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

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

Course Modules

Lecture 1: Proposotional Logic (2 September 2024)

Lecture 1: Proposotional Logic (2 September 2024)
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Lecture 1: Proposotional Logic (2 September 2024) 214187  
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    Please read the syllabus!

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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Reading: Chapter 2 of Grimaldi (Fundamentals of Logic)

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    Video: Proofs Video: Proofs
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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)
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Lecture 2: Predicate Logic and Peano's Axioms (2 September 2024) 214188  
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Reading: Chapter 2 of Grimaldi (Fundamentals of Logic)

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    Video: Peano Axioms Video: Peano Axioms
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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)
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Lecture 3: Induction, Well-ordering and Infinite Descent (4 September 2024) 214490  
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Video: Induction Video: Induction
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    Video: 2+2=4 Video: 2+2=4
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    Reading: Mathematical Induction Reading: Mathematical Induction
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    Weekly Problem Set 1 Weekly Problem Set 1
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Lecture 4: Induction Problems and Strong Induction (9 September 2024)

Lecture 4: Induction Problems and Strong Induction (9 September 2024)
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Lecture 4: Induction Problems and Strong Induction (9 September 2024) 214796  
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Zhaorun's Notes Zhaorun's Notes
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    Video: Strong Induction Video: Strong Induction
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    Video: Proof by Strong Induction Video: Proof by Strong Induction
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    Pause the videos whenever a problem is posed and try to solve it on your own first, before watching the solution.

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

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    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.

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

Lecture 5: Solving More Induction Problems (9 September 2024)
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Lecture 5: Solving More Induction Problems (9 September 2024) 215183  
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Zhaorun's Notes Zhaorun's Notes
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    Video: Induction Problems Video: Induction Problems
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    Video: Divisibility Problems Solved by Induction Video: Divisibility Problems Solved by Induction
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    Video: Epic Induction Video: Epic Induction
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    Reading: Chatpers 3 and 8 of Engel (The Extremal Principle, The Induction Principle)

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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)
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Lecture 6: Counting, Permutations, Combinations, Balls and Walls (11 September 2024) 215205  
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Zhaorun's Notes Zhaorun's Notes
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    Reading: Chapter 1 of Grimaldi (Fundamental Principles of Counting)

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

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    Reading: Chapter 1 of Ross (Combinatorial Analysis)

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

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    Weekly Problem Set 2 Weekly Problem Set 2
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    Fun to Read: Which Rectangular Chessboards Have a Knight's Tour? Fun to Read: Which Rectangular Chessboards Have a Knight's Tour?
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Lecture 7: Solving Counting Problems (16 September 2024)

Lecture 7: Solving Counting Problems (16 September 2024)
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Reading: Chapter 1 of Chen and Koh (Permutations and Combinations) -- Very Important

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    Solve the first 24 Problems of Andreescu and Feng

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Lecture 8: More Counting (16 September 2024)

Lecture 8: More Counting (16 September 2024)
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Lecture 8: More Counting (16 September 2024) 215472  
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Weekly Problem Set 3 Weekly Problem Set 3
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    Solve Problems 25 to 51 of Andreescu and Feng

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Homework 1

Homework 1
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Homework 1 215737  
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    Homework 1 Homework 1
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TA Session 1 (20 September 2024)

TA Session 1 (20 September 2024)
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TA Session 1 (20 September 2024) 215748  
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    Xuran's Notes (Solutions of Weekly Problem Set 1) Xuran's Notes (Solutions of Weekly Problem Set 1)
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Lecture 9: Principle of Inclusion and Exclusion (23 September 2024)

Lecture 9: Principle of Inclusion and Exclusion (23 September 2024)
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Reading: Chaptes 2 and 4 of Chen and Koh (Binomial Coefficients, Inclusion-Exclusion)

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    Video: Inclusion-Exclusion Example Video: Inclusion-Exclusion Example
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    Video: 3-set PIE Video: 3-set PIE
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    Video: Counting using PIE Video: Counting using PIE
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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)
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Reading: Chaptes 2 and 4 of Chen and Koh (Binomial Coefficients, Inclusion-Exclusion)

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    Reading: Chapter 8 of Grimaldi (Inclusion-Exclusion)

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    Video: Inclusion-Exclusion Video: Inclusion-Exclusion
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    Video: PIE Problems Video: PIE Problems
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    Video: Generalized PIE Video: Generalized PIE
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    Video: Derangements Video: Derangements
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Lecture 11: Pigeonhole Principle (25 September 2024)

Lecture 11: Pigeonhole Principle (25 September 2024)
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Reading: Chapter 3 of Chen and Koh (Pigeonhole and Ramsey)

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    Reading: Chapter 4 of Engel (Box Principle)

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    Solve Advanced Problems 1 to 15 of Andreescu and Feng

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    Video: Pigeonhole Principle Video: Pigeonhole Principle
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    Video: Pigeonhole Principle Examples Video: Pigeonhole Principle Examples
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    Video: Pigeonhole Principle - Establishing a Pattern Video: Pigeonhole Principle - Establishing a Pattern
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    Video: Pigeonhole Principle - Generalizing the Cases Video: Pigeonhole Principle - Generalizing the Cases
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    Playlist: More Advanced Pigeonhole Principle Problems Playlist: More Advanced Pigeonhole Principle Problems
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    Weekly Problem Set 4 Weekly Problem Set 4
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TA Session 2 (27 September 2024)

TA Session 2 (27 September 2024)
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TA Session 2 (27 September 2024) 216112  
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Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024)

Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024)
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    Amir's Notes Amir's Notes
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    Reading: Sections 1.1 and 1.2 of West (What is a Graph?, Paths, Cycles and Trails)

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    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.

