Instructor: Brant Jones (brant at math dot ucdavis dot edu)
Office: Mathematical Sciences Building 3147
Office Hours: Wednesday 12:00 pm - 1:00 pm and 3:00 pm - 4:00 pm in MSB 3147, or by appointment.
Class Meetings: MWF 2:10 pm - 3:00 pm in Haring Hall Room 2016
Class Webpage: http://www.math.ucdavis.edu/~brant/146/
TAs: Benjamin Fineman and Gus Wiseman ([fineman, gus] at math dot ucdavis dot edu)
Discussion section: Th 2:10 pm - 3:00 pm in Haring Hall Room 2016
TA Office Hours: Thursday 10:00 am - 11:00 am in MSB 3123.
Midterm exam: May 5, in class.
Final exam: Saturday June 7, 10:30 am - 12:30 pm in our usual room Haring 2016.
Final grades have been posted and exam solutions are available.
The Online Encyclopedia of Integer Sequences is a great resource for finding generating functions and connections between various sequences.
Math cafe is a free-form peer study group available to any interested party. We provide an informal environment where individuals can help each other or receive help from grad students. The main focus is on females as they are an underrepresented minority in mathematics, but all people are welcome to visit. Come for snacks, conversation and answers to all your math concerns. We meet every Monday 5-7 pm in 114 North Hall inside the Women's Center Library. For more information, see http://wrrc.ucdavis.edu/mathcafe/
| March 31: | Introduction to generating functions. How to test a sequence for a recurrence. |
| April 2: | Discuss 1.1 - 1.2. |
| April 4: | Discuss 1.2 - 1.3. Homework 1 due! (1.7: 1.abcdf, 3.abceg) |
| April 7: | Discuss 1.5. |
| April 9: | Discuss 1.6. |
| April 11: | Discuss 1.6 - 2.1. Homework 2 due! (1.7: 5, 6, 11, 12, 16) |
| April 14: | Discuss 2.1. |
| April 16: | Discuss 2.2. |
| April 18: | Discuss 2.2 - 2.3. Homework 3 due! (1.7: 2.abcfg, 4.abceg, 14; 2.7: 1.ab, 2.ade) |
| April 21: | Discuss 2.3. |
| April 23: | Discuss 2.4. (Guest lecture by Benjamin Fineman, Office hours noon-1pm with Gus Wiseman.) |
| April 25: | Discuss 2.6. Homework 4 due! (2.7: 4.abcef, 6, 7, 20) |
| April 28: | Discuss 2.6. |
| April 30: | Ordinary composition formula. Classification of generating functions. |
| May 2: | Review for midterm exam. Homework 5 due! (2.7: 21.ab, 27, 32) |
| May 5: | Midterm exam, in class. The exam covers Chapters 1 and 2. |
| May 7: | Discuss 3.1 - 3.3. |
| May 9: | Discuss 3.3 - 3.4. |
| May 12: | Discuss 3.5 - 3.6. |
| May 14: | Discuss 3.7 - 3.8. |
| May 16: | Discuss 3.9 - 3.11. Homework 6 due! (3.19: 2, 5ac, 6, 12) |
| May 19: | Discuss 3.12, 5.1. |
| May 21: | Discuss 3.14 - 3.16. |
| May 23: | Discuss 4.1 - 4.2. Homeword 7 due! (3.19: 7, 10, 13a, 18) |
| May 26: | No class. |
| May 28: | Discuss 4.2. |
| May 30: | Discuss Polya enumeration. |
| June 2: | Discuss Polya enumeration. |
| June 4: | Review for final exam. Homeword 8 due! (Solutions are also available.) |
This class is an introduction to the use of generating functions in combinatorics. Over the course of the quarter, we'll discuss how to use recurrences and formal power series to enumerate various discrete mathematical objects. The text generatingfunctionology by Wilf is available at the University Bookstore. You can also find it at the Shields Library and online at http://www.math.upenn.edu/%7Ewilf/DownldGF.html.
The only formal prerequisite for this class is Math 145 (Combinatorial Mathematics), and I will strive to keep the course relatively self-contained. I encourage you to use a computer algebra system (such as Mathematica, Maple, MuPad or Sage) to perform generating function manipulations and series expansions on your homework. The department has an Undergraduate Computer Lab on the 2nd floor of the Math building. You will not be able to use any computers/calculators on the exams however.
There are several components to the grade you will receive in this class:
No books or calculating devices will be allowed during the exams. There will be no exam makeups.
Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the Student Disability Center (SDC). Faculty are authorized to provide only the accommodations requested by the SDC. If you have any questions, please contact the SDC at 530/752-3184 or sdc@ucdavis.edu.