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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Please read the syllabus!
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Chapter 2 of Grimaldi (Fundamentals of Logic)
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External UrlVideo: Proofs Video: ProofsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Chapter 2 of Grimaldi (Fundamentals of Logic)
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External UrlVideo: Peano Axioms Video: Peano AxiomsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Induction Video: InductionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: 2+2=4 Video: 2+2=4Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlReading: Mathematical Induction Reading: Mathematical InductionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 4: Induction Problems and Strong Induction (9 September 2024)
Lecture 4: Induction Problems and Strong Induction (9 September 2024)
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External UrlVideo: Strong Induction Video: Strong InductionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Proof by Strong Induction Video: Proof by Strong InductionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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.
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External UrlVideo: Strong Induction Examples Video: Strong Induction ExamplesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
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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External UrlVideo: Induction Problems Video: Induction ProblemsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Divisibility Problems Solved by Induction Video: Divisibility Problems Solved by InductionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Epic Induction Video: Epic InductionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
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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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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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External UrlFun to Read: Which Rectangular Chessboards Have a Knight's Tour? Fun to Read: Which Rectangular Chessboards Have a Knight's Tour?Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 7: Solving Counting Problems (16 September 2024)
Lecture 7: Solving Counting Problems (16 September 2024)
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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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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Solve Problems 25 to 51 of Andreescu and Feng
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TA Session 1 (20 September 2024)
TA Session 1 (20 September 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 9: Principle of Inclusion and Exclusion (23 September 2024)
Lecture 9: Principle of Inclusion and Exclusion (23 September 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Reading: Chaptes 2 and 4 of Chen and Koh (Binomial Coefficients, Inclusion-Exclusion)
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External UrlVideo: Inclusion-Exclusion Example Video: Inclusion-Exclusion ExampleScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: 3-set PIE Video: 3-set PIEScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Counting using PIE Video: Counting using PIEScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
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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External UrlVideo: Inclusion-Exclusion Video: Inclusion-ExclusionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: PIE Problems Video: PIE ProblemsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Generalized PIE Video: Generalized PIEScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Derangements Video: DerangementsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 11: Pigeonhole Principle (25 September 2024)
Lecture 11: Pigeonhole Principle (25 September 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
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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Context Module Sub Header
Solve Advanced Problems 1 to 15 of Andreescu and Feng
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External UrlVideo: Pigeonhole Principle Video: Pigeonhole PrincipleScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Pigeonhole Principle Examples Video: Pigeonhole Principle ExamplesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Pigeonhole Principle - Establishing a Pattern Video: Pigeonhole Principle - Establishing a PatternScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Pigeonhole Principle - Generalizing the Cases Video: Pigeonhole Principle - Generalizing the CasesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlPlaylist: More Advanced Pigeonhole Principle Problems Playlist: More Advanced Pigeonhole Principle ProblemsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
TA Session 2 (27 September 2024)
TA Session 2 (27 September 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024)
Lecture 12: Graphs, Trees, Paths and Walks (30 September 2024)
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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)
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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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External UrlVideo Playlist: Introduction to Graph Theory Video Playlist: Introduction to Graph TheoryScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo Playlist: Watch Lectures 1 to 4 Video Playlist: Watch Lectures 1 to 4Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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Context Module Sub Header
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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External UrlVideo Playlist: Watch from 10.1.1 to 11.1.1 Video Playlist: Watch from 10.1.1 to 11.1.1Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlRecommended to Watch: Graph Theory Background Recommended to Watch: Graph Theory BackgroundScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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Context Module Sub Header
Reading: Sections 2.1 and 2.2 of West (Trees and Distance: Basic Properties, Spanning Trees)
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Reading: Chapters 11 and 12 of Grimaldi (Graph Theory, Trees)
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TA Session 3 (4 October 2024)
TA Session 3 (4 October 2024)
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External UrlVideo: Recurrence for Number of Partitions Video: Recurrence for Number of PartitionsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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External UrlVideo: Kruskal's Algorithm Video: Kruskal's AlgorithmScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Prim's Algorithm Video: Prim's AlgorithmScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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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External UrlVideo: Minimum Spanning Trees Video: Minimum Spanning TreesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Chapters 1 and 2 of West (Fundamental Concepts, Trees and Distance)
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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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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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Reading: Section 2.3 of West (Optimization and Trees)
