Course Modules: COMP2711H (L1) - Honors Discrete Mathematical Tools for Computer Science

Lecture 1: Proposotional Logic (2 September 2024)

Lecture 1: Proposotional Logic (2 September 2024) Lecture 1: Proposotional Logic (2 September 2024)

Context Module Sub Header

Please read the syllabus! 1

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External Url

Lecture Video Lecture Video 2

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Attachment

Amir's Notes Amir's Notes 3

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Attachment

Xuran's Notes Xuran's Notes 5

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Context Module Sub Header

Reading: Chapter 2 of Grimaldi (Fundamentals of Logic) 6

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External Url

Video: Proofs Video: Proofs 7

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Lecture 2: Predicate Logic and Peano's Axioms (2 September 2024)

Lecture 2: Predicate Logic and Peano's Axioms (2 September 2024) Lecture 2: Predicate Logic and Peano's Axioms (2 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chapter 2 of Grimaldi (Fundamentals of Logic) 4

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External Url

Video: Peano Axioms Video: Peano Axioms 5

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Lecture 3: Induction, Well-ordering and Infinite Descent (4 September 2024)

Lecture 3: Induction, Well-ordering and Infinite Descent (4 September 2024) Lecture 3: Induction, Well-ordering and Infinite Descent (4 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Video: Induction Video: Induction 4

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External Url

Video: 2+2=4 Video: 2+2=4 5

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External Url

Reading: Mathematical Induction Reading: Mathematical Induction 6

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Attachment

Weekly Problem Set 1 Weekly Problem Set 1 7

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Lecture 4: Induction Problems and Strong Induction (9 September 2024)

Lecture 4: Induction Problems and Strong Induction (9 September 2024) Lecture 4: Induction Problems and Strong Induction (9 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: Strong Induction Video: Strong Induction 4

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External Url

Video: Proof by Strong Induction Video: Proof by Strong Induction 5

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Context Module Sub Header

Pause the videos whenever a problem is posed and try to solve it on your own first, before watching the solution. 6

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External Url

Video: Strong Induction Examples Video: Strong Induction Examples 7

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Context Module Sub Header

Reading: Chatpers 3 and 8 of Engel (The Extremal Principle, The Induction Principle) 8

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Context Module Sub Header

It is really important that you give **every** problem an honest and serious attempt before reading its solution. You must reach mastery in using mathematical induction and its equivalent forms. All of the future modules in this course depend on such mastery. 9

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Lecture 5: Solving More Induction Problems (9 September 2024)

Lecture 5: Solving More Induction Problems (9 September 2024) Lecture 5: Solving More Induction Problems (9 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: Induction Problems Video: Induction Problems 4

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Video: Divisibility Problems Solved by Induction Video: Divisibility Problems Solved by Induction 5

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Video: Epic Induction Video: Epic Induction 6

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Context Module Sub Header

Reading: Chatpers 3 and 8 of Engel (The Extremal Principle, The Induction Principle) 7

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Lecture 6: Counting, Permutations, Combinations, Balls and Walls (11 September 2024)

Lecture 6: Counting, Permutations, Combinations, Balls and Walls (11 September 2024) Lecture 6: Counting, Permutations, Combinations, Balls and Walls (11 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Context Module Sub Header

Reading: Chapter 1 of Grimaldi (Fundamental Principles of Counting) 4

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Context Module Sub Header

Reading: Chapter 1 of Chen and Koh (Permutations and Combinations) -- Very Important 5

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Context Module Sub Header

Reading: Chapter 1 of Ross (Combinatorial Analysis) 6

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Context Module Sub Header

It is crucial that you solve **every** exercise at the end of these chapters. 7

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Attachment

Weekly Problem Set 2 Weekly Problem Set 2 8

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External Url

Fun to Read: Which Rectangular Chessboards Have a Knight's Tour? Fun to Read: Which Rectangular Chessboards Have a Knight's Tour? 9

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Lecture 7: Solving Counting Problems (16 September 2024)

Lecture 7: Solving Counting Problems (16 September 2024) Lecture 7: Solving Counting Problems (16 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chapter 1 of Chen and Koh (Permutations and Combinations) -- Very Important 4

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Context Module Sub Header

Solve the first 24 Problems of Andreescu and Feng 5

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Lecture 8: More Counting (16 September 2024)

Lecture 8: More Counting (16 September 2024) Lecture 8: More Counting (16 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Attachment