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    Video Playlist: Introduction to Graph Theory Video Playlist: Introduction to Graph Theory
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    Video Playlist: Watch Lectures 1 to 4 Video Playlist: Watch Lectures 1 to 4
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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)
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    Amir's Notes Amir's Notes
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    Zhaorun's Notes Zhaorun's Notes
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    Reading: Sections 1.3 and 1.4 of West (Vertex Degrees & Counting, Directed Graphs)

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    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.

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    Solve Advanced Problems 16 to 30 of Andreescu and Feng

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    Video Playlist: Watch from 10.1.1 to 11.1.1 Video Playlist: Watch from 10.1.1 to 11.1.1
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    Recommended to Watch: Graph Theory Background Recommended to Watch: Graph Theory Background
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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)
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    Amir's Notes Amir's Notes
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    Reading: Sections 2.1 and 2.2 of West (Trees and Distance: Basic Properties, Spanning Trees)

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    Recommended to Watch: DFS and BFS Recommended to Watch: DFS and BFS
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    Reading: Chapters 11 and 12 of Grimaldi (Graph Theory, Trees)

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    Weekly Problem Set 5 Weekly Problem Set 5
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TA Session 3 (4 October 2024)

TA Session 3 (4 October 2024)
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TA Session 3 (4 October 2024) 216270  
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    Lecture Video Lecture Video
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    Zhaorun's Notes Zhaorun's Notes
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    Video: Recurrence for Number of Partitions Video: Recurrence for Number of Partitions
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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)
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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  • External Url
    Video: Kruskal's Algorithm Video: Kruskal's Algorithm
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    Video: Prim's Algorithm Video: Prim's Algorithm
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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?

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    Video: Minimum Spanning Trees Video: Minimum Spanning Trees
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  • Context Module Sub Header

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

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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.

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  • Context Module Sub Header

    Solve Advanced Problems 31 to 40 of Andreescu and Feng

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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)
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Reading: Section 2.3 of West (Optimization and Trees)

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    Video: Huffman Coding and Huffman Trees Video: Huffman Coding and Huffman Trees
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    Video: Huffman Coding Example Video: Huffman Coding Example
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    Recommended Video: Huffman Coding + Code Recommended Video: Huffman Coding + Code
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    Recommended Video: Dynamic Programming on Trees Recommended Video: Dynamic Programming on Trees
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Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024)

Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024)
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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    Video: BFS Visualized and Explained Video: BFS Visualized and Explained
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    Video: Dijkstra's Algorithm Video: Dijkstra's Algorithm
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    Video: Strongly Connected Components and Dijkstra's Algorithm Video: Strongly Connected Components and Dijkstra's Algorithm
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    Video: Matchings Video: Matchings
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    Video: Maximal and Maximum Matchings Video: Maximal and Maximum Matchings
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    Video: Matchings and Augmenting Paths Video: Matchings and Augmenting Paths
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    Video: Incremental Improvement - Matching Video: Incremental Improvement - Matching
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    Weekly Problem Set 6 Weekly Problem Set 6
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Homework 2

Homework 2
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Homework 2 216472  
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    Homework 2 Homework 2
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TA Session 4 (11 October 2024)

TA Session 4 (11 October 2024)
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TA Session 4 (11 October 2024) 216558  
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    Lecture Video Lecture Video
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    Xuran's Notes Xuran's Notes
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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)
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Lecture 18: Matchings, Vertex Covers, Edge Covers and Independent Sets (14 October 2024) 216593  
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    Amir's Notes Amir's Notes
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    Zhaorun's Notes Zhaorun's Notes
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  • Context Module Sub Header

    Reading: Section 3.1 of West (Matchings and Covers)

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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)
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    Amir's Notes Amir's Notes
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    Zhaorun's Notes Zhaorun's Notes
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  • Context Module Sub Header

    Reading: Section 4.3 of West (Network Flow Problems)

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    Video: Maximum Flow and Ford-Fulkerson Video: Maximum Flow and Ford-Fulkerson
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    Video: Flow Networks and Maximum Flow Video: Flow Networks and Maximum Flow
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    Video: Maximum-Flow Minimum-Cut Algorithm Video: Maximum-Flow Minimum-Cut Algorithm
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    Video: Max-flow and Ford-Fulkerson Video: Max-flow and Ford-Fulkerson
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    Video: Ford-Fulkerson in 5 minutes Video: Ford-Fulkerson in 5 minutes
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Lecture 20: Stable Matchings and Graph Coloring (16 October 2024)

Lecture 20: Stable Matchings and Graph Coloring (16 October 2024)
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    Amir's Notes Amir's Notes
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    Zhaorun's Notes Zhaorun's Notes
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  • Context Module Sub Header

    Reading: Subsection 3.2.3 of West (Stable Matchings)

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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

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    Video: Introduction to Graph Colouring Video: Introduction to Graph Colouring
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    Video: Coloring Code - How Compilers Use Graph Theory Video: Coloring Code - How Compilers Use Graph Theory
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    Video: Applications of Graph Colouring Video: Applications of Graph Colouring
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  • Context Module Sub Header

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

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Midterm Exam

Midterm Exam
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Midterm Exam 216834  
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    Midterm Exam Midterm Exam
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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    Xuran's Notes Xuran's Notes
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Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024)

Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024)
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Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024) 216924  
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    Lecture Video Lecture Video
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    Amir's Notes Amir's Notes
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  • Attachment
    Xuran's Notes Xuran's Notes
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  • Context Module Sub Header

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

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  • External Url
    Video: Number Theory I Video: Number Theory I