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CS285: Discrete Math for Computing

الدروس المجانية Sample Lesson

Course Walkthrough – START HERE – مهم جدا

0.1: Big Picture

0.2: How to Get an A+

1.2: Converse, Inverse, & Counterpositive

1.4: Biconditional

1.6: Logical Equivalence Laws

Foundation of Logic – Study Guide

Number Theory and Cryptography – Study Guide

0 – Introduction

0.1: Big Picture

0.2: How to Get an A+

1 – Foundation of Logic

Course Walkthrough – START HERE – مهم جدا

1.1: Propositions

1.2: Converse, Inverse, & Counterpositive

1.3: Translating English to Propositions

1.4: Biconditional

1.5: Exercise on truth table

1.6: Logical Equivalence Laws

1.7: Exercises on Logical Equivalence

1.8: Consistency

1.10: Quantifiers

1.11: Negating Quantifiers

1.12: Nested Quantifiers

1.13: Exercise on Nested Quantifiers

1.14: Predicate Logic

1.15: Rules of Inference

1.16: Quantified Rules of Inference

1.17: Proofs (Not included this semester)

1.18: Direct Proof (Not included this semester)

1.19: Indirect Proof (Not included this semester)

1.20: Exercise on Indirect Proof (Not included this semester)

1.21: Proof by Contradiction (Not included this semester)

2 – Revision for Foundations of Logic

2.1: Propositions

2.2: Truth Tables

2.3: Proposition Translation & Consistency

2.4: Equivalence Proofs

2.5: Predicate Logic & Quantifiers

2.6: Rules of Inference

Foundation of Logic – Study Guide

3 – Sets, Functions, and Sequences

3.3: Set Equality and Subsets

3.4: Set Cardinality and Power Sets

3.5: Excercise on cardinality

3.6: Set Operations

3.7: Exersise on Set Operations

3.8: Extended Set Operations

3.9: Set Identities

3.10: Proving Set Identities

3.11: Functions

3.12: Functions(2)

3.13: Exercise on Functions

3.14: Inverse Functions

3.15: Composition of Functions

3.16: Sequences

3.17: Geometric Sequence

3.18: Guessing Sequences

3.19: Exercise on Guessing Sequences

3.20: Summation

3.21: Summation of Arithmetic Sequence

3.22: Summation of Geometric Sequence

3.23: Recurrence Relations

3.24: Recurrence Relations (2)

3.25: Exercise on Recurrence Relations

3.27: Adding Matrices

3.28: Multiplying Matrices

3.29: Matrix Conjunction & Disjunction

3.30: Properties of Matrices

10.1: Venn Diagrams

4 – Revision for Sets, Functions, & Sequences

4.1: Set Properties

4.2: Set Cardinality

4.3: Set Operations

4.6: Summations

4.7: Recurrence Relations

Sets, Functions, and Sequences – Study Guide

5 – Number Theory and Cryptography

5.2: Division Algorithm

5.3: Modular Arithmetic

5.4: Modular Arithmetic (2)

5.5: Prime Numbers

5.6: Trial Division

5.7: Greatest Common Divisor

5.8: Dividing Congruences

5.9: Least Common Multiple

5.10: Division Algorithm (2) (Not included this semester)

5.11: Euclidean Algorithm (Not included this semester)

5.12: Linear Combination (Not included this semester)

5.13: Linear Combination (2) (Not included this semester)

5.14: Inverse of Linear Congruence

5.15: Inverse Using Euclidean Algorithm (Not included this semester)

5.16: Solving Congruences Using Inverse (Not included this semester)

5.17: Chinese Theorem (Not included this semester)

5.18: Exercise on Chinese Theorem (Not included this semester)

5.19: Fermat’s Theorem (Not included this semester)

5.20: Euler’s Totient Function (Not included this semester)

5.21: Euler’s Generalization (Not included this semester)

UPCs (Not included this semester)

ISBN (Not included this semester)

5.22: Shift Cipher

5.23: Aphine Cypher

5.24: RSA Cryptosystem

5.25: Note on RSA

5.26: Diffie-Hellman Protocol

5.27: Digital Signatures

6 – Revision for Nymber Theory & Cryptography

6.1: Number Theory

6.2: Cryptography

Number Theory and Cryptography – Study Guide

7 – Induction and Recursion

7.1: Mathematical induction

7.2: Exercise on Induction

7.3: Strong Induction (Not Included This Semester)

7.4: Recursive Functions

7.5: Recursive Definitions

7.6: Exercise on Recursive Definitions

7.7: Proving Recursive Definitions

8 – Revision for Induction & Recursion

8.1: Mathematical Induction

8.3: Exercise on Induction II

8.4: Exercise on Induction III

8.5: Recursive Definitions

Induction and Recursion – Study Guide

9.1: Intro to Counting

9.2: Product Rule

9.4: Combining Sum and Product Rules

9.5: Permutations and Combinations

9.6: Permutations and Combinations with Repetition

9.7: Principle of Inclusion-Exclusion

9.8: Pigeonhole Principle

9.9: Exercise on Pigeonhole Principle

9.10: Indistinguishable Objects

9.11: Binomial Theorem

9.12: Binomial Theorem (2)

9.13: Useful Identity

Counting Exercises

10 – Revision for Counting

10.1: Counting Fundamentals

10.2: Permutations and Combinations

10.3: Binomial Coefficients

Counting – Study Guide

12 – Advanced Counting

12.1: Recurrence Relations

12.2: Recurrence Relations (2)

12.3: Degree of Recurrence Relations

12.4: Exercise on Recurrence Relations

12.5: Homogeneous Recurrence Relations

12.6: Solutions of Recurrence Relations

12.7: Solving Recurrence Relations

12.8: Exercise on Solving Recurrence Relations

12.9: General Rule for Recurrence Relations

12.10: Solving Non-Homogeneous Recurrence Relations

12.11: Exercise on Non-Homogeneous Recurrence Relations

12.12: Generating Functions (Not included this semester)

Advanced Counting Techniques – Study Guide

13 – Relations

13.1: Relations

13.2: Composition of Relations

13.3: Composition Using Matrices

13.4: Union and Intersection of Relations

13.5: Equivalence Relations

13.6: Proving Equivalence Relations

13.7: Equivalence Classes (Not included this semester)

13.8: Partial Ordering (Not included this semester)

13.9: Total Ordering (Not included this semester)

13.10: Hasse Diagram (Not included this semester)

13.11: Hasse Diagram (2) (Not included this semester)

14 – Revision for Relations

14.1: Relations

14.2: Representing Relations

14.3: Closures of Relations

Relations – Study Guide

15 – Graphs (Not included this semester)

15.1: Graphs (Not included this semester)

15.2: Graph Properties (Not included this semester)

15.3: Special Graphs (Not included this semester)

15.4: Regular Graphs (Not included this semester)

15.5: Bipartite Graphs (Not included this semester)

15.6: Representing Graphs (Not included this semester)

15.7: Adjacency List (Not included this semester)

15.8: Isomorphism (Not included this semester)

15.9: Graph Paths (Not included this semester)

15.10: Connectivity (Not included this semester)

16 – Live Sessions

16.1: Chapter 1 (Quiz 1)

16.2: Chapter 3,4,5 (Major II)

16.3: Major Review

16.4: Final Review

16.5: Final Revision 242

16.6: Solving final 242 – 30/11/2025

Final Revision 2026 2nd Semester

Previous Lesson

Course Walkthrough – START HERE – مهم جدا

⏱ 09:35

CS285: Discrete Math for Computing 499.00

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