Weekly Problem Set 3 Weekly Problem Set 3 4

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Context Module Sub Header

Solve Problems 25 to 51 of Andreescu and Feng 5

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Homework 1

Homework 1 Homework 1

Assignment

Homework 1 Homework 1 10 1

assignment 1433025 1

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TA Session 1 (20 September 2024)

TA Session 1 (20 September 2024) TA Session 1 (20 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Xuran's Notes (Solutions of Weekly Problem Set 1) Xuran's Notes (Solutions of Weekly Problem Set 1) 2

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Lecture 9: Principle of Inclusion and Exclusion (23 September 2024)

Lecture 9: Principle of Inclusion and Exclusion (23 September 2024) Lecture 9: Principle of Inclusion and Exclusion (23 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chaptes 2 and 4 of Chen and Koh (Binomial Coefficients, Inclusion-Exclusion) 4

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External Url

Video: Inclusion-Exclusion Example Video: Inclusion-Exclusion Example 5

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External Url

Video: 3-set PIE Video: 3-set PIE 6

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External Url

Video: Counting using PIE Video: Counting using PIE 7

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Lecture 10: Generalized Principle of Inclusion and Exclusion (23 September 2023)

Lecture 10: Generalized Principle of Inclusion and Exclusion (23 September 2023) Lecture 10: Generalized Principle of Inclusion and Exclusion (23 September 2023)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chaptes 2 and 4 of Chen and Koh (Binomial Coefficients, Inclusion-Exclusion) 4

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Context Module Sub Header

Reading: Chapter 8 of Grimaldi (Inclusion-Exclusion) 5

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External Url

Video: Inclusion-Exclusion Video: Inclusion-Exclusion 6

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External Url

Video: PIE Problems Video: PIE Problems 7

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External Url

Video: Generalized PIE Video: Generalized PIE 8

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External Url

Video: Derangements Video: Derangements 9

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Lecture 11: Pigeonhole Principle (25 September 2024)

Lecture 11: Pigeonhole Principle (25 September 2024) Lecture 11: Pigeonhole Principle (25 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chapter 3 of Chen and Koh (Pigeonhole and Ramsey) 4

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Context Module Sub Header

Reading: Chapter 4 of Engel (Box Principle) 5

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Context Module Sub Header

Solve Advanced Problems 1 to 15 of Andreescu and Feng 6

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External Url

Video: Pigeonhole Principle Video: Pigeonhole Principle 7

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External Url

Video: Pigeonhole Principle Examples Video: Pigeonhole Principle Examples 8

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External Url

Video: Pigeonhole Principle - Establishing a Pattern Video: Pigeonhole Principle - Establishing a Pattern 9

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External Url

Video: Pigeonhole Principle - Generalizing the Cases Video: Pigeonhole Principle - Generalizing the Cases 10

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External Url

Playlist: More Advanced Pigeonhole Principle Problems Playlist: More Advanced Pigeonhole Principle Problems 11

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Attachment

Weekly Problem Set 4 Weekly Problem Set 4 12

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TA Session 2 (27 September 2024)

TA Session 2 (27 September 2024) TA Session 2 (27 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Zhaorun's Notes Zhaorun's Notes 2

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Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024)

Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024) Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Context Module Sub Header

Reading: Sections 1.1 and 1.2 of West (What is a Graph?, Paths, Cycles and Trails) 4

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Context Module Sub Header

Most of the theorems we proved in class were from these sections, but the proofs are often different. So, you should read the book and also solve the exercises. 5

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External Url

Video Playlist: Introduction to Graph Theory Video Playlist: Introduction to Graph Theory 6

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External Url

Video Playlist: Watch Lectures 1 to 4 Video Playlist: Watch Lectures 1 to 4 7

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Lecture 13: More Theorems on Graphs and Trees (30 September 2024)

Lecture 13: More Theorems on Graphs and Trees (30 September 2024) Lecture 13: More Theorems on Graphs and Trees (30 September 2024)

External Url

Lecture Video Lecture Video 1

external_url 1437783 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Context Module Sub Header

Reading: Sections 1.3 and 1.4 of West (Vertex Degrees & Counting, Directed Graphs) 4

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Context Module Sub Header

When reading this text, read each theorem but try to prove it yourself first before reading the proof. Also, make sure you solve all the exercises. 5

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Context Module Sub Header

Solve Advanced Problems 16 to 30 of Andreescu and Feng 6

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External Url

Video Playlist: Watch from 10.1.1 to 11.1.1 Video Playlist: Watch from 10.1.1 to 11.1.1 7

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External Url

Recommended to Watch: Graph Theory Background Recommended to Watch: Graph Theory Background 8

