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

Lecture 1: Proposotional Logic (2 September 2024)

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

Context Module Sub Header

Please read the syllabus! 1

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External Url

Lecture Video Links to an external site. Lecture Video 2

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Attachment

Amir's Notes Amir's Notes 3

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Attachment

Xuran's Notes Xuran's Notes 5

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Context Module Sub Header

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

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External Url

Video: Proofs Links to an external site. Video: Proofs 7

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

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

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External Url

Video: Peano Axioms Links to an external site. Video: Peano Axioms 5

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Video: Induction Links to an external site. Video: Induction 4

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External Url

Video: 2+2=4 Links to an external site. Video: 2+2=4 5

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External Url

Reading: Mathematical Induction Links to an external site. Reading: Mathematical Induction 6

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Attachment

Weekly Problem Set 1 Weekly Problem Set 1 7

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: Strong Induction Links to an external site. Video: Strong Induction 4

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External Url

Video: Proof by Strong Induction Links to an external site. Video: Proof by Strong Induction 5

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Context Module Sub Header

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

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External Url

Video: Strong Induction Examples Links to an external site. Video: Strong Induction Examples 7

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Context Module Sub Header

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

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Context Module Sub Header

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

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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External Url

Video: Induction Problems Links to an external site. Video: Induction Problems 4

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External Url

Video: Divisibility Problems Solved by Induction Links to an external site. Video: Divisibility Problems Solved by Induction 5

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External Url

Video: Epic Induction Links to an external site. Video: Epic Induction 6

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Context Module Sub Header

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

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Context Module Sub Header

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

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Context Module Sub Header

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

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Context Module Sub Header

Reading: Chapter 1 of Ross (Combinatorial Analysis) 6

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Context Module Sub Header

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

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Attachment

Weekly Problem Set 2 Weekly Problem Set 2 8

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External Url

Fun to Read: Which Rectangular Chessboards Have a Knight's Tour? Links to an external site. Fun to Read: Which Rectangular Chessboards Have a Knight's Tour? 9

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Lecture 7: Solving Counting Problems (16 September 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

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

context_module_sub_header 1429887 0

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Context Module Sub Header

Solve the first 24 Problems of Andreescu and Feng 5

context_module_sub_header 1429890 0

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Lecture 8: More Counting (16 September 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1430018 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1430010 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Xuran's Notes Xuran's Notes 3

attachment 1432355 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Weekly Problem Set 3 Weekly Problem Set 3 4

attachment 1432653 0

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Context Module Sub Header

Solve Problems 25 to 51 of Andreescu and Feng 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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

Homework 1

Homework 1 Homework 1

Assignment

Homework 1 Homework 1 10 1

assignment 1433025 1

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TA Session 1 (20 September 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1434109 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

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

attachment 1434071 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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 9: Principle of Inclusion and Exclusion (23 September 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1434094 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1434068 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Xuran's Notes Xuran's Notes 3

attachment 1434145 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Context Module Sub Header

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

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Inclusion-Exclusion Example Links to an external site. Video: Inclusion-Exclusion Example 5

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: 3-set PIE Links to an external site. Video: 3-set PIE 6

external_url 1434077 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Counting using PIE Links to an external site. Video: Counting using PIE 7

external_url 1434078 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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 10: Generalized Principle of Inclusion and Exclusion (23 September 2023)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1434095 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Xuran's Notes Xuran's Notes 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Context Module Sub Header

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

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Context Module Sub Header

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

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Inclusion-Exclusion Links to an external site. Video: Inclusion-Exclusion 6

external_url 1434079 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: PIE Problems Links to an external site. Video: PIE Problems 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Generalized PIE Links to an external site. Video: Generalized PIE 8

external_url 1434081 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Derangements Links to an external site. Video: Derangements 9

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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 11: Pigeonhole Principle (25 September 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1435187 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Xuran's Notes Xuran's Notes 3

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Context Module Sub Header

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

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Context Module Sub Header

Reading: Chapter 4 of Engel (Box Principle) 5

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Context Module Sub Header

Solve Advanced Problems 1 to 15 of Andreescu and Feng 6

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External Url

Video: Pigeonhole Principle Links to an external site. Video: Pigeonhole Principle 7

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Pigeonhole Principle Examples Links to an external site. Video: Pigeonhole Principle Examples 8

