CS285: Discrete Math for Computing

ي مقرر CS285: Discrete Math for Computing، راح نتعلم الـ fundamentals اللي تشكل العمود الفقري لعلوم الـ Computer Science.

أ. عمر النقيب

أنا عمر النقيب، كنت طالب موهوب وحاصل على منحة دراسية كاملة من الابتدائي الين ما تخرجت من الثانوي من مؤسسة موهبة ضمن برنامج الشراكة مع المدارس. أدرس حاليا علوم الحاسب، وعملت كمدرب في مجالات متععدة. عملت كمدرب لاختبار القدرات في مؤسسة "أنا أسطوري", ولدي خبرة تدريبية واسعة في الدسكريت ماث بالذات، فعندي 4 دورات مختلفة من جامعات متعددة في الرياضيات المتقطعة والمنطق الرياضي. حياكم الله

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Course Content

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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

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0.1: Big Picture

0.2: How to Get an A

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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

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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

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4.1: Set Properties

4.2: Set Cardinality

4.3: Set Operations

4.6: Summations

4.7: Recurrence Relations

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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

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6.1: Number Theory

6.2: Cryptography

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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

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8.1: Mathematical Induction

8.2: Recursive Definitions

8.3: Exercise on Induction II

8.4: Exercise on Induction III

8.5: Recursive Definitions

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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

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10.1: Counting Fundamentals

10.2: Permutations and Combinations

10.3: Binomial Coefficients

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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)

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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 (not included in the final exam)

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)

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14.1: Relations

14.2: Representing Relations

14.3: Closures of Relations

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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)

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16.1: Chapter 1 (Quiz 1)

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

16.3: Final Review

Solving final 242 – 30/11/2025