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Lecture 14: Even More Theorems on Graphs and Trees (2 October 2024)

Lecture 14: Even More Theorems on Graphs and Trees (2 October 2024) Lecture 14: Even More Theorems on Graphs and Trees (2 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1437784 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Context Module Sub Header

Reading: Sections 2.1 and 2.2 of West (Trees and Distance: Basic Properties, Spanning Trees) 4

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External Url

Recommended to Watch: DFS and BFS Recommended to Watch: DFS and BFS 5

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Context Module Sub Header

Reading: Chapters 11 and 12 of Grimaldi (Graph Theory, Trees) 6

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Attachment

Weekly Problem Set 5 Weekly Problem Set 5 7

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TA Session 3 (4 October 2024)

TA Session 3 (4 October 2024) TA Session 3 (4 October 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Zhaorun's Notes Zhaorun's Notes 2

attachment 1438830 0

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External Url

Video: Recurrence for Number of Partitions Video: Recurrence for Number of Partitions 3

external_url 1439232 0

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Lecture 15: Minimum Spanning Trees, Directed Graphs, DAGs (7 October 2024)

Lecture 15: Minimum Spanning Trees, Directed Graphs, DAGs (7 October 2024) Lecture 15: Minimum Spanning Trees, Directed Graphs, DAGs (7 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1439296 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1439241 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1440089 0

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External Url

Video: Kruskal's Algorithm Video: Kruskal's Algorithm 4

external_url 1439249 0

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External Url

Video: Prim's Algorithm Video: Prim's Algorithm 5

external_url 1439252 0

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Context Module Sub Header

Before watching the next video, try to prove that Prim's algorithm is correct. Can you find a proof similar to the one we saw for Kruskal? 6

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External Url

Video: Minimum Spanning Trees Video: Minimum Spanning Trees 7

external_url 1439245 0

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Context Module Sub Header

Reading: Chapters 1 and 2 of West (Fundamental Concepts, Trees and Distance) 8

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Context Module Sub Header

You should read everything in these two chapters, including parts that are marked as "optional" in the book and solve all exercises. 9

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Context Module Sub Header

Solve Advanced Problems 31 to 40 of Andreescu and Feng 10

context_module_sub_header 1439279 0

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Lecture 16: Tree-based Algorithms and Huffman Coding (7 October 2024)

Lecture 16: Tree-based Algorithms and Huffman Coding (7 October 2024) Lecture 16: Tree-based Algorithms and Huffman Coding (7 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1439557 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1439534 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1440642 0

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Context Module Sub Header

Reading: Section 2.3 of West (Optimization and Trees) 4

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External Url

Video: Huffman Coding and Huffman Trees Video: Huffman Coding and Huffman Trees 5

external_url 1439543 0

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External Url

Video: Huffman Coding Example Video: Huffman Coding Example 6

external_url 1439546 0

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External Url

Recommended Video: Huffman Coding + Code Recommended Video: Huffman Coding + Code 7

external_url 1439549 0

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External Url

Recommended Video: Dynamic Programming on Trees Recommended Video: Dynamic Programming on Trees 8

external_url 1439550 0

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Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024)

Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024) Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

attachment 1440201 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1441118 0

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External Url

Video: BFS Visualized and Explained Video: BFS Visualized and Explained 4

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External Url

Video: Dijkstra's Algorithm Video: Dijkstra's Algorithm 5

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External Url

Video: Strongly Connected Components and Dijkstra's Algorithm Video: Strongly Connected Components and Dijkstra's Algorithm 6

external_url 1440473 0

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External Url

Video: Matchings Video: Matchings 7

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External Url

Video: Maximal and Maximum Matchings Video: Maximal and Maximum Matchings 8

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External Url

Video: Matchings and Augmenting Paths Video: Matchings and Augmenting Paths 9

external_url 1440520 0

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External Url

Video: Incremental Improvement - Matching Video: Incremental Improvement - Matching 10

external_url 1440514 0

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Attachment

Weekly Problem Set 6 Weekly Problem Set 6 11

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Homework 2

Homework 2 Homework 2

Assignment

Homework 2 Homework 2 10 1

assignment 1440609 1

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TA Session 4 (11 October 2024)

TA Session 4 (11 October 2024) TA Session 4 (11 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1441314 0

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Attachment

Xuran's Notes Xuran's Notes 2

attachment 1441306 0

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Lecture 18: Matchings, Vertex Covers, Edge Covers and Independent Sets (14 October 2024)