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External UrlVideo: Huffman Coding and Huffman Trees Video: Huffman Coding and Huffman TreesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlRecommended Video: Huffman Coding + Code Recommended Video: Huffman Coding + CodeScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlRecommended Video: Dynamic Programming on Trees Recommended Video: Dynamic Programming on TreesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024)
Lecture 17: Distance, Shortest Paths and Matchings (9 October 2024)
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External UrlVideo: BFS Visualized and Explained Video: BFS Visualized and ExplainedScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Dijkstra's Algorithm Video: Dijkstra's AlgorithmScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Strongly Connected Components and Dijkstra's Algorithm Video: Strongly Connected Components and Dijkstra's AlgorithmScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Matchings Video: MatchingsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Maximal and Maximum Matchings Video: Maximal and Maximum MatchingsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Matchings and Augmenting Paths Video: Matchings and Augmenting PathsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Incremental Improvement - Matching Video: Incremental Improvement - MatchingScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
TA Session 4 (11 October 2024)
TA Session 4 (11 October 2024)
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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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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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Context Module Sub Header
Reading: Section 4.3 of West (Network Flow Problems)
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External UrlVideo: Flow Networks and Maximum Flow Video: Flow Networks and Maximum FlowScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Maximum-Flow Minimum-Cut Algorithm Video: Maximum-Flow Minimum-Cut AlgorithmScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Max-flow and Ford-Fulkerson Video: Max-flow and Ford-FulkersonScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Ford-Fulkerson in 5 minutes Video: Ford-Fulkerson in 5 minutesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 20: Stable Matchings and Graph Coloring (16 October 2024)
Lecture 20: Stable Matchings and Graph Coloring (16 October 2024)
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Context Module Sub Header
Reading: Subsection 3.2.3 of West (Stable Matchings)
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Reading: Section 5.1 of West (Vertex Colorings and Upper Bounds) -- Brooks' Theorem is not part of the syllabus
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External UrlVideo: Introduction to Graph Colouring Video: Introduction to Graph ColouringScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Coloring Code - How Compilers Use Graph Theory Video: Coloring Code - How Compilers Use Graph TheoryScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Applications of Graph Colouring Video: Applications of Graph ColouringScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024)
Lecture 21: Divisibility and Greatest Common Divisor (21 October 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Chapters 1 and 2 of Burton (Preliminaries, Divisibility Theory)
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External UrlVideo: Number Theory I Video: Number Theory IScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlPlaylist: Introduction to Number Theory (Watch Lectures 3 and 4) Playlist: Introduction to Number Theory (Watch Lectures 3 and 4)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Sections 2.4 to 3.3 of Burton (Euclid to Goldbach)
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External UrlVideo: Primes Video: PrimesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlSolve Problems 1 to 10 of ProjectEuler.net Solve Problems 1 to 10 of ProjectEuler.netScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlFun to read: Collatz Conjecture Fun to read: Collatz ConjectureScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Chapter 4 of Burton (Congruences)
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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.
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External UrlVideo Playlist: Chinese Remainder Theorem Video Playlist: Chinese Remainder TheoremScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Make sure you watch all of this playlist, especially the last video.
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External UrlSolve 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.netScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
TA Session 5 (25 October 2024)
TA Session 5 (25 October 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Order of an integer modulo n Video: Order of an integer modulo nScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Fermat's Little Theorem Video: Fermat's Little TheoremScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Euler's Theorem Video: Euler's TheoremScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Wilson's Theorem Video: Wilson's TheoremScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlPlaylist: 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)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: COMP 4541's Number Theory Tutorial - Part II Video: COMP 4541's Number Theory Tutorial - Part IIScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Proof that the Totient Function is Multiplicative Video: Proof that the Totient Function is MultiplicativeScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Explicit Formula for Euler's Totient Function Video: Explicit Formula for Euler's Totient FunctionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Euler's Totient Theorem and Fermat's Little Theorem Video: Euler's Totient Theorem and Fermat's Little TheoremScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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)
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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)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Secret Key Exchange Video: Secret Key ExchangeScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: The Mathematics behind Diffie-Hellman Video: The Mathematics behind Diffie-HellmanScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: COMP 4541's Diffie-Hellman Lecture Video: COMP 4541's Diffie-Hellman LectureScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: COMP 4541's Number Theory Tutorial - Part I Video: COMP 4541's Number Theory Tutorial - Part IScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: COMP 4541's ElGamal Lecture Video: COMP 4541's ElGamal LectureScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: ElGamal Encryption Video: ElGamal EncryptionScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Recommended Reading: Chapter 10 of Burton (Intro to Crypto)
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Lecture 26: RSA Encryption and Digital Signatures (30 October 2024)
Lecture 26: RSA Encryption and Digital Signatures (30 October 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Breaking RSA Video: Breaking RSAScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: What are Digital Signatures? Video: What are Digital Signatures?Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: COMP 4541's RSA Lecture Video: COMP 4541's RSA LectureScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: COMP 4541's Digital Signatures Lecture Video: COMP 4541's Digital Signatures LectureScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: The RSA Cryptosystem and Efficient Exponentiation Video: The RSA Cryptosystem and Efficient ExponentiationScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Diffie-Hellman Key Exchange and the Discrete Log Problem Video: Diffie-Hellman Key Exchange and the Discrete Log ProblemScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlReading: Side-channel Attacks (Wikipedia) Reading: Side-channel Attacks (Wikipedia)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlReading: Power Analysis (Wikipedia) Reading: Power Analysis (Wikipedia)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
