## Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

**Approved:**2003-05-01 (revised 2013-01-01, G. Kuperberg)

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Search by ISBN on Amazon: 978-0321500311

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1-5 |
ch. 7.4, 7.3 |
Famous functions of number theory: Möbius inversion, multiplicative functions, sum of positive divisors, Morton’s conjecture, perfect numbers |

6-13 |
ch. 9.1-9.3 ch. 10.1, ch. 10.2 |
More congruences, primitive roots, applications: pseudorandom numbers, the ElGamal Crypto System |

14-21 |
ch 11.1-11.3 |
Quadratic reciprocity, Legendre symbol, Jacobi symbol, the law of quadratic reciprocity |

22-27 |
ch. 13 |
Nonlinear Diophantine, equation and continued fractions, Pythagorean triples, Fermat’s last Theorem, Pell’s equation, sums of squares |

**Additional Notes:**

**Learning Goals:**

Mastery of this course enhances the students' ability to construct and write proofs; to not only see beautiful ideas of number theory in the time of Gauss, but also reach some of those ideas themselves; and adds to their experience with algebra in general, in particular in association with the Math 150 modern algebra series.

**Assessment:**