一、課程說明 (Course Description)

This course is an extension to the Discrete Mathematics.

We will introduce a couple of interesting and useful

combinatorial mathematics tools and concepts, and we hope

that by mastering these techniques, we can strengthen our

problem solving abilities.

Most of our topics have direct application to important CS

areas, including coding, crypotography, network design,

data compression, theory of computation, and analysis of

algorithms.

二、指定用書 (Text Book)

Introduction to Combinatorial Mathematics

by C. L. Liu

三、參考書籍 (References)

1. Discrete Mathematics and Its Applications

by K. H. Rosen

更多參考書籍 (More References)

2. Introduction to Algorithms, by T. H. Cormen and others

3. Concrete Mathematics, by R. Graham and others

四、教學方式 (Teaching Method)

Lectures and Tutorials (Lectures in English)

五、教學進度 (Syllabus)

1. Permutations and Combinations

2. Generating Functions

3. Recurrence Relations

4. Methods of Proving

5. Special Numbers

6. Graphs and Trees

7. Group Theory

8. Number Theory

Example Applications:

1. Coding (Group Codes)

2. Cryptography (RSA)

3. Network Design (Matching)

4. Compression (Tree Representation)

5. Theory (Halting Problem)

6. Analysis (AVL Tree)

六、成績考核 (Evaluation)

To be announced

七、可連結之網頁位址 (Web links)

None