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CS285: Discrete Math for Computing
الدروس المجانية
Sample Lesson
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الدروس المجانية
8 Topics
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
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0 – Introduction
2 Topics
0.1: Big Picture
0.2: How to Get an A+
1 – Foundation of Logic
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1 – Foundation of Logic
16 Topics
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
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2 – Revision for Foundations of Logic
6 Topics
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
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3 – Sets, Functions, and Sequences
31 Topics
3.1: Sets
3.2: Sets(2)
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
3.27: Matrices
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
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4 – Revision for Sets, Functions, & Sequences
8 Topics
4.1: Set Properties
4.2: Set Cardinality
4.3: Set Operations
4.4: Functions
4.5: Sequences
4.6: Summations
4.7: Recurrence Relations
4.8: Matrices
Sets, Functions, and Sequences – Study Guide
Major I
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Major I
10 Topics
1: Propositional Functions’ Truth Values & Evaluating Functions
2: Checking Primes, Evaluating Mod, & Matrix Operations
3: Mathematical Induction
4: Recursive Functions
5: Recursive Defenitions
6: Counting
7: Mathematical Induction
8: Functions
9: Relations
10: Set Operations
5 – Number Theory and Cryptography
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5 – Number Theory and Cryptography
14 Topics
5.1: Division
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
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6 – Revision for Nymber Theory & Cryptography
2 Topics
6.1: Number Theory
6.2: Cryptography
Number Theory and Cryptography – Study Guide
7 – Induction and Recursion
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7 – Induction and Recursion
6 Topics
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
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8 – Revision for Induction & Recursion
4 Topics
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 – Counting
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9 – Counting
11 Topics
9.1: Intro to Counting
9.2: Product Rule
9.3: Sum 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
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Counting Exercises
11 Topics
Tutorial(1)
Tutorial(2)
Tutorial(3)
Tutorial(4)
Tutorial(5)
Tutorial(6)
Tutorial(7)
Tutorial(8)
Tutorial(9)
Tutorial(10)
Tutorial(11)
10 – Revision for Counting
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10 – Revision for Counting
3 Topics
10.1: Counting Fundamentals
10.2: Permutations and Combinations
10.3: Binomial Coefficients
Counting – Study Guide
Major II
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Major II
11 Topics
1: Shift Cypher
2: Binomial Theorem
3: Counting
4: Equivalence Relations
Prime Factorization, GCD, & LCM
6: Prime Factorization, GCD, & LCM
7: Devision Algorithm & Modular Arithmetic
8: Binomial Algorithm
9: Counting
10: Shift Cypher
11: Mathematical Induction
12 – Advanced Counting
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12 – Advanced Counting
11 Topics
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
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13 – Relations
6 Topics
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
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14 – Revision for Relations
3 Topics
14.1: Relations
14.2: Representing Relations
14.3: Closures of Relations
Relations – Study Guide
15 – Graphs (Not included this semester)
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15 – Graphs (Not included this semester)
10 Topics
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)
Cheat Sheet
Final
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Final
10 Topics
1: Truth Table, Translation, Propositions, Proof, & Mathematical Induction
2: Summations, Functions’ Evaluation, Modular Arithmetic, & Boolean Matrices
3: Unified Union & Intersection & Counting
4: Binomial Algorithm
5: Relations
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
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16 – Live Sessions
7 Topics
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
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0.2: How to Get an A+
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CS285: Discrete Math for Computing
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