GENERAL INFO: This is a pre-core 300 level course; no advanced classes are assumed, but if you have not taken linear algebra please contact me. Using math competitions such as the Putnam Exam as a springboard, in this class we follow the dictum of the Ross Program and ``think deeply of simple things''. The
two main goals of this course are to prepare students for competitive math competitions, and to get a sense of the mathematical landscape encompassing elementary number theory, combinatorics, graph theory, and group theory (among others). While elementary frequently is not synonymous with easy, we will see many beautiful proofs and `a-ha' moments in the course of our investigations. Students will be encouraged to explore these topics at levels compatible with their backgrounds. The textbook for the class is Famous Puzzles of Great Mathematics by Miodrag S Petkovic (published by the AMS: Language: ISBN-10: 0821848143, available http://www.amazon.com/Famous-Puzzles-Mathematicians-Miodrag-Petkovic/dp/0821848143 and http://www.ams.org/bookstore-getitem/item=mbk/63); see the links page for other recommended books (especially Polya's classic text).

OBJECTIVES: The goal is to use interesting problems, puzzles and riddles as springboards to great mathematics, as well as to uphold Williams’ honor in several math competitions (Green Chicken, Putnam, VirginiaTech).

GRADING POLICY: Homework: 42%, Midterm 30%, Final 5%^*, Class Presentation: 12%, Project Euler: 11%.        

• Week 13: Nov 24, 2014:

  • Return of Project Euler: https://projecteuler.net/

    • Make sure you have a Project Euler account.

    • Make sure you are comfortable with Mathematica or some other language.

      • Mathematica YouTube tutorial by Miller: http://www.youtube.com/watch?v=g1oj7CIqGM8

      • Mathematica  template to download: http://web.williams.edu/Mathematics/sjmiller/public_html/math/LaTexMathematica/MathematicaIntroVer6.nb (note: this was written awhile ago and some of the commands may or may not run, depending on what version you're using).

    • Homework: To receive full credit for the Project Euler portion of the course you must have 15 problems solved if  you have worked in groups of 4 or less, 19 if you have worked in groups of 5 to 8, and 27 if you have worked in groups larger than 9). You are on the honor system to have the code done, so when we meet you will be able to show it to me and discuss the ideas behind it and have it run. (If you are doing massive numbers of Putnam problems instead please let me know). Remember part of the course grade is described as a presentation; I want to meet with people at your convenience during reading period / exam period to get a good data point on what you've done and learned, and that will be an excellent opportunity. If you would rather show some of your work to the entire class, that's an option and just let me know. These problems ideally will be done and ready to show me by the start of reading period; if you need more time you need to let me know ASAP.

    • Homework: Monday's class will be split like this again.

    • Useful inequalities:
      • http://www.math.wustl.edu/~victor/putnam/01ineq.pdf
      • http://www.math.union.edu/activities/local/putnam/Inequalities.pdf

  • Video: http://youtu.be/KCTl8yRIzfk (slowly uploading)

CONTACTING ME: You can reach me in Bronfman 202 (if I'm there it's office hours), email sjm1@williams.edu, or anonymously through ephsmath@gmail.com (password 011235813).

• welcome letter
• objectives
• links (contests, books)