TA Session 6 (1 November 2024)
TA Session 6 (1 November 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlLecture Video: Addendum on Problem 3 Lecture Video: Addendum on Problem 3Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 27: Russell's Paradox and Zermelo–Fraenkel Axioms (4 November 2024)
Lecture 27: Russell's Paradox and Zermelo–Fraenkel Axioms (4 November 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo Playlist: Intro to Set Theory (Watch the first 10 lectures) Video Playlist: Intro to Set Theory (Watch the first 10 lectures)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 28: Axiom of Infinity and Bijections (4 November 2024)
Lecture 28: Axiom of Infinity and Bijections (4 November 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlReading: Oxford Lecture Notes on Set Theory (Pages 1-20) Reading: Oxford Lecture Notes on Set Theory (Pages 1-20)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Hilbert Hotel Video: Hilbert HotelScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlReading: Oxford Lecture Notes on Set Theory (Pages 1-26) Reading: Oxford Lecture Notes on Set Theory (Pages 1-26)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
TA Session 7 (8 November 2024)
TA Session 7 (8 November 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 30: The Set of Real Numbers (11 November 2024)
Lecture 30: The Set of Real Numbers (11 November 2024)
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External UrlVideo: Real Numbers Video: Real NumbersScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Equinumerosity Video: EquinumerosityScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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)
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External UrlVideo: The Halting Problem (Watch the first 18 minutes) Video: The Halting Problem (Watch the first 18 minutes)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Cardinality of the Continuum Video: Cardinality of the ContinuumScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Comparability of Cardinals Video: Comparability of CardinalsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Axiom of Choice Video: Axiom of ChoiceScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlRecommended: History of the Axiom of Choice Recommended: History of the Axiom of ChoiceScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlRecommended to Read: Banach–Tarski Paradox Recommended to Read: Banach–Tarski ParadoxScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 32: Introduction to Probability Theory (13 November 2024)
Lecture 32: Introduction to Probability Theory (13 November 2024)
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Context Module Sub Header
Reading: Chapter 2 of Ross (Axioms of Probability), including sections marked by *
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TA Session 8 (15 November 2024)
TA Session 8 (15 November 2024)
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Lecture 33: Conditional Probability, Independence and Expectation (18 November 2024)
Lecture 33: Conditional Probability, Independence and Expectation (18 November 2024)
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External UrlRead: The Monty Hall Problem Read: The Monty Hall ProblemScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlRead: The Sleeping Beauty Problem Read: The Sleeping Beauty ProblemScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlWatch: Philosophers are not smart enough for probability theory! Watch: Philosophers are not smart enough for probability theory!Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Chapters 3 and 4 of Ross (Conditional Probability, Independence, Random Variables)
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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.
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External UrlVideo: Bayes Theorem Video: Bayes TheoremScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: The Bayesian Trap Video: The Bayesian TrapScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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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External UrlVideo: Linearity of Expectation Video: Linearity of ExpectationScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Expectation, Indicator Random Variables, Linearity Video: Expectation, Indicator Random Variables, LinearityScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Expectation Video: ExpectationScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 35: Markov Chains (20 November 2024)
Lecture 35: Markov Chains (20 November 2024)
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External UrlVideo: Markov Chains Video: Markov ChainsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Recurrence and Irreducibility Video: Recurrence and IrreducibilityScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: n-step Transition Matrix Video: n-step Transition MatrixScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Markov Decision Processes Video: Markov Decision ProcessesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 36: Nim and the Sprague-Grundy Theorem (25 November 2024)
Lecture 36: Nim and the Sprague-Grundy Theorem (25 November 2024)
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External UrlReading: Ferguson's Lecture Notes (Chapters 1-4) Reading: Ferguson's Lecture Notes (Chapters 1-4)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Lecture 37: One-shot Games and Nash Equilibria (25 November 2024)
Lecture 37: One-shot Games and Nash Equilibria (25 November 2024)
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External UrlVideo: Nash Equilibrium in 5 Minutes Video: Nash Equilibrium in 5 MinutesScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Prisoners' Dilemma Video: Prisoners' DilemmaScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlVideo: Repeated Prisoners' Dilemma Video: Repeated Prisoners' DilemmaScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
Reading: Chapter 1 of the Algorithmic Game Theory Book (Basic Solution Concepts)
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Lecture 38: Two-player Infinite-duration Games on Graphs (27 November 2024)
Lecture 38: Two-player Infinite-duration Games on Graphs (27 November 2024)
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External UrlLecture Video Lecture VideoScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlPlaylist: COMP 6613B's Lectures on Graph Games (Watch Lectures 6 and 7, Lecture 8 is Optional) Playlist: COMP 6613B's Lectures on Graph Games (Watch Lectures 6 and 7, Lecture 8 is Optional)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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External UrlRecommended Playlist: Linear-time Temporal Logic Recommended Playlist: Linear-time Temporal LogicScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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Context Module Sub Header
LTL is not part of the syllabus. It's just a recommendation for you to see what the deal with ♢s and □s was.
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TA Session 9 (27 November 2024)
TA Session 9 (27 November 2024)
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TA Session 10 (6 December 2024)
TA Session 10 (6 December 2024)
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TA Session 11 (15 December 2024)
TA Session 11 (15 December 2024)
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