Discrete Mathematics | Ayman Alzaid

Course Resources

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Course Overview

All 37 lectures organized by module with learning objectives and course outcomes.

Curated Resources →

Learning Paths

Textbook, practice tools, and curated resources — with a recommended study order.

Reference →

Symbol & Glossary Guide

Every symbol, term, proof template, and Canvas typing guide — all in one searchable page.

Watch the Lectures

All 37 lectures are available free on YouTube

Watch all 37 lectures in order on the dedicated course playlist. Each video is 6–9 minutes, captioned, and organized to follow the module sequence below. No account required to watch.

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All 14 Modules · 37 Lectures

Set Theory

6 lectures · Sections 1.1–1.4, 8.1, 10.1

01Membership of a SetObj 1-1

02Set-Builder NotationObj 1-1

03Subsets & Proper SubsetsObj 1-2

04Number of Elements in a SetObj 1-3

05Elements of a RelationObj 1-4

06Graph Theory Basic DefinitionsObj 1-5

Logic

4 lectures · Section 2.1–2.4

07Symbolic FormObj 2-1

08Logically Equivalent StatementsObj 2-2

09Testing Validity of ArgumentsObj 2-3

10Constructing CircuitsObj 2-4

Predicate Logic

3 lectures · Section 3.1–3.3

11Translating StatementsObj 3-1

12Negating a StatementObj 3-2

13Validity with Quantified StatementsObj 3-3

Proof Methods

2 lectures · Section 4.1–4.2

14Proving a Statement or CounterexampleObj 4-1

15Proof Writing TipsObj 4-2

Advanced Proof Techniques

3 lectures · Section 4.3–4.7

16Proof by CasesObj 5-1

17Proof by ContradictionObj 5-2

18Proof by ContrapositiveObj 5-3

Number Theory, Graph Degrees & Algorithms

3 lectures · Sections 4.4, 10.2, 11.1

19Number Theory ProofsObj 6-1

20Degree of a VertexObj 6-2

21Variables After an AlgorithmObj 6-3

Summation & Mathematical Induction

1 lecture · Sections 5.1–5.2

22Summation Notation & Mathematical InductionObj 7-1, 7-2, 7-3

Midterm Examination

No video lectures — covers Modules 1–7

Exam

Sequences

3 lectures · Section 5.7

23Recursively Defined SequencesObj 9-1

24Arithmetic & Geometric SequencesObj 9-2

25Proving a Sequence Formula by InductionObj 9-3

M10

Sets

2 lectures · Sections 6.1–6.2

26Operations on SetsObj 10-1

27Proving Statements About SetsObj 10-2

M11

Functions & Countability

2 lectures · Sections 7.1, 7.4

28Properties of FunctionsObj 11-1, 11-2, 11-3

29Proving a Set is CountableObj 11-4

M12

Relations & Modular Arithmetic

2 lectures · Sections 8.3–8.4

30Proving a Relation is an Equivalence RelationObj 12-1, 12-2, 12-3

31Modular ArithmeticObj 12-4

M13

Probability, Counting & Pigeonhole Principle

3 lectures · Sections 9.1, 9.2, 9.4

32Finding the Probability of an EventObj 13-1

33Possibility Trees & Counting RulesObj 13-2, 13-3

34The Pigeonhole PrincipleObj 13-4

M14

Combinations & Binomial Theorem

3 lectures · Sections 9.5–9.7

35R-CombinationsObj 14-1

36R-Combinations with RepetitionObj 14-2

37The Binomial TheoremObj 14-3

Course Learning Outcomes

Logic & Argumentation

Specify precise meaning of statements, demonstrate equivalence, and test the validity of arguments.

Proof Techniques

Construct and recognize valid proofs using direct proof, contradiction, contrapositive, and induction.

Summations & Sequences

Use summations and formulas for arithmetic and geometric sequences.

Sets & Functions

Explain and apply the concepts of sets, relations, and functions including countability.

Counting & Combinatorics

Apply counting principles to determine the number of combinatorial configurations.

These outcomes map directly to ABET criteria and align with QM Standard 2.1.

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Watch all 37 lectures free on YouTube, explore curated resources, or open the symbol and glossary reference.

Watch Playlist → Symbol Guide

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