## 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:**2006-02-28, A. Schilling

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

http://www.math.upenn.edu/%7Ewilf/DownldGF.html

Search by ISBN on Amazon: 1-56881-279-5

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

2 |
Chapter 1 |
Recurrences, generating functions |

3 |
Chapter 1 |
Examples: Fibonacci numbers, binomial coefficients, Stirling numbers of second kind |

1 |
Chapter 1 |
Bell numbers, exponential generating functions |

6 |
Chapter 2 |
Formal power series, calculus of formal power series. Examples: Fibonacci numbers (again), Catalan numbers, derangements, Moebius function |

3 |
Chapter 3 |
Exponential formula: Cards, decks, hands |

5 |
Chapter 3 |
Examples: Permutations and their cycles, involutions, 2-regular graphs, connected bipartite graphs, labeled trees, money changing problem, partitions of integers, rooted trees and forests |

3 |
Chapter 4 |
Sieve method, fixed points in permutations, k-cycles, Stirling numbers (again), rooks on chessboard, snake oil method |

5 |
Chapter 4; Biggs Chapter 27 |
Cycle index of symmetric group, cyclic, dihedral symmetry symmetries in 3 dimensions, Polya theory |