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Pigeonhole Principle - Establishing a Pattern Links to an external site. Video: Pigeonhole Principle - Establishing a Pattern 9

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External Url

Video: Pigeonhole Principle - Generalizing the Cases Links to an external site. Video: Pigeonhole Principle - Generalizing the Cases 10

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External Url

Playlist: More Advanced Pigeonhole Principle Problems Links to an external site. Playlist: More Advanced Pigeonhole Principle Problems 11

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Weekly Problem Set 4 Weekly Problem Set 4 12

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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 2 (27 September 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1437032 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Zhaorun's Notes Zhaorun's Notes 2

attachment 1441348 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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 12: Graphs, Trees, Paths and Walks (30 September 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1437035 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1437033 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1437381 0

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Context Module Sub Header

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

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Context Module Sub Header

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

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External Url

Video Playlist: Introduction to Graph Theory Links to an external site. Video Playlist: Introduction to Graph Theory 6

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External Url

Video Playlist: Watch Lectures 1 to 4 Links to an external site. Video Playlist: Watch Lectures 1 to 4 7

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Context Module Sub Header

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

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Context Module Sub Header

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

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Context Module Sub Header

Solve Advanced Problems 16 to 30 of Andreescu and Feng 6

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External Url

Video Playlist: Watch from 10.1.1 to 11.1.1 Links to an external site. Video Playlist: Watch from 10.1.1 to 11.1.1 7

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External Url

Recommended to Watch: Graph Theory Background Links to an external site. Recommended to Watch: Graph Theory Background 8

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

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Context Module Sub Header

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

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External Url

Recommended to Watch: DFS and BFS Links to an external site. Recommended to Watch: DFS and BFS 5

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Context Module Sub Header

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

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Attachment

Weekly Problem Set 5 Weekly Problem Set 5 7

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TA Session 3 (4 October 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1438844 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 2

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External Url

Video: Recurrence for Number of Partitions Links to an external site. Video: Recurrence for Number of Partitions 3

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1439296 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Video: Kruskal's Algorithm Links to an external site. Video: Kruskal's Algorithm 4

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External Url

Video: Prim's Algorithm Links to an external site. Video: Prim's Algorithm 5

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Context Module Sub Header

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

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External Url

Video: Minimum Spanning Trees Links to an external site. Video: Minimum Spanning Trees 7

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Context Module Sub Header

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

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Context Module Sub Header

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

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Context Module Sub Header

Solve Advanced Problems 31 to 40 of Andreescu and Feng 10

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1439557 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

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

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External Url

Video: Huffman Coding and Huffman Trees Links to an external site. Video: Huffman Coding and Huffman Trees 5

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External Url

Video: Huffman Coding Example Links to an external site. Video: Huffman Coding Example 6

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External Url

Recommended Video: Huffman Coding + Code Links to an external site. Recommended Video: Huffman Coding + Code 7

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External Url

Recommended Video: Dynamic Programming on Trees Links to an external site. Recommended Video: Dynamic Programming on Trees 8

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1440466 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Video: BFS Visualized and Explained Links to an external site. Video: BFS Visualized and Explained 4

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External Url

Video: Dijkstra's Algorithm Links to an external site. Video: Dijkstra's Algorithm 5

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External Url

Video: Strongly Connected Components and Dijkstra's Algorithm Links to an external site. Video: Strongly Connected Components and Dijkstra's Algorithm 6

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Matchings Links to an external site. Video: Matchings 7

external_url 1440522 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Maximal and Maximum Matchings Links to an external site. Video: Maximal and Maximum Matchings 8

external_url 1440516 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Matchings and Augmenting Paths Links to an external site. Video: Matchings and Augmenting Paths 9

external_url 1440520 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Incremental Improvement - Matching Links to an external site. Video: Incremental Improvement - Matching 10

external_url 1440514 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Weekly Problem Set 6 Weekly Problem Set 6 11

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Homework 2

Homework 2 Homework 2

Assignment

Homework 2 Homework 2 10 1

assignment 1440609 1

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Attachment

Homework2 Solution Homework2 Solution 2

attachment 1461180 0

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TA Session 4 (11 October 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1441314 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Xuran's Notes Xuran's Notes 2

attachment 1441306 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1441976 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1441591 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1442171 0

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Context Module Sub Header

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

context_module_sub_header 1442834 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1443039 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1442832 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1443857 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Context Module Sub Header

