Office: Armstrong Hall 408H

Office Hours: TuTh 2:15pm-3:15pm, W 10:00am-11:00am, and by appointment

Class Meetings: TuTh 1:00pm-2:15pm in Armstrong Hall 121

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

1 | Aug 18 | Introduction; Induction | 1.1,1.2 | - | - | HW1 assigned. |

2 | Aug 20 | Basis representation; Division definition | 1.2,2.1 | - | - | HW Workshop at 5pm |

3 | Aug 25 | GCDs and integral linear combinations | 2.2 | - | - | - |

4 | Aug 27 | Euclidean algorithm; Linear Diophantine equations | 2.2,2.3 | - | - | HW Workshop at 5pm |

5 | Sep 1 | Fundamental Theorem of Algebra; Combinatorics | 2.4,3.1 | - | - | HW1 due; HW2 assigned. |

6 | Sep 3 | Fermat's Little Theorem; Congruences | 3.2,4.1 | - | - | - |

7 | Sep 8 | Residue Systems; Riffling | 4.2,4.3 | - | - | - |

8 | Sep 10 | Linear Congruences; Fermat and Wilson | 5.1-5.3 | - | - | - |

9 | Sep 15 | Chinese Remainder Theorem; Polynomial Recurrences; Euler's Phi Function | 5.3,5.4,6.1 | - | - | HW2 due; HW3 assigned this evening. |

10 | Sep 17 | Inclusion/Exclusion; Arithmetic Functions | 6.2,6.3 | - | - | - |

11 | Sep 22 | Arithmetic Functions; Mobius Inversion | 6.3,6.4 | - | - | - |

12 | Sep 24 | Mobius Inversion; Primitive Roots | 6.4,7.1 | - | - | - |

13 | Sep 29 | Primitive Roots II | 7.1 | - | - | HW3 due. HW4 assigned. |

14 | Oct 1 | Existence of primitive roots modulo p; prime numbers | 7.2,8.1 | - | - | - |

15 | Oct 6 | Midterm (Chapters 1 to 6) | - | - | - | - |

16 | Oct 8 | Prime Numbers | 8.2 | - | - | - |

17 | Oct 15 | Prime Numbers: Chebyshev's Theorem | 8.2 | - | - | HW5 posted. |

18 | Oct 20 | Prime Numbers: Chebyshev's Theorem II | 8.2 | - | - | - |

19 | Oct 22 | Prime Numbers: Bertrand's Postulate | 8.2 | - | - | - |

20 | Oct 27 | Quadratic Reciprocity: Euler's Criterion and Gauss's Lemma | 9.1,9.2 | - | - | - |

21 | Oct 29 | Quadratic Reciprocity: Legendre Symbols (-1/p) and (2/p) | 9.3 | - | - | - |

22 | Nov 3 | Quadratic Reciprocity Law: Proof | 9.3 | - | - | HW5 due. HW6 assigned. |

23 | Nov 5 | Quadratic Reciprocity Law: Proof II; quadratic congruences | 9.3 | - | - | - |

24 | Nov 10 | Consecutive Residues | 10.1-10.2 | - | - | - |

25 | Nov 12 | Consecutive Residues II; sums of two squares | 10.2,11.1 | - | - | - |

26 | Nov 17 | Lagrange's four square theorem I | 11.2 | - | - | HW6 due. |

27 | Nov 19 | Lagrange's four square theorem II | 11.2 | - | - | HW7 assigned (as of Tues. Nov 24). |

28 | Dec 1 | Partitions; Euler's Partition Theorem | 12 | - | - | - |

29 | Dec 3 | Generating Functions | 13.1 | - | - | - |

30 | Dec 8 | Lattice Points | 15 | - | - | HW7 due. |

- | Dec 15 | Final Exam: Tues. Dec 15, 3pm-5pm | - | - | - | - |

milans@math.wvu.edu