1 CSC 281 Discrete Mathematics for Computer Science Dr.Yuan Tian Syllabus

Course Overview Course title: Discrete mathematics for Computer Science Instructors: – Dr. Yuan Tian —Course Coordinator Office Hour : Sun. Tue. Thu.(11:00-13:00), Mon.(9:00- 13:00) – Ms.Noura AlAngari Office Hour : Sun. Tue. Thu. (9:00 – 12:00) Credit hours: 3 Hours Lecture/week 1 Hour Tutorial/week Prerequisite – Engineering Probability & Statistics – Data structure 2

3 Textbook Discrete Mathematics and Its Applications by Kenneth H. Rosen Use lecture notes as study guide.

4 Acknowledgement Most of these slides are adapted from ones created by Professor Bart Selman at Cornell University.

5 Course Themes, Goals, and Course Outline

Goals of CSC 281 Introduce students to a range of mathematical tools from discrete mathematics that are key in computer science Mathematical Sophistication How to write statements rigorously How to read and write theorems, lemmas, etc. How to write rigorous proofs Areas we will cover: Logic and proofs Set Theory Induction and Recursion Counting and combinatorics Probability theory Number Theory Trees and Graphs Discrete Probability Aside: We’re not after the shortest or most elegant proofs; verbose but rigorous is just fine! Practice works! Actually, only practice works! Note: Learning to do proofs from watching the slides is like trying to learn to play tennis from watching it on TV! So, do the exercises!

Topics of CSC 281 Logic and Methods of Proof Propositional Logic --- SAT as an encoding language! Predicates and Quantifiers Methods of Proofs Sets Sets and Set operations Functions Counting Basics of counting Pigeonhole principle Permutations and Combinations Number Theory Modular arithmetic RSA cryptosystems

Topics of CSC 281 Probability Probability Axioms, events, random variable Independence, expectation, example distributions Birthday paradox Monte Carlo method Graphs and Trees Graph terminology Example of graph problems and algorithms: graph coloring TSP shortest path

Grading Quizzes: 10 points Tutorial: 10 points Project(Presentation+report): 10 points Midterm 1: 15 points Midterm 2: 15 points Final Exam: 40 points 9

About Project… Content  Use the methods you lean from CSC281 to solve a new problem (not discussed in the slide) Requirements:  2 (or 1) students/group  Final Report (Problem statement, Mathematical modelling, Complete solution, Program(bonus) )  A detailed written report of the project should be submitted in the first week after finishing all lectures.

Exam Dates Quiz1: Oct.4 (Sunday) 13:00-14:00 Mid1: Oct. 20 (Tuesday ) Quiz2: Nov.15(Sunday) 13:00-14:00 Mid2:Dec. 8 (Tuesday)

Notes for Communication 12 Your header must start with [section no.-CSC281] Send your to / address. Please write your name and your ID at the end of the