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

context_module_sub_header 1442835 0

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External Url

Video: Maximum Flow and Ford-Fulkerson Links to an external site. Video: Maximum Flow and Ford-Fulkerson 5

external_url 1443089 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Flow Networks and Maximum Flow Links to an external site. Video: Flow Networks and Maximum Flow 6

external_url 1443084 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Maximum-Flow Minimum-Cut Algorithm Links to an external site. Video: Maximum-Flow Minimum-Cut Algorithm 7

external_url 1443085 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Max-flow and Ford-Fulkerson Links to an external site. Video: Max-flow and Ford-Fulkerson 8

external_url 1443087 0

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External Url

Video: Ford-Fulkerson in 5 minutes Links to an external site. Video: Ford-Fulkerson in 5 minutes 9

external_url 1443088 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1443041 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1442833 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1444336 0

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Context Module Sub Header

Reading: Subsection 3.2.3 of West (Stable Matchings) 4

context_module_sub_header 1442837 0

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Context Module Sub Header

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

context_module_sub_header 1442836 0

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External Url

Video: Introduction to Graph Colouring Links to an external site. Video: Introduction to Graph Colouring 6

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External Url

Video: Coloring Code - How Compilers Use Graph Theory Links to an external site. Video: Coloring Code - How Compilers Use Graph Theory 7

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External Url

Video: Applications of Graph Colouring Links to an external site. Video: Applications of Graph Colouring 8

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Context Module Sub Header

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

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Midterm Exam

Midterm Exam Midterm Exam

Attachment

Midterm Exam Midterm Exam 1

attachment 1444251 0

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External Url

Lecture Video Links to an external site. Lecture Video 2

external_url 1445111 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 3

attachment 1445092 0

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Attachment

Xuran's Notes Xuran's Notes 4

attachment 1445992 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1444821 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1444810 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1445260 0

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Context Module Sub Header

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

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External Url

Video: Number Theory I Links to an external site. Video: Number Theory I 5

external_url 1444827 0

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External Url

Playlist: Introduction to Number Theory (Watch Lectures 3 and 4) Links to an external site. Playlist: Introduction to Number Theory (Watch Lectures 3 and 4) 6

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1445224 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1445208 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1446033 0

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Context Module Sub Header

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

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External Url

Video: Primes Links to an external site. Video: Primes 5

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External Url

Solve Problems 1 to 10 of ProjectEuler.net Links to an external site. Solve Problems 1 to 10 of ProjectEuler.net 6

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External Url

Fun to read: Collatz Conjecture Links to an external site. Fun to read: Collatz Conjecture 7

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1446427 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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Context Module Sub Header

Reading: Chapter 4 of Burton (Congruences) 4

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Context Module Sub Header

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

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External Url

Video Playlist: Chinese Remainder Theorem Links to an external site. Video Playlist: Chinese Remainder Theorem 6

external_url 1446322 0

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Context Module Sub Header

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

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Attachment

Weekly Problem Set 7 Weekly Problem Set 7 8

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External Url

Solve Problems 14, 20, 27, 47, 50, 69, 77, 112, 122 and 451 of ProjectEuler.net Links to an external site. Solve Problems 14, 20, 27, 47, 50, 69, 77, 112, 122 and 451 of ProjectEuler.net 9

external_url 1446356 0

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TA Session 5 (25 October 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1450138 0

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Attachment

Xuran's Notes Xuran's Notes 2

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1450161 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1450125 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1452889 0

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Attachment

cycles.cpp cycles.cpp 4

attachment 1450160 0

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External Url

Video: Order of an integer modulo n Links to an external site. Video: Order of an integer modulo n 5

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External Url

Video: Fermat's Little Theorem Links to an external site. Video: Fermat's Little Theorem 6

external_url 1450145 0

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External Url

Video: Euler's Theorem Links to an external site. Video: Euler's Theorem 7

external_url 1450147 0

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External Url

Video: Wilson's Theorem Links to an external site. Video: Wilson's Theorem 8

external_url 1450146 0

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External Url

Playlist: Introduction to Number Theory (Watch Lectures 5 to 14, Primes to Euler's Totient) Links to an external site. Playlist: Introduction to Number Theory (Watch Lectures 5 to 14, Primes to Euler's Totient) 9

external_url 1450139 0

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External Url

Video: COMP 4541's Number Theory Tutorial - Part II Links to an external site. Video: COMP 4541's Number Theory Tutorial - Part II 10

