Number Theory

The following is a **tentative** schedule for the course.
Please check back regularly for updates as the term progresses.

Day | Date | Brief Description |
---|---|---|

1 | 13 Sep (M) | The integers; divisors and multiplies |

2 | 15 Sep (W) | GCD and Euclidean algorithm |

3 | 17 Sep (F) | Consequences of the Euclidean algorithm; Fundamental Theorem of Arithmetic |

4 | 20 Sep (M) | Primes |

5 | 22 Sep (W) | Perfect numbers and sum-of-divisors theorem |

6 | 24 Sep (F) | Residues and congruences |

7 | 27 Sep (M) | Units; Fermat's little theorem |

8 | 29 Sep (W) | Euler's totient function; Chinese Remainder theorem |

9 | 2 Oct (F) | More CRT; RSA cryptography |

10 | 4 Oct (M) | Primality testing |

11 | 6 Oct (W) | Order and primitive roots |

12 | 8 Oct (F) | Exam 1 |

13 | 11 Oct (M) | Primitive roots mod p |

14 | 13 Oct (W) | Primitive roots mod n |

15 | 15 Oct (F) | Quadratic residues |

16 | 18 Oct (M) | Quadratic reciprocity and applications |

17 | 20 Oct (W) | Proof of quadratic reciprocity; Generalized quadratic reciprocity |

18 | 22 Oct (F) | Which numbers are sums of two squares?, I |

19 | 25 Oct (M) | More sums of squares; Pythagorean triples and the unit circle |

20 | 27 Oct (W) | Gaussian integers, I |

21 | 29 Oct (F) | Exam 2 |

22 | 1 Nov (M) | Gaussian integers, II |

23 | 3 Nov (W) | Gaussian integers, III |

24 | 5 Nov (F) | Pell's equation and diophantine approximation, I |

25 | 8 Nov (M) | Pell's equation and diophantine approximation, II; Continued Fractions, I |

26 | 10 Nov (W) | Continued fractions, II |

27 | 12 Nov (F) | Arithmetic Functions, I |

28 | 15 Nov (M) | Arithmetic Functions, II |

TBD |
Final Exam |