Lectures

Lectures

Class notes will generally not be posted. Lecture topics are tentative. You are highly encouraged to attend all classes.

Date Topics Book Sections
January 21 Introduction, Set, Element, Subset, Empty Set, Bijective Proof I

4.1, 4.4

January 23 Proposition, Predicate, Theorem, Direct Proof, Proof by Contradition 1.1, 1.2, 1.3, 1.5, 1.8
January 26 Set-Builder Notation, Cardinality, Set Operations, Element Method, Proof by Cases, Proof by Counterexample 1.7, 2.2, 4.1, 5.1
January 28 Cartesian Product, Quantification I, Power Set, Relations, Set Equality, Set Identities 3.6, 4.1, 4.4
January 30 Properties of Relations, Equivalence Relations, Equivalence Classes, Set Partitions 9.11, 9.12
February 2 Functions, Injectivity, Surjectivity, Bijectivity I 4.4
February 4 Bijective Proof II, Bijectivity II, Cardinality of Sets, Countable Infinity 4.4, 5.1, 5.2, 15
February 6 Induction I 6.1
February 9 Induction II, Strong Induction, Divisibility, Division Algorithm 6.2, 6.3, 8.1
February 11 Induction III, Primes, Fundamental Theory of Arithmetic, Summation and Product Notation 8.3
February 13 GCD, Division Algorithm, Divisibility, Euclidean Algorithm 8.2
February 18 Modular Arithmetic I 8.5
February 20 Modular Arithmetic II, Fermat's Little Theorem 8.6
February 23 Euler's Totient Function, Euler-Fermat Theorem 8.7
February 25 RSA Encryption
February 27 Logical Operators, Conditional, Proposition, Predicate, Truth Tables
March 2 Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II
March 4 Logical Algebra, Combinational Circuits
March 6 Binary Representation, Half-Adder, Full-Adder, Feedback Circuits
March 9 R/S Latch, D Latch, D Flip Flop, Clocks, Memory Circuits
March 11 Counting, Product Rule, Permutations I, Factorials
March 13 Sum Rule, Permutations II, Binomial Theorem
March 16 Binomial Identities, Multinomial Coefficients, Inclusion/Exclusion I
March 18 Inclusion/Exclusion II, Derangements
March 20 Pigeonhole Principle, Stars and Bars Problem
March 30 Asymptotics, Big-O, Big-Omega, Big-Theta
April 1 Algorithms, Time Complexity
April 3 Probability, Sample Space, Event, Distributions
April 6 Product rule, Generalized Product Rule, Independence
April 8 Bayes' Rule, Law of Total Probability, Extended Bayes' Rule
April 10 Random Variables I, Expected Value II, Linearity of Expectation
April 13 Random Variables II, Expected Value II, Binomial Distribution
April 15 Variance, Independence, Random Variables III
April 17 Markov/Chebyshev Bounds, Intro to Graph Theory (Vertex, Edge, Path, Degree, Simplicity, Completeness, Connectivity)
April 20 Euler Paths, Circuits, Isomorphism
April 22 Hamiltonian Circuits, Trees, Spanning Trees, Prufer Code
April 24 Planar Graphs, Counting Trees
April 27 Graph Coloring, Four Color Theorem, Euler's Formula
April 29 Markov Process, Finite Markov Chain, Random Text Generation