CENG 115
Discrete Structures
Logic, propositions and proof methods. Sets. Functions, sequences and summations. Algorithms and complexity analysis. Integers and division. Matrices. Mathematical induction. Recursive definitions and algorithms. Probability theory. Counting techniques. Graphs. Trees.
Course Objectives
1.To teach the problem solving strategies, techniques, and tools
2.To provide students with the ability of logical and mathematical thinking
3.To form the background related to the discrete mathematics concepts and the corresponding mathematical notations
4.To develop the critical thinking ability by introducing algorithmic solutions to some abstract problems
Recommended or Required Reading
Zeitz, Paul; 1999; “The Art and Craft of Problem Solving”; John Wiley & Sons, Inc. ,Rosen, Kenneth H.; 2007; “Discrete Mathematics and its Applications”; 6th Ed.; McGraw-Hill ,Stein, Clifford, Drysdale, Robert L., Bogart, Kenneth; 2011; “Discrete Mathematics for Computer Scientists”; Pearson
Learning Outcomes:
1. To be able to compare and use different discrete structures
2. To be able to analyze problems and identify appropriate solution schemes
3. To be able to demonstrate abstraction ability
Topics |
Propositional Logic |
Predicate Logic |
Proof Techniques |
Sets and Functions |
Sequences and Summations |
Algorithms and complexity analysis |
Integers, divisibility, and matrices |
Mid-term Exam |
Induction and recursion |
Counting, pigeonhole principle, permutation, and combination
|
Discrete probability |
Recurrences |
Relations |
Graphs |
Grading
Midterm 25%
Quiz 15%
Homework 30%
Final 30%