Lecture 18: Matchings, Vertex Covers, Edge Covers and Independent Sets (14 October 2024) Lecture 18: Matchings, Vertex Covers, Edge Covers and Independent Sets (14 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1441976 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1441591 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1442171 0

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Context Module Sub Header

Reading: Section 3.1 of West (Matchings and Covers) 4

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Lecture 19: Network Flow and the Ford-Fulkerson Algorithm (14 October 2024)

Lecture 19: Network Flow and the Ford-Fulkerson Algorithm (14 October 2024) Lecture 19: Network Flow and the Ford-Fulkerson Algorithm (14 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1443039 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1442832 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1443857 0

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Context Module Sub Header

Reading: Section 4.3 of West (Network Flow Problems) 4

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External Url

Video: Maximum Flow and Ford-Fulkerson Video: Maximum Flow and Ford-Fulkerson 5

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External Url

Video: Flow Networks and Maximum Flow Video: Flow Networks and Maximum Flow 6

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External Url

Video: Maximum-Flow Minimum-Cut Algorithm Video: Maximum-Flow Minimum-Cut Algorithm 7

external_url 1443085 0

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External Url

Video: Max-flow and Ford-Fulkerson Video: Max-flow and Ford-Fulkerson 8

external_url 1443087 0

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External Url

Video: Ford-Fulkerson in 5 minutes Video: Ford-Fulkerson in 5 minutes 9

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Lecture 20: Stable Matchings and Graph Coloring (16 October 2024)

Lecture 20: Stable Matchings and Graph Coloring (16 October 2024) Lecture 20: Stable Matchings and Graph Coloring (16 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1443041 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1442833 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1444336 0

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Context Module Sub Header

Reading: Subsection 3.2.3 of West (Stable Matchings) 4

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Context Module Sub Header

Reading: Section 5.1 of West (Vertex Colorings and Upper Bounds) -- Brooks' Theorem is not part of the syllabus 5

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External Url

Video: Introduction to Graph Colouring Video: Introduction to Graph Colouring 6

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External Url

Video: Coloring Code - How Compilers Use Graph Theory Video: Coloring Code - How Compilers Use Graph Theory 7

external_url 1443091 0

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External Url

Video: Applications of Graph Colouring Video: Applications of Graph Colouring 8

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Context Module Sub Header

Due to the midterm exam, there will be no weekly problem set or tutorial this week. 9

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Midterm Exam

Midterm Exam Midterm Exam

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Midterm Exam Midterm Exam 1

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External Url

Lecture Video Lecture Video 2

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Amir's Notes Amir's Notes 3

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Xuran's Notes Xuran's Notes 4

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Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024)

Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024) Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024)

External Url

Lecture Video Lecture Video 1

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Amir's Notes Amir's Notes 2

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Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chapters 1 and 2 of Burton (Preliminaries, Divisibility Theory) 4

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External Url

Video: Number Theory I Video: Number Theory I 5

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External Url

Playlist: Introduction to Number Theory (Watch Lectures 3 and 4) Playlist: Introduction to Number Theory (Watch Lectures 3 and 4) 6

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Lecture 22: Prime Factorizations and the Fundamental Theorem of Arithmetic (21 October 2024)

Lecture 22: Prime Factorizations and the Fundamental Theorem of Arithmetic (21 October 2024) Lecture 22: Prime Factorizations and the Fundamental Theorem of Arithmetic (21 October 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Sections 2.4 to 3.3 of Burton (Euclid to Goldbach) 4

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External Url

Video: Primes Video: Primes 5

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External Url

Solve Problems 1 to 10 of ProjectEuler.net Solve Problems 1 to 10 of ProjectEuler.net 6

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External Url

Fun to read: Collatz Conjecture Fun to read: Collatz Conjecture 7

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Lecture 23: Congruence, Modular Multiplicative Inverse and the Chinese Remainder Theorem (23 October 2024)

Lecture 23: Congruence, Modular Multiplicative Inverse and the Chinese Remainder Theorem (23 October 2024) Lecture 23: Congruence, Modular Multiplicative Inverse and the Chinese Remainder Theorem (23 October 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chapter 4 of Burton (Congruences) 4

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Context Module Sub Header

It is really important that you read the book since it provides different proofs than the ones covered in the lecture. 5

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External Url

Video Playlist: Chinese Remainder Theorem Video Playlist: Chinese Remainder Theorem 6

