Course No 05355 : Discrete Mathematics (離散數學)

• 講義下載
• 第一次小考
  • 時間: 2008/10/07
  • 考古題
  • 建議練習題目
    • 上課範例
    • Section 1.1
      • Exercises: 2, 11
    • Section 1.2
      • Exercises: 26~30
    • Section 1.3
      • Exercises: 23, 25
    • Section 1.4
      • Exercises: 26, 27, 28, 31, 33
    • Section 1.5
      • Exercises: 3, 19, 23, 24
    • Section 1.6
      • Exercise: 1, 5, 9
    • Section 2.3
      • Exercises: 8, 9, 14, 15, 18, 19
• Course Previous (先修課程)---Computer Programming, Data Structure
• Course Description: Discrete mathematics is a basic course of computer science. We wish to provide a foundation for the study of database theory, compiler, computer security and so on. This course includes five categories:
  1. Logic and proof strategy
  2. Complexity of algorithms
  3. Number theory
  4. Functions, sets and relations
  5. Graph theories and their applications
• Learning Objectives : On completion of the course, you should be able to understand:
  1. Logic and mathematical arguments
  2. Proof methods: direct proof, indirect proof and proof by contradiction .
  3. Analysis of algorithms: time and space complexities
  4. Mathematical and Structural inductions
  5. Analysis of recursive algorithms and difference equations
  6. Relations and its applications
  7. Related theories of graphs and trees and their applications
• Learning Outcome : On completion of the course, you should be able to:
  1. Understand mathematical reasoning to read, comprehend, and construct mathematical arguments.
  2. Perform combinational analysis to solve counting problem.
  3. Represent the relationships between discrete objects, including sets, graphs, trees, finite-state machine and so on
  4. Develop algorithms to solve a problem, analysis time and space complexity of these algorithms, and verify the correctness of these algorithms.
• Course Outline : This course is designed for the general college audience, and cover the following topics
  1. Logic
  2. Methods of Proof
  3. Sets and Functions
  4. Algorithms
  5. Integers-related Algorithm
  6. Mathematical Induction
  7. Recursion
  8. Counting Techniques
  9. Relations
  10. Graphs
  11. Trees
• Textbook
  • Discrete Mathematics and Its Applications (6th edition)
  • Author: Kenneth H. Rosen
  • Publication Date: 2007
  • Publisher: McGraw-Hill College
  • ISBN-10: 007-124474-3
• Lecture Notes (講義)
  • Chapter 01
  • Chapter 01(修正排版錯誤)
  • Chapter 02
  • Chapter 03
  • Chapter 04
  • Chapter 06