Mathematics 331, Problem Solving

Term 2, 2004/05, MWF 10-11

• Instructor : David Boyd
 Office: 200 Mathematics Office hours: Mon 1:30-2:30 and Weds 1:30-2:30 or by appointment Phone: 604-822-4457 e-mail: boyd at math dot ubc dot ca URL of this web page: http://www.math.ubc.ca/~boyd/math331/

• Final Exam Cancelled:
 The final examination which had been scheduled for Wednesday, April 20, 3:30--6:00 PM, MATH 102 has now been cancelled. The final mark will be based on the performance on the best 5 out of the 6 assignments.

• Textbook:
 Herbert S. Wilf, generatingfunctionology This text is out of print but due to the generosity of the author and the publisher it can be downloaded free from Herb Wilf's web site.

• Other useful books:
 R. L. Graham, D.E. Knuth & O. Patashnik, Concrete Mathematics This book has been used previously as a text for the course. It is much more extensive than our chosen text and has a very large selection of further problems and advice on solving them. G. Polya, How to Solve it This is a classic text on the art of problem solving. It provides inspiration and good advice if you are having difficulties finding the solution of a problem or the proof of a theorem. Here are a couple of pages scanned from my copy.

• Course description:
 The course is intended for honours students. This year the intention is to work through the book generatingfunctionology by Herb Wilf which is an introduction to generating functions and their applications to solving combinatorial enumeration problems. The main focus of the course will be the solution of problems from the text and other sources. Students will be expected to present their solutions to some of the problems in class. The background for the course is an honours sequence in calculus and linear algebra. The text also develops uses some of the elementary theory of power series considered as functions of a complex variable. This is mainly needed in the final chapter, on asymptotics, and is the most natural approach to such questions. We will also consider some more elementary approaches to some of these questions as time permits. Prerequisites MATH 120 (MATH 121 or MATH 100/101), MATH 223 (or MATH 221), MATH 226 (or MATH 200)

• Marking:
 There will be regular homework assignments which will be assigned at regular intervals. Be sure to do these and hand them on on time! You are encouraged to try as many of the problems in the text as you can, in addition to those assigned. You may discuss the problems with the other students in the class but your submitted solutions must be written by you in your own words. The final mark will be based on the marks on the best 5 out of the 6 assignments.

• Assignments and Supplementary course material:
 There will be no paper handouts in class. Any such material will be linked to this web page and be in pdf format. To read pdf you need Adobe's free acrobat reader.
 Assignment #1, due Friday, January 14 A solution from #1 Assignment #2, due Friday, January 28 Assignment #3, due Friday, February 11 Assignment #4, due Friday, March 4 Assignment #5, due Friday, March 18 Assignment #6, due Monday, April 4