Math H90

Seminar on mathematical problem solving

MF 16:10-18:00, 71 Evans Hall

Mock Putnam exam (5 problems, 2 hours) took place in class on Monday, October 4th. Test problems in PS and in PDF and their solutions in PS and in PDF are available.

Results of the Putnam exam on 12/04/04 can be found here. The UC-Berkeley team (Boris Bukh, Carol Xia Hua and Vedran Sohinger) received an honorable mention. Jeremy Tauzer received an honorable mention as an individual. Congratulations.

Table of Contents


Resources


Academic honesty

The instructor welcomes cooperation among students and the use of books . However, handing in homework that makes use of other people's work (be it from a fellow student, a book or paper, or whatever) without explicit acknowledgement is considered academic misconduct. Make sure to include proper acknowledgement when quoting anything directly or paraphrasing.


Assignments

Homework is due at 4:15p.m. on the day specified. No late homework. If you cannot make it to class, find a way to submit your work before the deadline.


Solutions


Misc. handouts

  • Mathematical induction, in PS and in PDF.
  • Integers and primes, in PS and in PDF.
  • Congruence, in PS and in PDF.
  • Rational and irrational numbers, in PS and in PDF.
  • Complex numbers, in PS and in PDF.
  • Progressions and sums, in PS and in PDF.
  • Diophantine equations, in PS and in PDF.
  • Quadratic reciprocity, in PS and in PDF.
  • Polynomials, in PS and in PDF.
  • Rolle's theorem and Descartes' rule of signs, in PS and in PDF.
  • Polynomial equations and symmetric functions, in PS and in PDF.
  • Classical inequalities, in PS and in PDF.
  • Complex analysis in a nutshell, in PS and in PDF.
  • Linear algebra in a nutshell, in PS and in PDF.
  • Inclusion-exclusion principle, in PS and in PDF.
  • Pigeonhole principle, in PS and in PDF.
  • Generating functions, in PS and in PDF.


    If you find a misstatement/omission/typo in a problem/solution/handout, please let me know as soon as you can. Thanks to Boris Bukh, Tanya Gordeeva, and Brock Mendel for corrections made so far.

    Thanks to Ioana Dumitriu for her help with the course.


    Last modified: Mar 15, 2005