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Context Module Sub Header

Make sure you watch all of this playlist, especially the last video. 7

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Attachment

Weekly Problem Set 7 Weekly Problem Set 7 8

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External Url

Solve Problems 14, 20, 27, 47, 50, 69, 77, 112, 122 and 451 of ProjectEuler.net Solve Problems 14, 20, 27, 47, 50, 69, 77, 112, 122 and 451 of ProjectEuler.net 9

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TA Session 5 (25 October 2024)

TA Session 5 (25 October 2024) TA Session 5 (25 October 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Xuran's Notes Xuran's Notes 2

attachment 1450121 0

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Lecture 24: Fermat's Little Theorem, Euler's Theorem, Wilson's theorem (28 October 2024)

Lecture 24: Fermat's Little Theorem, Euler's Theorem, Wilson's theorem (28 October 2024) Lecture 24: Fermat's Little Theorem, Euler's Theorem, Wilson's theorem (28 October 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Attachment

cycles.cpp cycles.cpp 4

attachment 1450160 0

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External Url

Video: Order of an integer modulo n Video: Order of an integer modulo n 5

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External Url

Video: Fermat's Little Theorem Video: Fermat's Little Theorem 6

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External Url

Video: Euler's Theorem Video: Euler's Theorem 7

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External Url

Video: Wilson's Theorem Video: Wilson's Theorem 8

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External Url

Playlist: Introduction to Number Theory (Watch Lectures 5 to 14, Primes to Euler's Totient) Playlist: Introduction to Number Theory (Watch Lectures 5 to 14, Primes to Euler's Totient) 9

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External Url

Video: COMP 4541's Number Theory Tutorial - Part II Video: COMP 4541's Number Theory Tutorial - Part II 10

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External Url

Video: Proof that the Totient Function is Multiplicative Video: Proof that the Totient Function is Multiplicative 11

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External Url

Video: Explicit Formula for Euler's Totient Function Video: Explicit Formula for Euler's Totient Function 12

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External Url

Video: Euler's Totient Theorem and Fermat's Little Theorem Video: Euler's Totient Theorem and Fermat's Little Theorem 13

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Context Module Sub Header

Reading: Chapters 5 and 7 of Burton (Fermat's Theorem, Euler's Generalization of Fermat's Theorem) 14

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Lecture 25: Diffie-Hellman-Merkle Key Exchange and ElGamal Encryption (28 October 2024)

Lecture 25: Diffie-Hellman-Merkle Key Exchange and ElGamal Encryption (28 October 2024) Lecture 25: Diffie-Hellman-Merkle Key Exchange and ElGamal Encryption (28 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1450162 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1450129 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: Secret Key Exchange Video: Secret Key Exchange 4

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External Url

Video: The Mathematics behind Diffie-Hellman Video: The Mathematics behind Diffie-Hellman 5

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External Url

Video: COMP 4541's Diffie-Hellman Lecture Video: COMP 4541's Diffie-Hellman Lecture 6

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External Url

Video: COMP 4541's Number Theory Tutorial - Part I Video: COMP 4541's Number Theory Tutorial - Part I 7

external_url 1450142 0

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External Url

Video: COMP 4541's ElGamal Lecture Video: COMP 4541's ElGamal Lecture 8

external_url 1450141 0

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External Url

Video: ElGamal Encryption Video: ElGamal Encryption 9

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Context Module Sub Header

Recommended Reading: Chapter 10 of Burton (Intro to Crypto) 10

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Lecture 26: RSA Encryption and Digital Signatures (30 October 2024)

Lecture 26: RSA Encryption and Digital Signatures (30 October 2024) Lecture 26: RSA Encryption and Digital Signatures (30 October 2024)

External Url

Lecture Video Lecture Video 1

external_url 1450810 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1450789 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: Breaking RSA Video: Breaking RSA 4

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Video: What are Digital Signatures? Video: What are Digital Signatures? 5

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External Url

Video: COMP 4541's RSA Lecture Video: COMP 4541's RSA Lecture 6

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External Url

Video: COMP 4541's Digital Signatures Lecture Video: COMP 4541's Digital Signatures Lecture 7

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Video: The RSA Cryptosystem and Efficient Exponentiation Video: The RSA Cryptosystem and Efficient Exponentiation 8

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Video: Diffie-Hellman Key Exchange and the Discrete Log Problem Video: Diffie-Hellman Key Exchange and the Discrete Log Problem 9

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External Url

Reading: Side-channel Attacks (Wikipedia) Reading: Side-channel Attacks (Wikipedia) 10

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External Url

Reading: Power Analysis (Wikipedia) Reading: Power Analysis (Wikipedia) 11

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Attachment

Weekly Problem Set 8 Weekly Problem Set 8 12

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TA Session 6 (1 November 2024)

