An Introduction to Mathematics Beyond Calculus

General Information | Syllabus | HW Assignments | Course Resources |
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On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures | Sections in Text | Brief Description |
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1/4 | Introduction, Elliptic curves in Fermat's Last Theorem, Congruent Numbers, and Cryptography | |

1/6 | Congruent numbers and rational points on conics; algebraic versus geometric structure on sets | |

1/8 | Rational curves and intersections; Bachet's duplication formula | |

1/11 | Rational points on the unit circle: Pythagorean triples, congruent numbers | |

1/13 | Well ordering, division algorithm, greatest common divisors and divisibility properties | |

1/15 | Euclid's algorithm, Bezout's theorem, congruences | |

1/18 | No Class Martin Luther King day (class moves to x-hour) | |

1/19 (x-hour) | congruences and equivalence relations; Caesar cipher | |

1/20 | Affine ciphers, general linear congruences | |

1/22 | Z_n as a ring, U_n as a group | |

1/25 | Groups, orders of elements | |

1/27 | More on groups, Euler's theorem, Fermat's little theorem | |

1/29 | Applications, fast modular exponentiation | |

2/1 | Public Key Cryptography, RSA | |

2/3 | Public Key Cryptography | |

2/5 | More about groups | |

2/8 | Fundamental Theorem of Finite Abelian Groups, Projective space | |

2/9 (x-hour) | Projective space and relating points on affine and projective curves | |

2/10 | Elliptic curves and the addition law | |

2/12 | No class: Snow Day (aka Winter Carnival) | |

2/15 | Elliptic curves and the addition law | |

2/17 | Pollard p-1 factoring algorithm | |

2/19 | Lenstra's elliptic curve method of factorization | |

2/22 | Congruent number problem and elliptic curves | |

2/24 | Congruent numbers and Tunnel's theorem; some complex analysis | |

2/26 | Elliptic Curves over C | |

3/1 | Elliptic Functions and Weierstrass function, wrap up | |

3/3 | Student Presentations | |

3/5 | Student Presentations | |

3/8 | Student Presentations |

T. R. Shemanske

Last updated June 27, 2012 12:25:54 EDT