The text is "Mathematical Journeys," Peter Schumer, John Wiley & Sons, 2004.
|Topics||Schumer book||HW due|
|Let's get cooking: a variety of mathematical ingredients (primes, induction...)||Chapter 1||Sept 5|
|The green chicken contest (miscellanous problems)||Chapter 2||Sept 19|
|The harmonic series...and less||Chapter 6||Oct 3|
|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|
|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.
Generating Functions (Ch 9 and 15)
The BBP Formula for Digits of Pi