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

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.

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.

Chapter 5: Sequences & Mathematical Induction

Sequences, summation, factorials, and mathematical induction · sections 5.1–5.3
5.1 Sequences
Slides
5.2–5.3 Mathematical Induction
Slides Recording
Chapter 5 Interactive Companion Sequence-term generator, summation and product calculator, telescoping and factorial tools, an induction proof walker, and divisibility, inequality and recurrence checkers, plus worked solutions to the recommended Epp exercises.

Chapter 6: Set Theory

Element method, set identities, algebraic proofs, Boolean algebra · sections 6.1–6.4
6.1–6.2 Set Basics & Properties of Sets
Slides
6.3–6.4 Algebraic Proofs & Boolean Algebra
Slides
Chapter 6 Interactive Companion Set-operations calculator, subset & equality checker, partition validator, power-set and Cartesian-product builders, element-method proof walker, algebraic-proof checker (one law per step), Boolean-algebra explorer, plus find-the-mistake drills and worked solutions to the recommended Epp exercises.

Chapter 7: Functions

Functions on general sets; one-to-one, onto, inverse; composition; the pigeonhole principle · sections 7.1–7.3 & 9.4
7.1 Introduction to Functions (functions on general sets)
Slides Recording
7.2–7.3, 9.4 One-to-One, Onto & Inverse Functions; Composition; the Pigeonhole Principle
Slides
Chapter 7 Interactive Companion Arrow-diagram “is it a function?” checker, a function evaluator, an equality-of-functions demonstrator, one-to-one / onto / bijection checker, a linear-function lab, a logarithm and change-of-base calculator, a composition tracer, and a pigeonhole calculator, plus worked solutions to the recommended Epp exercises.

Chapter 8: Relations

Relations on sets, their properties, and equivalence relations · sections 8.1–8.3 · slides & recordings by Prof. Mustafa Jarrar
8.1 Introduction to Relations (relations on sets)
Slides Video
8.2 Properties of Relations (reflexivity, symmetry, transitivity)
Slides Video
8.3 Equivalence Relations
Slides Video
Chapter 8 Interactive Companion Relation explorer (live matrix & directed graph), standard-relation generator, the reflexive / symmetric / transitive property checker that names the exact witness, a transitive-closure tool, an equivalence-class & partition builder, and a congruence-mod-n explorer, plus worked solutions and challenge problems.

Chapter 9: Counting & Probability

Introduction to counting & probability, possibility trees and the multiplication rule · sections 9.1–9.2 · slides & recordings by Prof. Mustafa Jarrar
9.1 The Basics of Counting & Probability
Slides Video
9.2 Possibility Trees & the Multiplication Rule
Slides Video
Chapter 9 Interactive Companion Equally-likely probability calculator, a two-dice sample-space explorer, a list-counting tool, the possibility-tree visualiser, a multiplication-rule calculator, and a permutation calculator with full derivations, plus worked solutions and challenge problems (sections 9.1–9.2).

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