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External Url

Video: Proof that the Totient Function is Multiplicative Links to an external site. Video: Proof that the Totient Function is Multiplicative 11

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External Url

Video: Explicit Formula for Euler's Totient Function Links to an external site. Video: Explicit Formula for Euler's Totient Function 12

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External Url

Video: Euler's Totient Theorem and Fermat's Little Theorem Links to an external site. Video: Euler's Totient Theorem and Fermat's Little Theorem 13

external_url 1450151 0

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Context Module Sub Header

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

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1450162 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1450129 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1452890 0

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External Url

Video: Secret Key Exchange Links to an external site. Video: Secret Key Exchange 4

external_url 1450152 0

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External Url

Video: The Mathematics behind Diffie-Hellman Links to an external site. Video: The Mathematics behind Diffie-Hellman 5

external_url 1450153 0

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External Url

Video: COMP 4541's Diffie-Hellman Lecture Links to an external site. Video: COMP 4541's Diffie-Hellman Lecture 6

external_url 1450140 0

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External Url

Video: COMP 4541's Number Theory Tutorial - Part I Links to an external site. Video: COMP 4541's Number Theory Tutorial - Part I 7

external_url 1450142 0

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External Url

Video: COMP 4541's ElGamal Lecture Links to an external site. Video: COMP 4541's ElGamal Lecture 8

external_url 1450141 0

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External Url

Video: ElGamal Encryption Links to an external site. Video: ElGamal Encryption 9

external_url 1450155 0

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Context Module Sub Header

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

context_module_sub_header 1450159 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1450810 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1450789 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1452891 0

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External Url

Video: Breaking RSA Links to an external site. Video: Breaking RSA 4

external_url 1450794 0

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External Url

Video: What are Digital Signatures? Links to an external site. Video: What are Digital Signatures? 5

external_url 1450795 0

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External Url

Video: COMP 4541's RSA Lecture Links to an external site. Video: COMP 4541's RSA Lecture 6

external_url 1450790 0

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External Url

Video: COMP 4541's Digital Signatures Lecture Links to an external site. Video: COMP 4541's Digital Signatures Lecture 7

external_url 1450791 0

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External Url

Video: The RSA Cryptosystem and Efficient Exponentiation Links to an external site. Video: The RSA Cryptosystem and Efficient Exponentiation 8

external_url 1450792 0

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External Url

Video: Diffie-Hellman Key Exchange and the Discrete Log Problem Links to an external site. Video: Diffie-Hellman Key Exchange and the Discrete Log Problem 9

external_url 1450793 0

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External Url

Reading: Side-channel Attacks (Wikipedia) Links to an external site. Reading: Side-channel Attacks (Wikipedia) 10

external_url 1450797 0

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External Url

Reading: Power Analysis (Wikipedia) Links to an external site. Reading: Power Analysis (Wikipedia) 11

external_url 1450798 0

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Attachment

Weekly Problem Set 8 Weekly Problem Set 8 12

attachment 1452101 0

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TA Session 6 (1 November 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1452108 0

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External Url

Lecture Video: Addendum on Problem 3 Links to an external site. Lecture Video: Addendum on Problem 3 2

external_url 1454742 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1454678 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1452717 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1452652 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1454246 0

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External Url

Video Playlist: Intro to Set Theory (Watch the first 10 lectures) Links to an external site. Video Playlist: Intro to Set Theory (Watch the first 10 lectures) 4

external_url 1452814 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1452819 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1452788 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1454574 0

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External Url

Reading: Oxford Lecture Notes on Set Theory (Pages 1-20) Links to an external site. Reading: Oxford Lecture Notes on Set Theory (Pages 1-20) 4

external_url 1452789 0

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External Url

Video: Hilbert Hotel Links to an external site. Video: Hilbert Hotel 5

external_url 1452790 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1453664 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1453665 0

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Attachment

Xuran's Notes Xuran's Notes 3

attachment 1454797 0

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External Url

Reading: Oxford Lecture Notes on Set Theory (Pages 1-26) Links to an external site. Reading: Oxford Lecture Notes on Set Theory (Pages 1-26) 4

external_url 1453666 0

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Attachment

Weekly Problem Set 9 Weekly Problem Set 9 5

attachment 1454100 0

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TA Session 7 (8 November 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1454552 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Xuran's Notes Xuran's Notes 2

attachment 1454547 0

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Homework 3

Homework 3 Homework 3

Assignment

Homework 3 Homework 3 10 1

assignment 1454755 1

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1455133 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1455114 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1456917 0

