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 No Class
February 24 GCD, Euclidean Algorithm, Relative Primes 8.2, 8.3, 8.7
February 26 Modular Arithmetic I 8.5
February 29 Modular Arithmetic II, Congruence Properties, Fermat's Little Theorem 8.5
March 2 Modular Arithmetic III, Fermat's Little Theorem, Euler's Totient Function 8.6
March 4 Encryption, RSA Encryption 8.7
March 7 Logical Operators, Conditional, Proposition, Predicate, Truth Tables 8.8
March 9 Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II, Logical Algebra 3.13.3, 3.4
March 11 Combinational Circuits Binary Representation, Half-Adder I Not in book!
March 14 Half Adder II, Full-Adder, Feedback Circuits Not in book!
March 16 RS-Latch, Clocks, D-Latch Not in book!
March 18 Full Circuit Notes Not in book!
March 21 Counting, Product Rule, Permutations I, Factorials, Binomial Coefficient 15.1, 15.3, 15.5
March 23 Permutations II, Binomial Theorem 15.2, 15.7
March 25 Inclusion/Exclusion, Derangements 15.12
April 4 Pigeonhole Principle, Strong Pigeonhole Principle 15.10
April 6 The Donut Problem, Asymptotics, Big-O, Big-Omega, Big-Theta 14.7
April 11 Probability, Sample Space, Event, Distributions 17.1, 17.2, 17.3
April 13 Product rule, Generalized Product Rule, Independence, Bayes' Rule 17.4, 17.6
April 15 Law of Total Probability, Extended Bayes' Rule 17.5
April 18 Random Variables I, Expected Value II, Binomial Distribution, Linearity of Expectation 18.1, 18.2, 18.4, 18.5
April 20 Random Variables II, Expected Value II, Variance I 18.3, 18.4
April 22 Variance II, Independence, Random Variables III 18.2, 19.3, 19.4
April 25 Markov Bounds, Chebyshev Bounds, Law of Large Numbers 19.2, 19.3, 11.1
April 27 Intro to Graph Theory (Leaf, Degree, Vertex, Edge, Path, Connectivity), Trees, Prufer Code Prob 9.12, 11.4
April 29 Planar Graphs, Complete Graphs, Bipartite Graphs, Euler's Formula 11.8, 11.11