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CS285: Discrete Math for Computing

الدروس المجانية Sample Lesson

Course Walkthrough – مهم جدددا

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 – مهم جدددا

1.1: Propositions

1.2: Converse, Inverse, & Counterpositive

1.3: Translating English to Propositions

1.5: Biconditional

1.6: Exercise on truth table

1.7: Logical Equivalence Laws

1.8: Exercises on Logical Equivalence

1.9: Consistency

1.10: Quantifiers

1.11: Negating Quantifiers

1.13: Predicate Logic

1.14: Rules of Inference

1.15: Quantified Rules of Inference

1.4: Exercise on Translating English to Propositions

1.12: Translating Quantified Expressions

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

3.7: Set Operations

3.8: Exersise on Set Operations

3.9: Extended Set Operations

3.10: Set Identities

3.11: Proving Set Identities

3.12: Functions

3.13: Functions(2)

3.14: Exercise on Functions

3.15: Inverse Functions

3.16: Composition of Functions

3.17: Sequences

3.18: Geometric Sequence

3.19: Guessing Sequences

3.20: Exercise on Guessing Sequences

3.21: Summation

3.22: Summation of Arithmetic Sequence

3.23: Summation of Geometric Sequence

3.24: Recurrence Relations

3.25: Recurrence Relations (2)

3.26: Exercise on Recurrence Relations

3.28: Adding Matrices

3.29: Multiplying Matrices

3.30: Matrix Conjunction & Disjunction

3.31: Properties of Matrices

3.6: 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

1: Propositional Functions’ Truth Values & Evaluating Functions

2: Checking Primes, Evaluating Mod, & Matrix Operations

3: Mathematical Induction

4: Recursive Functions

5: Recursive Defenitions

7: Mathematical Induction

10: Set Operations

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

5.9: Least Common Multiple

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

7.4: 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

9.10: 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

1: Shift Cypher

2: Binomial Theorem

4: Equivalence Relations

Prime Factorization, GCD, & LCM

6: Prime Factorization, GCD, & LCM

7: Devision Algorithm & Modular Arithmetic

8: Binomial Algorithm

10: Shift Cypher

11: Mathematical Induction

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

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

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)

1: Truth Table, Translation, Propositions, Proof, & Mathematical Induction

2: Summations, Functions’ Evaluation, Modular Arithmetic, & Boolean Matrices

3: Unified Union & Intersection & Counting

4: Binomial Algorithm

6: Truth Table, Quantifiers, & Propositions

7: Functions & Sets

Shift Cypher, Modular Arithmetic, Functions, Devision Algorithm, & Checking Primes

9: Counting, Recurrence Relations, & Recursive Defenitions

10: Equivalence Relations, Closures, & Mathematical Induction

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

1.6: Logical Equivalence Laws

⏱ 15:42

CS285: Discrete Math for Computing 499.00

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