About the Course

Lecture 0: Sep 10

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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: Chow Chi Wang

Kwok Tsz Piu

Lee Chin Ho

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) Oct 8 (Monday), in class

(2) Nov 5 (Monday), in class

(3) Dec 3 (Monday), in class

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).

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 10 Sep 12 introduction, sets

Sep 17 Sep 19 basic counting

Sep 24 Sep 26 functions, counting by mapping

Oct 1 (holiday) Oct 3 counting by mapping

Oct 8 (quiz) Oct 10 number sequences

Oct 15 Oct 17 recursion

Oct 22 Oct 24 recursion, logic

Oct 29 Oct 31 logic and proofs

Nov 5 (quiz) Nov 7 induction

Nov 12 Nov 14 induction

Nov 19 Nov 21 graphs, paths and cycles, trees

Nov 26 Nov 28 graph matchings

Dec 3 (quiz) Dec 5 graph colorings, planar graphs

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

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