TA Session 6 (1 November 2024) TA Session 6 (1 November 2024)

External Url

Lecture Video Lecture Video 1

external_url 1452108 0

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External Url

Lecture Video: Addendum on Problem 3 Lecture Video: Addendum on Problem 3 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Lecture 27: Russell's Paradox and Zermelo–Fraenkel Axioms (4 November 2024)

Lecture 27: Russell's Paradox and Zermelo–Fraenkel Axioms (4 November 2024) Lecture 27: Russell's Paradox and Zermelo–Fraenkel Axioms (4 November 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Video Playlist: Intro to Set Theory (Watch the first 10 lectures) Video Playlist: Intro to Set Theory (Watch the first 10 lectures) 4

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Lecture 28: Axiom of Infinity and Bijections (4 November 2024)

Lecture 28: Axiom of Infinity and Bijections (4 November 2024) Lecture 28: Axiom of Infinity and Bijections (4 November 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Reading: Oxford Lecture Notes on Set Theory (Pages 1-20) Reading: Oxford Lecture Notes on Set Theory (Pages 1-20) 4

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External Url

Video: Hilbert Hotel Video: Hilbert Hotel 5

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Lecture 29: Countability and the Theorems of Cantor, Tarski and Schröder–Bernstein (6 November 2024)

Lecture 29: Countability and the Theorems of Cantor, Tarski and Schröder–Bernstein (6 November 2024) Lecture 29: Countability and the Theorems of Cantor, Tarski and Schröder–Bernstein (6 November 2024)

External Url

Lecture Video Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Reading: Oxford Lecture Notes on Set Theory (Pages 1-26) Reading: Oxford Lecture Notes on Set Theory (Pages 1-26) 4

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Attachment

Weekly Problem Set 9 Weekly Problem Set 9 5

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TA Session 7 (8 November 2024)

TA Session 7 (8 November 2024) TA Session 7 (8 November 2024)

External Url

Lecture Video Lecture Video 1

external_url 1454552 0

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Attachment

Xuran's Notes Xuran's Notes 2

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Homework 3

Homework 3 Homework 3

Assignment

Homework 3 Homework 3 10 1

assignment 1454755 1

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Lecture 30: The Set of Real Numbers (11 November 2024)

Lecture 30: The Set of Real Numbers (11 November 2024) Lecture 30: The Set of Real Numbers (11 November 2024)

External Url

Lecture Video Lecture Video 1

external_url 1455133 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: Real Numbers Video: Real Numbers 4

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External Url

Video: Equinumerosity Video: Equinumerosity 5

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Lecture 31: |ℝ|=|P(ℕ)| and the Axiom of Choice (11 November 2024)

Lecture 31: |ℝ|=|P(ℕ)| and the Axiom of Choice (11 November 2024) Lecture 31: |ℝ|=|P(ℕ)| and the Axiom of Choice (11 November 2024)

External Url

Lecture Video Lecture Video 1

external_url 1455191 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: The Halting Problem (Watch the first 18 minutes) Video: The Halting Problem (Watch the first 18 minutes) 4

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External Url

Video: Cardinality of the Continuum Video: Cardinality of the Continuum 5

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External Url

Video: Comparability of Cardinals Video: Comparability of Cardinals 6

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External Url

Video: Axiom of Choice Video: Axiom of Choice 7

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External Url

Recommended: History of the Axiom of Choice Recommended: History of the Axiom of Choice 8

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External Url

Recommended to Read: Banach–Tarski Paradox Recommended to Read: Banach–Tarski Paradox 9

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Lecture 32: Introduction to Probability Theory (13 November 2024)

Lecture 32: Introduction to Probability Theory (13 November 2024) Lecture 32: Introduction to Probability Theory (13 November 2024)

External Url

Lecture Video Lecture Video 1

external_url 1457434 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Attachment

coin.cpp coin.cpp 4

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Attachment

doors.cpp doors.cpp 5

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Attachment

sleeping.cpp sleeping.cpp 6

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Attachment

cancer.cpp cancer.cpp 7

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Context Module Sub Header

Reading: Chapter 2 of Ross (Axioms of Probability), including sections marked by * 8

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Attachment

Weekly Problem Set 10 Weekly Problem Set 10 9

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TA Session 8 (15 November 2024)

TA Session 8 (15 November 2024) TA Session 8 (15 November 2024)

External Url

Lecture Video Lecture Video 1

external_url 1457431 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 2

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Lecture 33: Conditional Probability, Independence and Expectation (18 November 2024)

