Discrete Mathematics Course

Mustafa Jarrar

Full Professor

Computer Science, Birzeit University

mjarrar(a)birzeit.edu

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 Inference in Propositional Logic (Slides)

Chapter 3: First Order logic

3.1 Introduction to First Order logic (Slides)

3.2 Conditional Statements in First Order logic (Slides)

3.3 Multiple Quantifiers in First Order logic (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)

Textbook
Susanna S. Epp: Discrete Mathematics with Applications (4rd Edition) . Brooks/Cole

Course Objectives:

By the end of the course the students will be able:

To apply logically valid forms of argument and avoid logical errors.

To employ both direct and indirect arguments to derive new results from those already known to be true.

To work with symbolic representations as if they were concrete objects.

To recursively think about problems and validate them using mathematical induction.

To count random and chance events and compute the likelihood of obtaining certain events in a sample space.

Evaluation:

Midterm exam 30%

Short Exams & Assignments 25%

Participation* 5%

Final Exam 40%

*Participation includes class attendance, contributions during lectures, and answering questions.

Student Responsibilities:

Office Hours:Please check my office hours on Ritaj. If you wan to meet me outside my public office hours please request an appointment by email.

Class participation and independent work: Students are expected to actively participate in all classes and perform independent work.

Attendance: Attendance is mandatory. University regulations regarding this matter will be strictly enforced.

Academic Honesty: Individual work must be each student’s own work. Plagiarism or cheating will result in official University disciplinary review.

Missed Exams: There are no makeup exams.

Class Etiquette: Please keep all cell phones and other electronic devices turned off during class. If your activities during class are deemed disruptive, you will be asked to leave. Use of a personal computer during class is prohibited except for note taking with Instructor permission.