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CS285: Discrete Math for Computing
الدروس المجانية
Sample Lesson
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الدروس المجانية
8 Topics
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
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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
22 Topics
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
1.9: DNF & CNF
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
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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
3.6: 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
3.26: Matrices
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
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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
11 Topics
Major I (1)
Major I (2)
Major I (3)
Major I (4)
Major I (5)
Major I (6)
Major I (7)
Major I (8)
Major I (9)
Major I (10)
Major I (11)
5 – Number Theory and Cryptography
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5 – Number Theory and Cryptography
29 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
5.8: 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
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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
7 Topics
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
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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
13 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
9.8: 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
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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
Major II (1)
Major II (2)
Major II (3)
Major II (4)
Major II (5)
Major II (6)
Major II (7)
Major II (8)
Major II (9)
Major II (10)
Major II (11)
12 – Advanced Counting
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12 – Advanced Counting
12 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
12.12: Generating Functions (Not included this semester)
Advanced Counting Techniques – Study Guide
13 – Relations
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13 – Relations
11 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
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
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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
Final (1)
Final (2)
Final (3)
Final (4)
Final (5)
Final (6)
Final (7)
Final (8)
Final (9)
Final (10)
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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Course Walkthrough – START HERE – مهم جدا
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CS285: Discrete Math for Computing
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