1. About the Course Lecture 0: Sep 10 AB C

2. Plan  Course Information and Arrangement  Course Requirement  Topics and objectives of this course

3. Basic Information  Course homepage: http://www.cse.cuhk.edu.hk/~chi/csc2110/http://www.cse.cuhk.edu.hk/~chi/csc2110/  Newsgroup: cuhk.cse.csc2110. at news.cse.cuhk.edu.hk  Instructor: Lau, Lap Chi  Office hour: Thesdays, Thursdays, 10am-12pm (SHB 911)  Lectures: M7-8 (SC L1), W6 (SC L1)  Tutors: Chow Chi Wang Kwok Tsz Piu Lee Chin Ho  Tutorials: W10 (LSB C2) or H5 (ERB 803) or H6 (LSB C1)

4. Course Material  Textbook: Discrete Mathematics with Applications Author: Susanna S. Epp Publisher: Brooks/Cole  Notes: Course notes from “mathematics for computer science” http://courses.csail.mit.edu/6.042/spring07/ (available to be downloaded in the course homepage)

5. Course Requirements  Quizzes, 45%  Final Exam, 55% Three Quizzes: (1) Oct 8 (Monday), in class (2) Nov 5 (Monday), in class (3) Dec 3 (Monday), in class

6. Discrete Mathematics Computer Science: use computer technology to solve problems. Many courses in our curriculum will talk about computer technology. This course will provide the mathematical foundation to solve problems. (E.g. to design a security system, to design a fast searching algorithm.) Why discrete mathematics? In computer science we usually deal with discrete objects (rather than continuous objects), and the techniques to work on these problems are often different (e.g. induction).

7. Topic 1: Counting Sets and Functions Combinations, Permutations, Binomial theorem Counting by mapping, pigeonhole principle Recursions Probability, data structures, algorithms AB C

8. Topic 1: Counting How many steps are needed to sort n numbers? Algorithm 1 (Bubble Sort): Every iteration moves the i-th smallest number to the i-th position Algorithm 2 (Merge Sort): Which algorithm runs faster?

9. Topic 2: Logic and Proofs Logic: propositional logic, first order logic Proof: induction, contradiction How do computers (and humans) think? Artificial intelligence, database, circuit, algorithms

10. Topic 3: Graph Theory Graphs Degree sequence, Eulerian graphs, isomorphism Trees Matching Coloring Computer networks, circuit design, data structures

11. Topic 3: Graph Theory How to color a map? How to send data efficiently? How to schedule exams?

12. Tentative Course Schedule MondayWednesdayTopic Sep 10Sep 12introduction, sets Sep 17Sep 19basic counting Sep 24Sep 26functions, counting by mapping Oct 1 (holiday)Oct 3counting by mapping Oct 8 (quiz)Oct 10number sequences Oct 15Oct 17recursion Oct 22Oct 24recursion, logic Oct 29Oct 31logic and proofs Nov 5 (quiz)Nov 7induction Nov 12Nov 14induction Nov 19Nov 21graphs, paths and cycles, trees Nov 26Nov 28graph matchings Dec 3 (quiz)Dec 5graph colorings, planar graphs

13. Objectives of This Course Knowledge will be used in future courses: CSC 2100, ERG 2040, CSC 3130, CSC 3160 To learn basic mathematical concepts, e.g. sets, functions, graphs To be familiar with formal mathematical reasoning, e.g. logic, proofs To improve problem solving skills, e.g. induction, recursion To see the connections between discrete mathematics and computer science

14. Expectations CUHK staff student expectations on teaching and learning http://www.cse.cuhk.edu.hk/~chi/csc2110/notes/expectation.doc No electronic devices in class, including phones, laptops, iPads, etc.

15. Academic Honesty http://www.cuhk.edu.hk/policy/academichonesty/ http://www.cuhk.edu.hk/policy/academichonesty/p02.htm Examples: see booklet and Definition: see booklet and http://www.cuhk.edu.hk/policy/academichonesty/p01.htm http://www.cuhk.edu.hk/policy/academichonesty/p06.htm Procedure: see booklet and Computer programs checking plagiarism Discussions of ideas may be allowed, in any case need to write your own solutions. State the source and let the marker make the adjustments. Academic Honesty in the Faculty of Engineering: http://www.cse.cuhk.edu.hk/~chi/honesty.ppt