About the Course Lecture 0: Sep 10 AB C. Plan Course Information and Arrangement Course...
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Transcript of About the Course Lecture 0: Sep 10 AB C. Plan Course Information and Arrangement 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
A B
C
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
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