Office: Armstrong Hall 408H

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

Class Meetings: TuTh 2:30pm-3:45pm in Hodges Hall 302

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

1 | Jan 12 | Introduction; Fundamental Theorem of Arithmetic | 1.1 | - | - | - |

2 | Jan 14 | Polynomial rings | 1.2,1.3 | - | - | HW1 assigned. |

3 | Jan 19 | Principal Ideal Domains | 1.3 | - | - | - |

4 | Jan 21 | F.T.A. for PID's; Gaussian integers | 1.3,1.4 | - | - | - |

5 | Jan 26 | Infinitely many primes; square-free; Mobius inversion | 2.1,2.2 | - | - | - |

6 | Jan 28 | Sum of 1/p over primes p; density of primes | 2.3,2.4 | - | - | HW1 due. HW2 assigned. |

7 | Feb 2 | Congruences; quotient rings | 3.2,3.3 | - | - | - |

8 | Feb 4 | Chinese Remainder Theorem | 3.4 | - | - | - |

9 | Feb 9 | Structure of the group of units modulo m |
4.1 | - | - | - |

10 | Feb 11 | Structure of the group of units modulo m II |
4.1 | - | - | HW2 due. HW3 assigned. |

11 | Feb 16 | Quadratic residues, nonresidues | 5.1 | - | - | - |

12 | Feb 18 | Quadratic reciprocity: applications | 5.2 | - | - | - |

13 | Feb 23 | Quadratic reciprocity: alternative forms | 5.2 | - | - | - |

14 | Feb 25 | Algebraic numbers and integers | 6.1 | - | - | HW3 due. HW4 assigned. |

15 | Mar 1 | Algebraic numbers and integers II | 6.1 | - | - | - |

16 | Mar 3 | Quadratic character of 2 | 6.2 | - | - | - |

17 | Mar 8 | Proof of QRL; sign of Quadratic Gauss Sum | 6.3,6.4 | - | - | - |

18 | Mar 10 | Finite fields | 7.1 | - | - | HW4 due. HW5 assigned. |

19 | Mar 15 | Finite fields; Field extensions | 7.1,7.2 | - | - | - |

20 | Mar 17 | Number of irreducible polynomials | 7.2 | - | - | HW4 due. HW5 assigned. |

21 | Mar 29 | Quadratic reciprocity via finite fields | 7.3 | - | - | - |

22 | Mar 31 | Characters; Gauss Sums | 8.1,8.2 | - | - | HW5 extended to next Thursday. |

23 | Apr 5 | Gauss Sums; Jacobi Sums | 8.2,8.3 | - | - | - |

24 | Apr 7 | Jacobi Sums | 8.3 | - | - | HW5 due. |

25 | Apr 12 | Counting solutions to the eqn x^n + y^n = 1; multi-arg Jacobi sums | 8.4,8.5 | - | - | - |

26 | Apr 14 | Multi-argument Jacobi sums | 8.5 | - | - | HW6 assigned; a few problems to be added. |

27 | Apr 19 | Multi-argument Jacobi sums and Gauss sums; counting solutions to x_{1}^{2} + ... + x_{n}^{2} = 1 |
8.5, 8.6 | - | - | - |

28 | Apr 21 | Cubic Reciprocity I: primes in Z[ω] | 9.1 | - | - | - |

29 | Apr 26 | Cubic Reciprocity II: residue rings, cubic character | 9.2,9.3 | - | - | - |

30 | Apr 28 | Cubic Reciprocity III: proof in the case of one rational and one complex prime | 9.4 | - | - | HW6 due. |

milans@math.wvu.edu