述：
1.自編教材 Handout by Instructor：
□ 1-1.簡報 Slides
□ 1-2.影音教材 Videos
□ 1-3.教具 Teaching Aids
□ 1-4.教科書 Textbook
□ 1-5.其他 Other
□ 2.自編評量工具/量表 Educational Assessment
□ 3.教科書作者提供 Textbook

教學方法：■ 課堂講授 Lecturing   ■ 分組討論   ■ 投影片   ■ 學生答問   ■ 實作  
評量方法： 平時成績：50%   期中考：25%   期末考：25%   其他：0%

教學資源(Teaching Resources)：
□ 教材電子檔(Soft Copy of the Handout or the Textbook)
□ 課程網站(Website)
扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php