About the Course

Lecture 0: Sep 5

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Plan

Course Information and Arrangement

Course Requirement

Topics and objectives of this course

Basic Information

Course homepage: 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: Kwok Tsz Chiu

Wong Chun Hoi (Hollis)

Yu Yuanming

Tutorials: W10 (LSB C2) or H5 (ERB 803) or H6 (LSB C1)

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)

Course Requirements

Quizzes, 45%

Final Exam, 55%

Three Quizzes: (1) Sep 26 (Monday), in class

(2) Oct 24 (Monday), in class

(3) Nov 28 (Monday), in class

Topic 1: Counting

• Sets and Functions

• Combinations, Permutations, Binomial theorem

• Counting by mapping, pigeonhole principle

• Recursions

Probability, data structures, algorithms

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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?

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

Topic 3: Graph Theory

• Graphs

• Degree sequence, Eulerian graphs, isomorphism

• Trees

• Matching

• Coloring

Computer networks, circuit design, data structures

Topic 3: Graph Theory

How to color a map?

How to send data efficiently?

How to schedule exams?

Tentative Course Schedule

Monday Wednesday Topic

Sep 5 Sep 7 introduction, sets, basic counting

Sep 12 Sep 14 basic counting, functions

Sep 19 Sep 21 counting by mapping

Sep 26 (quiz) Sep 28 number sequences

Oct 3 Oct 5 (holiday) recursion

Oct 10 Oct 12 recursion, logic

Oct 17 Oct 19 logic, proofs

Oct 24 (quiz) Oct 26 induction

Oct 31 Nov 2 induction

Nov 7 Nov 9 graphs, paths and cycles, trees

Nov 14 Nov 16 matchings

Nov 21 Nov 23 graph colorings, planar graphs

Nov 28 (quiz) Nov 30

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

Time Table

M T W H F

1

2

3

4

5 Tut

6 Lec Tut

7 Lec X

8 Lec X

9 X

10 Tut

11

(1) Tutorials (2) Office hours (3) TA office hours

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.

Academic Honesty

http://www.cuhk.edu.hk/policy/academichonesty/

http://www.cuhk.edu.hk/policy/academichonesty/p02.htmExamples: see booklet and

Definition: see booklet and http://www.cuhk.edu.hk/policy/academichonesty/p01.htm

http://www.cuhk.edu.hk/policy/academichonesty/p06.htmProcedure: 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