Lectures

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Lectures

Only very high-level class notes will be released: they are meant to reinforce the lecture, not replace it. Lecture topics are tentative. You are highly encouraged to attend all lectures and write your own notes.

Date Topics Book Sections
January 25 Lecture 1: Proof, Set, Subset

4.1

January 27 Lecture 2: Proposition, Predicate, Proof by Contradiction

1.1, 1.2, 1.8

January 30 Lecture 3: Rational Numbers, Set, Set-Builder Notation, Cardinality, Set Operations, Power Set

4.1, 5.1

February 01 Lecture 4: Element Method, Quantifiers, Existential Proof, Constructive Proof, Proof by Cases

1.7, 3.6

February 03 Lecture 5: Cartesian Product, Relation, Properties of Relations, Equivalence Relation, Equivalence Class, Partition

4.2, 4.4, 9.11, 9.12

February 06 Lecture 6: Function

4.3

February 08 Lecture 7: Injectivity, Surjectivity, Bijectivity, Cardinality of Sets

4.4, 5.1, 5.2, 15.1

February 10 Lecture 8: Bijective Proof, Induction I

15.1, 6.1

February 13 Lecture 9: Induction II, Strong Induction

6.2, 6.3

February 15 Lecture 10: Divisibility, Primes

2.3, 8.1

February 17 Lecture 11: Division Algorithm, GCD, Euclidean Algorithm, Relative Primes

8.2, 8.3, 8.7

February 22 Lecture 12: Modular Arithmetic I, Congruence Properties

8.5

February 24 Lecture 13: Modular Arithmetic II, Fermat's Little Theorem

8.5

February 27 Lecture 14: Modular Arithmetic III, Euler's Totient Function, Encryption

8.6, 8.7

March 01 Lecture 15: RSA Encryption

8.8

March 03 Lecture 16: Logical Operators, Conditional, Proposition, Predicate, Truth Tables

3.1, 3.3, 3.4

March 06 Lecture: TBD

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March 08 Lecture: TBD

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March 10 Lecture: TBD

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March 13 Lecture: TBD

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March 15 Lecture: TBD

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March 17 Lecture: TBD

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March 20 Lecture: TBD

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March 22 Lecture: TBD

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March 24 Lecture: TBD

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April 03 Lecture: TBD

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April 05 Lecture: TBD

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April 07 Lecture: TBD

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April 10 Lecture: TBD

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April 12 Lecture: TBD

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April 14 Lecture: TBD

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April 17 Lecture: TBD

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April 19 Lecture: TBD

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April 21 Lecture: TBD

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April 24 Lecture: TBD

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April 26 Lecture: TBD

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