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External Url

Video: Real Numbers Links to an external site. Video: Real Numbers 4

external_url 1455172 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Video: Equinumerosity Links to an external site. Video: Equinumerosity 5

external_url 1455173 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1455191 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1455170 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1456919 0

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External Url

Video: The Halting Problem (Watch the first 18 minutes) Links to an external site. Video: The Halting Problem (Watch the first 18 minutes) 4

external_url 1455185 0

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External Url

Video: Cardinality of the Continuum Links to an external site. Video: Cardinality of the Continuum 5

external_url 1455190 0

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External Url

Video: Comparability of Cardinals Links to an external site. Video: Comparability of Cardinals 6

external_url 1455174 0

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External Url

Video: Axiom of Choice Links to an external site. Video: Axiom of Choice 7

external_url 1455175 0

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External Url

Recommended: History of the Axiom of Choice Links to an external site. Recommended: History of the Axiom of Choice 8

external_url 1455179 0

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External Url

Recommended to Read: Banach–Tarski Paradox Links to an external site. Recommended to Read: Banach–Tarski Paradox 9

external_url 1455183 0

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1457434 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1457430 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1458082 0

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Attachment

coin.cpp coin.cpp 4

attachment 1457420 0

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Attachment

doors.cpp doors.cpp 5

attachment 1457425 0

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Attachment

sleeping.cpp sleeping.cpp 6

attachment 1457427 0

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Attachment

cancer.cpp cancer.cpp 7

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Context Module Sub Header

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

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Attachment

Weekly Problem Set 10 Weekly Problem Set 10 9

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TA Session 8 (15 November 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Zhaorun's Notes Zhaorun's Notes 2

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1457432 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Read: The Monty Hall Problem Links to an external site. Read: The Monty Hall Problem 4

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External Url

Read: The Sleeping Beauty Problem Links to an external site. Read: The Sleeping Beauty Problem 5

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External Url

Watch: Philosophers are not smart enough for probability theory! Links to an external site. Watch: Philosophers are not smart enough for probability theory! 6

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Context Module Sub Header

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

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Context Module Sub Header

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

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External Url

Video: Bayes Theorem Links to an external site. Video: Bayes Theorem 9

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External Url

Video: The Bayesian Trap Links to an external site. Video: The Bayesian Trap 10

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

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1457433 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Video: Linearity of Expectation Links to an external site. Video: Linearity of Expectation 4

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External Url

Video: Expectation, Indicator Random Variables, Linearity Links to an external site. Video: Expectation, Indicator Random Variables, Linearity 5

external_url 1458168 0

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External Url

Video: Expectation Links to an external site. Video: Expectation 6

external_url 1458169 0

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Lecture 35: Markov Chains (20 November 2024)

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

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1458614 0

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Attachment

Amir's Notes Amir's Notes 2

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Attachment

Xuran's Notes Xuran's Notes 3

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External Url

Video: Markov Chains Links to an external site. Video: Markov Chains 4

external_url 1458607 0

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External Url

Video: Recurrence and Irreducibility Links to an external site. Video: Recurrence and Irreducibility 5

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External Url

Video: n-step Transition Matrix Links to an external site. Video: n-step Transition Matrix 6

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External Url

Video: Markov Decision Processes Links to an external site. Video: Markov Decision Processes 7

external_url 1458611 0

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Attachment

Recommended to Read: What Amir does when he is not teaching Recommended to Read: What Amir does when he is not teaching 8

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Attachment

Weekly Problem Set 11 Weekly Problem Set 11 9

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Homework 4

Homework 4 Homework 4

Assignment

Homework 4 Homework 4 10 1

assignment 1458152 1

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Lecture 36: Nim and the Sprague-Grundy Theorem (25 November 2024)

Lecture 36: Nim and the Sprague-Grundy Theorem (25 November 2024) Lecture 36: Nim and the Sprague-Grundy Theorem (25 November 2024)

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1459347 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1459293 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1461393 0

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External Url

Reading: Ferguson's Lecture Notes (Chapters 1-4) Links to an external site. Reading: Ferguson's Lecture Notes (Chapters 1-4) 4

external_url 1459352 0

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Lecture 37: One-shot Games and Nash Equilibria (25 November 2024)

