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 27 Introduction, Set, Element, Subset, Empty Set, Bijective Proof I

4.1, 4.4

January 29 Proposition, Predicate, Theorem, Direct Proof, Proof by Contradiction 1.1, 1.2, 1.3, 1.5, 1.8
February 1 Set-Builder Notation, Cardinality, Set Operations, Element Method, Proof by Cases, Power Set, Disproof by Counterexample 1.7, 2.2, 4.1, 5.1
February 3 Cartesian Product, Quantification I, Power Set, Relations 3.6, 4.1, 4.2, 4.4
February 5 Properties of Relations, Equivalence Relations, Equivalence Classes, Set Partitions 9.11, 9.12
February 10 Functions, Injectivity, Surjectivity, Bijectivity I 4.3, 4.4
February 12 Bijective Proof II, Bijectivity II, Cardinality of Sets, Countable Infinity 4.4, 5.1, 5.2, 15
February 15 Induction I 6.1
February 17 Induction II, Strong Induction 6.2, 6.3
February 19 Divisibility, Primes, Division Algorithm 2.3, 8.1
February 22 GCD, Euclidean Algorithm, Relative Primes 8.2, 8.3, 8.7
February 24 No class
February 26 Modular Arithmetic I 8.5
March 2 Modular Arithmetic II, Fermat's Little Theorem 8.6
March 4 Euler's Totient Function, Encryption 8.7
March 7 RSA Encryption 8.8
March 9 Logical Operators, Conditional, Proposition, Predicate, Truth Tables 3.1
March 11 Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II, Logical Algebra 3.3, 3.4
March 14 Combinational Circuits Binary Representation, Half-Adder I Not in book!
March 16 Half Adder II, Full-Adder, Feedback Circuits Not in book!
March 18 RS-Latch, Clocks, D-Latch I Not in book!
March 21 D-Latch II Not in book!
March 23 Counting, Product Rule, Permutations I, Factorials, Binomial Coefficient 15.1, 15.3, 15.5
March 25 Permutations II, Binomial Theorem 15.2, 15.7
April 4 Inclusion/Exclusion, Derangements 15.12
April 6 Pigeonhole Principle, Strong Pigeonhole Principle 15.10
April 8 The Donut Problem, Asymptotics, Big-O, Big-Omega, Big-Theta 14.7
April 11 Algorithms, Time Complexity Not in book!
April 13 Probability, Sample Space, Event, Distributions 17.1, 17.2, 17.3
April 15 Product rule, Generalized Product Rule, Independence 17.4, 17.6
April 18 Bayes' Rule, Law of Total Probability, Extended Bayes' Rule 17.5
April 20 Random Variables I, Expected Value II, Binomial Distribution, Linearity of Expectation 18.1, 18.2, 18.4, 18.5
April 22 Random Variables II, Expected Value II, Variance I 18.3, 18.4
April 25 Variance II, Independence, Random Variables III, Markov Bounds 18.2, 19.3, 19.4
April 27 Chebyshev Bounds, Intro to Graph Theory (Vertex, Edge, Path, Connectivity) 19.2, 19.3, 11.1
April 29 Intro to Graph Theory (Leaf, Degree), Trees, Prufer Code Prob 9.12, 11.4
May 2 Planar Graphs, Complete Graphs, Bipartite Graphs, Euler's Formula 11.8, 11.11
May 4 Euler's Formula, Subdivisions, Kuratowski’s Theorem, Graph Coloring 12.1, 12.2
May 6 Bipartite Graphs, Four Color Theorem 11.7, 12.3, 12.6