Office: Armstrong Hall 408H

Office Hours: MTuTh 11:30am-12:30pm, and by appointment

Class Meetings: TuTh 10:00am-11:15am in Armstrong Hall 313

No. | Date | Class Summary | Section(s) | Quiz | Quiz Soln | Comments |

1 | Jan 12 | Introduction; Argument and Proof | 1.1 | - | - | HW1 assigned. |

2 | Jan 14 | An extremal argument; Pythagorean Theorem | 1.1 | - | - | - |

3 | Jan 19 | More "proofs" of the Pythagorean Theorem | 1.1 | - | - | HW1 due. HW2 assigned. |

4 | Jan 21 | Primes; definitions; proof by contradiction | 1.1.2 | - | - | - |

5 | Jan 26 | Irrational numbers | 1.1.3 | Q1 | Q1-soln | - |

6 | Jan 28 | Irrational numbers; Algebra in mathematical arguments | 1.2.2 | - | - | HW3 assigned. |

7 | Feb 2 | Language of math: or and implications | 1.2.2-1.2.4 | Q2 | Q2-soln | HW2 due. |

8 | Feb 4 | Language of math: quantifiers; polynomials | 1.2.4,1.3.3 | - | - | HW3 due. HW4 assigned. |

9 | Feb 9 | Roots and factors of polyomials | 1.3.3 | Q3 | Q3-soln | - |

10 | Feb 11 | Quadratic formula | 1.3,3,1.4 | - | - | HW4 due. HW5 assigned. |

11 | Feb 16 | Abstraction and examples; executing proofs; large gaps between primes | - | - | - | - |

12 | Feb 18 | Test 1 | 1 | T1 | T1-soln | HW5 assigned. |

13 | Feb 23 | The sum 1+2+...+n |
1.4 | - | - | - |

14 | Feb 25 | Sigma/Pi sum/product notation; application: how many regions are created by n lines? |
1.4,2.2.2 | - | - | HW5 due. HW6 assigned. |

15 | Mar 1 | Patterns: a cautionary tale; Intro to sets | 3.1 | Q5 | Q5-soln | - |

16 | Mar 3 | Set operations | 3.5 | - | - | HW6 due. HW7 assigned. |

17 | Mar 8 | Proofs with sets; Russell's Paradox | 3.3,3.9 | Q6 | Q6-soln | - |

18 | Mar 10 | Cartesian products; indexed operations | 3.6,3.7 | - | - | HW7 due. HW8 assigned. |

19 | Mar 15 | Indexed operations; applications (bounds on n!, harmonic series); proofs | 3.9 | Q7 | Q7-soln | - |

20 | Mar 17 | Mathematical logic: statements | 4.1 | - | - | HW8 due. |

21 | Mar 29 | Mathematical logic: statements, variable propositions, quantifiers | 4.1-4.3 | - | - | HW9 assigned. |

22 | Mar 31 | Negation of quantified statements, Logical connectives, implications | 4.4-4.7 | - | - | - |

23 | Apr 5 | Proofs, sets, and mathematical logic | 4.8-4.10 | - | - | HW9 due. |

24 | Apr 7 | Test 2 | - | T2 | T2-soln | - |

25 | Apr 12 | Review Test 2; Converse and Contrapositive | 4.8 | - | - | HW10 assigned. |

26 | Apr 14 | Proof techinique: no minimum counter-example | - | Q9 | Q9-soln | - |

27 | Apr 19 | A combinatorial game; geometric coloring example | 5 | - | - | HW11 assigned. |

28 | Apr 21 | Induction and the no minimum counter-example technique | 5 | - | - | - |

29 | Apr 26 | Induction | 5 | - | - | - |

30 | Apr 28 | Review Final Exam; Intro to Ramsey Theory | - | - | - | HW11 due. |

-- | May 3 | Final Exam: 7pm to 9pm | - | - | - | - |

milans@math.wvu.edu