Lecture 37: One-shot Games and Nash Equilibria (25 November 2024) Lecture 37: One-shot Games and Nash Equilibria (25 November 2024)

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1459433 0

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Attachment

Amir's Notes Amir's Notes 2

attachment 1459432 0

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Attachment

Zhaorun's Notes Zhaorun's Notes 3

attachment 1461394 0

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External Url

Video: Nash Equilibrium in 5 Minutes Links to an external site. Video: Nash Equilibrium in 5 Minutes 4

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External Url

Video: Prisoners' Dilemma Links to an external site. Video: Prisoners' Dilemma 5

external_url 1459820 0

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External Url

Video: Repeated Prisoners' Dilemma Links to an external site. Video: Repeated Prisoners' Dilemma 6

external_url 1459821 0

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Context Module Sub Header

Reading: Chapter 1 of the Algorithmic Game Theory Book (Basic Solution Concepts) 7

context_module_sub_header 1459822 0

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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) Lecture 38: Two-player Infinite-duration Games on Graphs (27 November 2024)

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1459902 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Amir's Notes Amir's Notes 2

attachment 1459813 0

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Attachment

Zhaorun's notes Zhaorun's notes 3

attachment 1461395 0

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External Url

Playlist: COMP 6613B's Lectures on Graph Games (Watch Lectures 6 and 7, Lecture 8 is Optional) Links to an external site. Playlist: COMP 6613B's Lectures on Graph Games (Watch Lectures 6 and 7, Lecture 8 is Optional) 4

external_url 1459814 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
External Url

Recommended Playlist: Linear-time Temporal Logic Links to an external site. Recommended Playlist: Linear-time Temporal Logic 5

external_url 1459816 0

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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. 6

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Attachment

Weekly Problem Set 12 Weekly Problem Set 12 7

attachment 1459888 0

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TA Session 9 (27 November 2024)

TA Session 9 (27 November 2024) TA Session 9 (27 November 2024)

External Url

Lecture Video Links to an external site. Lecture Video 1

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Attachment

Xuran's Notes Xuran's Notes 2

attachment 1461184 0

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TA Session 10 (6 December 2024)

TA Session 10 (6 December 2024) TA Session 10 (6 December 2024)

External Url

Lecture Video Links to an external site. Lecture Video 1

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Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Xuran's Notes Xuran's Notes 2

attachment 1462070 0

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TA Session 11 (15 December 2024)

TA Session 11 (15 December 2024) TA Session 11 (15 December 2024)

External Url

Lecture Video Links to an external site. Lecture Video 1

external_url 1462387 0

Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least 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
Attachment

Zhaorun's Notes Zhaorun's Notes 2

attachment 1462386 0

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Final Exam

Final Exam Final Exam

Attachment

Final Exam Final Exam 1

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Course Modules

Lecture 1: Proposotional Logic (2 September 2024)

Please read the syllabus! 1

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

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

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

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

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

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

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

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

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

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

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

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

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

Reading: Chapter 1 of Ross (Combinatorial Analysis) 6

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

Lecture 7: Solving Counting Problems (16 September 2024)

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

Solve the first 24 Problems of Andreescu and Feng 5

Lecture 8: More Counting (16 September 2024)

Solve Problems 25 to 51 of Andreescu and Feng 5

Homework 1

TA Session 1 (20 September 2024)

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

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

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

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

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

Lecture 11: Pigeonhole Principle (25 September 2024)

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

Reading: Chapter 4 of Engel (Box Principle) 5

Solve Advanced Problems 1 to 15 of Andreescu and Feng 6

TA Session 2 (27 September 2024)

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

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

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

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

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

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

Solve Advanced Problems 16 to 30 of Andreescu and Feng 6

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

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

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

TA Session 3 (4 October 2024)

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

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

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

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

Solve Advanced Problems 31 to 40 of Andreescu and Feng 10

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

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

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

Homework 2

TA Session 4 (11 October 2024)

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

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

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

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

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

Reading: Subsection 3.2.3 of West (Stable Matchings) 4

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

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

Midterm Exam

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

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

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

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

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

Reading: Chapter 4 of Burton (Congruences) 4

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

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

TA Session 5 (25 October 2024)

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

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

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

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

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

TA Session 6 (1 November 2024)

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

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