Lecture 33: Conditional Probability, Independence and Expectation (18 November 2024) Lecture 33: Conditional Probability, Independence and Expectation (18 November 2024)

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Lecture Video Lecture Video 1

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Amir's Notes Amir's Notes 2

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Xuran's Notes Xuran's Notes 3

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Read: The Monty Hall Problem Read: The Monty Hall Problem 4

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Read: The Sleeping Beauty Problem Read: The Sleeping Beauty Problem 5

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Watch: Philosophers are not smart enough for probability theory! Watch: Philosophers are not smart enough for probability theory! 6

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Context Module Sub Header

Reading: Chapters 3 and 4 of Ross (Conditional Probability, Independence, Random Variables) 7

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Context Module Sub Header

Note: We did not cover variance and common probability distributions in the lectures (due to being too easy), but they are part of the syllabus. So, make sure you read everything in these chapters. 8

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Video: Bayes Theorem Video: Bayes Theorem 9

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Video: The Bayesian Trap Video: The Bayesian Trap 10

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Lecture 34: Solving Problems using Linearity of Expectation (18 November 2024)

Lecture 34: Solving Problems using Linearity of Expectation (18 November 2024) Lecture 34: Solving Problems using Linearity of Expectation (18 November 2024)

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Lecture Video Lecture Video 1

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Amir's Notes Amir's Notes 2

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Xuran's Notes Xuran's Notes 3

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Video: Linearity of Expectation Video: Linearity of Expectation 4

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Video: Expectation, Indicator Random Variables, Linearity Video: Expectation, Indicator Random Variables, Linearity 5

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Video: Expectation Video: Expectation 6

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Lecture 35: Markov Chains (20 November 2024)

Lecture 35: Markov Chains (20 November 2024) Lecture 35: Markov Chains (20 November 2024)

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Lecture Video Lecture Video 1

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Amir's Notes Amir's Notes 2

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External Url

Video: Markov Chains Video: Markov Chains 3

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Video: Recurrence and Irreducibility Video: Recurrence and Irreducibility 4

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Video: n-step Transition Matrix Video: n-step Transition Matrix 5

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Video: Markov Decision Processes Video: Markov Decision Processes 6

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Recommended to Read: What Amir does when he is not teaching Recommended to Read: What Amir does when he is not teaching 7

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Weekly Problem Set 11 Weekly Problem Set 11 8

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Homework 4

Homework 4 Homework 4

Assignment

Homework 4 Homework 4 10 1

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Course Modules

Lecture 1: Proposotional Logic (2 September 2024)

Please read the syllabus! 1

Reading: Chapter 2 of Grimaldi (Fundamentals of Logic) 6

Lecture 2: Predicate Logic and Peano's Axioms (2 September 2024)

Reading: Chapter 2 of Grimaldi (Fundamentals of Logic) 4

Lecture 3: Induction, Well-ordering and Infinite Descent (4 September 2024)

Lecture 4: Induction Problems and Strong Induction (9 September 2024)

Pause the videos whenever a problem is posed and try to solve it on your own first, before watching the solution. 6

Reading: Chatpers 3 and 8 of Engel (The Extremal Principle, The Induction Principle) 8

It is really important that you give **every** problem an honest and serious attempt before reading its solution. You must reach mastery in using mathematical induction and its equivalent forms. All of the future modules in this course depend on such mastery. 9

Lecture 5: Solving More Induction Problems (9 September 2024)

Reading: Chatpers 3 and 8 of Engel (The Extremal Principle, The Induction Principle) 7

Lecture 6: Counting, Permutations, Combinations, Balls and Walls (11 September 2024)

Reading: Chapter 1 of Grimaldi (Fundamental Principles of Counting) 4

Reading: Chapter 1 of Chen and Koh (Permutations and Combinations) -- Very Important 5

Reading: Chapter 1 of Ross (Combinatorial Analysis) 6

It is crucial that you solve **every** exercise at the end of these chapters. 7

Lecture 7: Solving Counting Problems (16 September 2024)

Reading: Chapter 1 of Chen and Koh (Permutations and Combinations) -- Very Important 4

Solve the first 24 Problems of Andreescu and Feng 5

Lecture 8: More Counting (16 September 2024)

Solve Problems 25 to 51 of Andreescu and Feng 5

Homework 1

TA Session 1 (20 September 2024)

Lecture 9: Principle of Inclusion and Exclusion (23 September 2024)

Reading: Chaptes 2 and 4 of Chen and Koh (Binomial Coefficients, Inclusion-Exclusion) 4

