COMP233: Discrete Mathematics

Second Semester 2025/2026

Hisham Ihshaish

Department of Computer Science, Birzeit University

Course Outline

Primary Text

Discrete Mathematics with Applications, 4th Edition
Susanna S. Epp · Brooks/Cole

Assessment

Three Quizzes30%
Midterm Exam30%
Final Exam40%

References

Barnier & Chan, Discrete Mathematics with Applications
Kenneth H. Rosen, Discrete Mathematics and its Applications
Aho & Ullman, Foundations of Computer Science

Released This Term

Quiz #1Chapters 1–3 · Released 6 May 2026
First Exam12 May 2026 · Released 14 May 2026

Lecture Material

Chapter 1: Speaking Mathematics

Introduction · variables, sets, relations, functions · the language of mathematics

1 Outline & Speaking Mathematics

Slides

Chapter 2: The Logic of Compound Statements

Propositional logic · sections 2.1–2.3

2.1 Logical Form & Logical Equivalence

Slides

2.2 Conditional Statements

Slides

2.3 Valid & Invalid Arguments

Slides

Chapter 2 Interactive Companion Truth-table builder, equivalence checker, De Morgan demo, tautology classifier, contrapositive comparison, and the argument validity checker.

Chapter 3: The Logic of Quantified Statements

First-order logic · sections 3.1–3.3

3.1 Predicates & Quantified Statements I

Slides

3.2 Predicates & Quantified Statements II

Slides

3.3 Statements with Multiple Quantifiers

Slides

Chapter 3 Interactive Companion Predicates, ∀ and ∃, Tarski's World (Figures 3.1.1 and 3.3.1), negation laws, contrapositive in FOL, and multi-quantifier reasoning.

Quiz #1 Released 6 May 2026 Weight 10% Click to expand for the paper and worked solutions

Section 9 · Second Semester 2025/2026 · Chapters 1 + 2 + 3

Quiz #1 & Answers

Here is the Quiz #1 paper, covering Chapters 1, 2, and 3, with my worked solutions and the marking criteria. Work each question on paper first, then click Show solution.

View questions & solutions

Step-by-step simplifications Worked truth-table tautology Marking guide for every part

Chapter 4: Elementary Number Theory & Methods of Proof

Direct proof, counterexample, divisibility · sections 4.1–4.4

4.1 Direct Proof & Counterexample I: Introduction

Slides

4.2 Direct Proof & Counterexample II: Rational Numbers

Slides

4.3 Direct Proof & Counterexample III: Divisibility

Slides

4.4 Direct Proof & Counterexample IV: Quotient-Remainder & Division into Cases

Slides

Chapter 4 Interactive Companion Definitions tester, conjecture lab for counterexamples, divisibility and prime factorisation explorers, quotient-remainder calculator, congruence checker, division into cases, plus a find-the-mistake exercise.

First Exam Released 14 May 2026 Weight 30% Click to expand for the paper and worked solutions

Section 9 · Second Semester 2025/2026

First Exam & Answers

Here is the First Exam paper you sat on 12 May 2026, with my worked solutions to every question and the full marking criteria. Work each question on paper first, then click Show solution; for Q1 click any option to check your answer.

View questions & solutions

MCQ with click-to-check answers Step-by-step worked proofs Marking guide for every part

Chapter 5: Sequences & Mathematical Induction

Sections 5.1–5.3 · sequences, weak & strong induction

5.1–5.3 Sequences and Mathematical Induction

Slides coming

Chapter 6: Set Theory

Sections 6.1–6.3 (+ 6.4 algebra of sets) · element method, set identities

6.1–6.4 Sets, Properties, Algebra

Slides coming

Chapter 7: Functions

Sections 7.1–7.2 · functions on general sets, one-to-one, onto, inverses

7.1–7.2 Functions, One-to-One, Onto, Inverse

Slides coming

Chapter 8: Relations

Sections 8.1–8.3 · relations on sets, properties, equivalence relations

8.1–8.3 Relations & Equivalence Relations

Slides coming

Chapter 9: Counting & Probability

Sections 9.1, 9.2, 9.3, 9.5, 9.6 · multiplication rule, permutations, combinations

9.1–9.6 Counting Theory

Slides coming

Chapter 10: Graphs & Trees

Sections 10.1–10.2 · basic graph theory · if time permits

10.1–10.2 Graphs, Trails, Paths, Circuits

Slides coming