lectures

Lectures

Class notes will generally not be posted. Lecture topics are tentative.

Date | Topics | Book Sections |
---|---|---|

January 24 | Introduction, Set, Element, Subset, Empty Set, Bijective Proof I | 4.1, 4.4 |

January 27 | Proposition, Predicate, Theorem, Direct Proof, Proof by Contradition | 1.1, 1.2, 1.3, 1.5, 1.8 |

January 29 | Set-Builder Notation, Cardinality, Set Operations, Element Method, Proof by Cases, Proof by Counterexample | 1.7, 2.2, 4.1, 5.1 |

January 31 | Cartesian Product, Quantification I, Power Set, Relations, Set Equality, Set Identities | 3.6, 4.1, 4.4 |

February 3 | Properties of Relations, Equivalence Relations, Equivalence Classes, Set Partitions | 9.11, 9.12 |

February 5 | Functions, Injectivity, Surjectivity, Bijectivity I | 4.4 |

February 7 | Bijective Proof II, Bijectivity II, Cardinality of Sets, Countable Infinity | 4.4, 5.1, 5.2, 15 |

February 10 | Induction I | 6.1 |

February 12 | Induction II, Strong Induction, Divisibility, Division Algorithm | 6.2, 6.3, 8.1 |

February 14 | Induction III, Primes, Fundamental Theory of Arithmetic, Summation and Product Notation | 8.3 |

February 17 | GCD, Division Algorithm, Divisibility, Euclidean Algorithm | 8.2 |

February 19 | Modular Arithmetic I | 8.5 |

February 21 | Modular Arithmetic II, Fermat's Little Theorem | 8.6 |

February 24 | Euler's Totient Function, Euler-Fermat Theorem | 8.7 |

February 26 | RSA Encryption | |

February 28 | Logical Operators, Conditional, Proposition, Predicate, Truth Tables | |

March 3 | Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II | |

March 5 | Logical Algebra, Combinational Circuits | |

March 7 | Binary Representation, Half-Adder, Full-Adder, Feedback Circuits | |

March 10 | R/S Latch, D Latch, D Flip Flop, Clocks, Memory Circuits | |

March 12 | Counting, Product Rule, Permutations I, Factorials | |

March 14 | Sum Rule, Permutations II, Binomial Theorem | |

March 17 | Binomial Identities, Multinomial Coefficients, Inclusion/Exclusion I | |

March 19 | Inclusion/Exclusion II, Derangements | |

March 21 | Pigeonhole Principle, Stars and Bars Problem | |

March 31 | Asymptotics, Big-O, Big-Omega, Big-Theta | |

April 2 | Algorithms, Time Complexity | |

April 4 | Probability, Sample Space, Event, Distributions | |

April 7 | Product rule, Generalized Product Rule, Independence | |

April 9 | Bayes' Rule, Law of Total Probability, Extended Bayes' Rule | |

April 11 | Random Variables I, Expected Value II, Linearity of Expectation | |

April 14 | Random Variables II, Expected Value II, Binomial Distribution | |

April 16 | Variance, Independence, Random Variables III | |

April 18 | Markov/Chebyshev Bounds, Intro to Graph Theory (Vertex, Edge, Path, Degree, Simplicity, Completeness, Connectivity) | |

April 21 | Euler Paths, Circuits, Isomorphism | |

April 23 | Hamiltonian Circuits, Trees, Spanning Trees, Prufer Code | |

April 25 | Planar Graphs, Counting Trees | |

April 28 | Graph Coloring, Four Color Theorem, Euler's Formula | |

April 30 | Markov Process, Finite Markov Chain, Random Text Generation |