Lecture 10: Generalized Principle of Inclusion and Exclusion (23 September 2023)

Reading: Chaptes 2 and 4 of Chen and Koh (Binomial Coefficients, Inclusion-Exclusion) 4

Reading: Chapter 8 of Grimaldi (Inclusion-Exclusion) 5

Lecture 11: Pigeonhole Principle (25 September 2024)

Reading: Chapter 3 of Chen and Koh (Pigeonhole and Ramsey) 4

Reading: Chapter 4 of Engel (Box Principle) 5

Solve Advanced Problems 1 to 15 of Andreescu and Feng 6

TA Session 2 (27 September 2024)

Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024)

Reading: Sections 1.1 and 1.2 of West (What is a Graph?, Paths, Cycles and Trails) 4

Most of the theorems we proved in class were from these sections, but the proofs are often different. So, you should read the book and also solve the exercises. 5

Lecture 13: More Theorems on Graphs and Trees (30 September 2024)

Reading: Sections 1.3 and 1.4 of West (Vertex Degrees & Counting, Directed Graphs) 4

When reading this text, read each theorem but try to prove it yourself first before reading the proof. Also, make sure you solve all the exercises. 5

Solve Advanced Problems 16 to 30 of Andreescu and Feng 6

Lecture 14: Even More Theorems on Graphs and Trees (2 October 2024)

Reading: Sections 2.1 and 2.2 of West (Trees and Distance: Basic Properties, Spanning Trees) 4

Reading: Chapters 11 and 12 of Grimaldi (Graph Theory, Trees) 6

TA Session 3 (4 October 2024)

Lecture 15: Minimum Spanning Trees, Directed Graphs, DAGs (7 October 2024)

Before watching the next video, try to prove that Prim's algorithm is correct. Can you find a proof similar to the one we saw for Kruskal? 6

Reading: Chapters 1 and 2 of West (Fundamental Concepts, Trees and Distance) 8

You should read everything in these two chapters, including parts that are marked as "optional" in the book and solve all exercises. 9

Solve Advanced Problems 31 to 40 of Andreescu and Feng 10

Lecture 16: Tree-based Algorithms and Huffman Coding (7 October 2024)

Reading: Section 2.3 of West (Optimization and Trees) 4

Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024)

Homework 2

TA Session 4 (11 October 2024)

Lecture 18: Matchings, Vertex Covers, Edge Covers and Independent Sets (14 October 2024)

Reading: Section 3.1 of West (Matchings and Covers) 4

Lecture 19: Network Flow and the Ford-Fulkerson Algorithm (14 October 2024)

Reading: Section 4.3 of West (Network Flow Problems) 4

Lecture 20: Stable Matchings and Graph Coloring (16 October 2024)

Reading: Subsection 3.2.3 of West (Stable Matchings) 4

Reading: Section 5.1 of West (Vertex Colorings and Upper Bounds) -- Brooks' Theorem is not part of the syllabus 5

Due to the midterm exam, there will be no weekly problem set or tutorial this week. 9

Midterm Exam

Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024)

Reading: Chapters 1 and 2 of Burton (Preliminaries, Divisibility Theory) 4

Lecture 22: Prime Factorizations and the Fundamental Theorem of Arithmetic (21 October 2024)

Reading: Sections 2.4 to 3.3 of Burton (Euclid to Goldbach) 4

Lecture 23: Congruence, Modular Multiplicative Inverse and the Chinese Remainder Theorem (23 October 2024)

Reading: Chapter 4 of Burton (Congruences) 4

It is really important that you read the book since it provides different proofs than the ones covered in the lecture. 5

Make sure you watch all of this playlist, especially the last video. 7

TA Session 5 (25 October 2024)

Lecture 24: Fermat's Little Theorem, Euler's Theorem, Wilson's theorem (28 October 2024)

Reading: Chapters 5 and 7 of Burton (Fermat's Theorem, Euler's Generalization of Fermat's Theorem) 14

Lecture 25: Diffie-Hellman-Merkle Key Exchange and ElGamal Encryption (28 October 2024)

Recommended Reading: Chapter 10 of Burton (Intro to Crypto) 10

Lecture 26: RSA Encryption and Digital Signatures (30 October 2024)

TA Session 6 (1 November 2024)

It is really important that you give every problem an honest and serious attempt before reading its solution. You must reach mastery in using mathematical induction and its equivalent forms. All of the future modules in this course depend on such mastery. 9

It is crucial that you solve every exercise at the end of these chapters. 7