Math 645/700 A Survey of Mathematical Problems I

Distance Learning Section

645 Course Home Page


The text is "Mathematical Journeys," Peter Schumer, John Wiley & Sons, 2004.

Topics covered
Topics Schumer book HW due
Let's get cooking: a variety of mathematical ingredients (primes, induction...) Chapter 1 Sept 5
(...continued) (...continued) Sept 12
The green chicken contest (miscellanous problems) Chapter 2 Sept 19
(...continued) (...continued) Sept 26
The harmonic series...and less Chapter 6 Oct 3
(...continued) (...continued) Oct 10
Mathematical variations on rolling dice Chapter 9 Oct 17
Pizza slicing, map coloring, pointillism and Jack-in-the-box Chapter 10 Oct 24
Episodes in the calculation of Pi Chapter 11 Oct 31
A sextet of scintillating problems Chapter 12 Nov 7
Choosing stamps to mail a letter, let me count the ways Chapter 15 Nov 14
(...continued) (...continued) Nov 21
Pascal potpourri Chapter 16 Nov 30
Final Exam (comprehensive) Dec 9-11

This course is about mathematical problem solving, so the specific material covered is not critical, what is important is that you learn the rules of mathematical logic, get a better feel for what constitutes a good proof, and learn certain useful mathematical tools such as induction and combinatorial counting techniques. A lot of the material could be considered "recreational mathematics", and you will hopefully find it entertaining as well as educational.

I suggest you read each chapter assigned above in the Schumer book, then try to work through all the problems in the chapter. Every problem in this book is worked out in the back, check the author's solutions after you have at least attempted the problems. Then I will assign (more or less) related problems from other sources, that you need to work out and turn in on the schedule above.


Introduction to 645

Generating Functions (Ch 9 and 15)

The BBP Formula for Digits of Pi