SES # | TOPICS | KEY DATES |
---|---|---|

1 | Introduction, Diophantine Equations, Divisibility, GCD | |

2 | Euclidean Algorithm, Primes | Pset 1 out |

3 | Binomial Coefficients, Congruences | |

4 | Fermat, Euler, Wilson, Linear Congruences | Pset 1 due, Pset 2 out |

5 | Linear Congruences, Chinese Remainder Theorem, Algorithms | Pset 2 due, Pset 3 out |

6 | Primality, Factoring, RSA, Hensel's Lemma | |

7 | Congruences mod Primes, Order, Primitive Roots | Pset 3 due, Pset 4–1 out |

8 | Primitive Roots (Prime Powers), Index Calculus | |

9 | Midterm 1 | Pset 4–2 out |

10 | Quadratic Residues, Quadratic Reciprocity | |

11 | Jacobi Symbol, Computation, Zolotareff's Definition | Pset 4 due |

12 | Square Roots, Tonelli's Algorithm, Number of Consecutive Pairs of Squares mod p | Pset 5 out |

13 | Cyclotomic Polynomials, Primes Congruent to 1 mod n | |

14 | Arithmetic Functions | |

15 | Mobius Inversion Formula, Zeta Functions | Pset 5 due, Pset 6 out |

16 | Linear Recurrences | |

17 | Generating Functions | Pset 6 due, Pset 7 out |

18 | Midterm 2 | |

19 | More on Generating Functions, Two Squares Theorem | |

20 | Continued Fractions I | Pset 7 due, Pset 8 out |

21 | Continued Fractions II: Inequalities | |

22 | Periodic Continued Fractions, Quadratic Irrationalities | Pset 8 due, Pset 9 out |

23 | Brahmagupta-Pell Equation | |

24 | Four Squares Theorem | Pset 9 due |

25 | Pythagorean Triples, Fermat Descent | |

26 | Rational Points on Conics |