# 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.

## MAT 115A: Number Theory

**Approved:**2003-03-01 (revised 2011-08-01, )

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

Search by ISBN on Amazon: 9780321500311

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1-3 |
ch 1.1-1.4 |
Well-ordering principle, induction, divisibility, prime numbers |

4-5 |
ch. 3.1-3.3 |
Greatest common divisor, Euclidean algorithm |

6-7 |
ch. 3.4 |
Fundamental theorem of arithmetic |

8 |
ch. 3.5 |
Factorization methods, sieve methods, Fermat numbers |

9-10 |
ch. 3.6 |
Linear Diophantine equations |

11-12 |
ch. 4.1-4.2 |
Congruences |

13-15 |
ch. 4.3 |
Linear congruences, Chinese remainders theorem |

16-18 |
ch. 6.1 |
Fermat’s little theorem, Wilson’s theorem |

19-20 |
ch. 6.3, ch. 7.1 |
Euler’s theorem, Euler-Phi function |

20-22 |
ch. 8.1, 8.4, 8.5 |
Public-key encryption (RSA) |

**Additional Notes:**

Have students use Mathematica, Maple or the open source computer algebra system SAGE to explore concepts such as the Carmichael numbers, the distribution of primes and the RSA algorithm.

**Learning Goals:**