Mustafa Jarrar
Associate Professor

Biomedical Informatics Department, University at Buffalo, USA
Computer Science Department, Birzeit University, Palestine
mjarrar(a) The Web              

Discrete Mathematics
The goal of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in computer science. Ultimately, students are expected to understand and use (abstract) discrete structures that are the backbones of computer science. In particular, this class is meant to introduce logic, proofs, sets, functions, relations, counting, graphs and trees and with an emphasis on applications in computer science.

Course Outline

Chapter 2: propositional logic
2.1 Logical Form and Logical Equivalence (Slides)
2.2 Conditional Statements (Slides)
2.3 Inferencing in Propositional Logic (Slides)

Chapter 3: First Order logic
3.1 Predicates and Quantified Statements (Slides)
3.2 Negation and Conditional Statements (Slides)
3.3 Statements with Multiple Quantifiers (Slides)

Chapter 4: Number Theory
4.1 Introduction (Slides)
4.2 Rational Numbers (Slides)
4.3 Divisibility (Slides)
4.4 Quotient-Remainder Theorem (Slides)

Chapter 5: Sequences and Mathematical Induction
5.1 Sequences (Slides)
5.2&3 Mathematical Induction (Slides)

Chapter 6: Set Theory
6.1 Basics of Set Theory (Slides)
6.2 Properties of Sets (Slides)
6.3 Algebric Proofs (Slides)
6.4 Boolean Algebra (Slides)

Chapter 7: Functions
7.1 Introduction to Functions (Slides)
7.2 One-to-One, Onto, Inverse functions (Slides)
7.3 The Pigeonhole Principle (Slides)

Chapter 8: Relations
8.1. Introduction to Relations (Slides)
8.2 Properties of Relations (Slides)
8.3 Equivalence Relations (Slides)

Chapter 9: Counting
9.1 Basics of Probability and Counting (Slides)
9.2 Possibility Trees and the Multiplication Rule (Slides)
9.3 Counting Elements of Disjoint Sets: Addition Rule (Slides)
9.5 Counting Subsets of a Set: Combinations (Slides)
9.6 r-Combinations with Repetition Allowed (Slides)

Chapter 10: Graphs and Trees
10.1 Graphs (Slides)
10.2 Graphs and Trees (Slides)

Susanna S. Epp: Discrete Mathematics with Applications (4rd Edition) . Brooks/Cole
*Participation includes class attendance, contributions during lectures, and answering questions.