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 |