Preparation for the 2012 Putnam Competition

• For other details (including prepaparation from past years) see this link.
• The 2012 competition is Saturday, December 1.
  • part A 9-noon, part B 2-5.
    Location TBA (most likely in PGH). Lunch will be provided.
    Can attend one or both sessions.
  • Note that you should only submit those notes that are useful for the solutions - may lose points for incorrect statements.
• November 16, 1:00-2:00 pm in 646 PGH: practice test
  • This test (2 problems) will be used to decide the UH team for the competition.
  • You can participate in the competition whether you are in the team or not; the team membership is only relevant to compute the UH score, has no effect on each person's score.
• November 9: 12:30-2:00 pm in 646 PGH.
  • Discussed a few problems from the American Mathematical Monthly.
• October 26: 12:30-2:00 pm in 646 PGH.
  • Discussed the example & Thm on page 132, and problems 394 (similar ones: 395, 399), 397, 398, 401 from the Putnam and beyond book
  • To think about:
    • 397: write the solution (we figured out the main ideas), bring it to the next meeting for checking
      NOTE: in order to obtain points at the Putnam competition, it is very important that you write the solutions properly.
    • 396, 403
    • other problems about the Intermediate Value Theorem and differentiability (up to 424); might post a more precise list later
• October 19: 12:30-2:00 pm in 646 PGH.
• October 16: Here is another link to math competition material, courtesy of Prof. Ed Barbeau, U. Toronto.
  • Putnam problems sorted by type
  • this Links for undergraduate students contains, in addition to the above list, also theory
• October 12: no official meeting, but you can discuss problems 12:30-2:00 pm in 646 PGH.
• October 4, THURSDAY: 12:30-1:30 pm in 646 PGH.
  • Discussed problems 383 and 386 from the Putnam and beyond book
  • To think about:
    • 388; note connection to convex/concave functions
    • 390; Hint: consider a sequence \(x_{n+1}=f(x_n)\) for some \(x_0\), and find its limit
    • 391, 392, 393 (good to know such an example)
• September 28
  See you between 12:30-2:00 pm in 646 PGH.
  • Discussed problems from earlier competitions: A2 in 2011, A4 in 2008 (both about series)
  • To think about: decide the (absolute) convergence of the series \[ \sum_{n=1}^{\infty} \frac {\sin(n)}{n} \]
• September 21
  See you between 12:30-2:00 pm in 646 PGH.
  • Discussed problems 377, 378, 380 and 381 from the Putnam and beyond book.
  • To think about: problems 379, 382 - 385.
  • I did not find a much better form of the infinite product convergence thm.
    A nice proof is at http://en.wikipedia.org/wiki/Infinite_product.
    See also http://cornellmath.wordpress.com/2008/01/26/convergence-of-infinite-products/ and http://ramanujan.math.trinity.edu/wtrench/research/papers/RP-93.pdf.
• September 14, first meeting
  See you between 12:30-2:00 pm in 646 PGH.
  The meetings will alternate b/w Friday and another day, to be announced (Tu or Th).
  • Discussed problems A3 and B3 from the 2011 competition.
• The 2012 competition is Saturday, December 1.
  • part A 9-noon, part B 2-5.
    Location TBA (most likely in PGH). Lunch will be provided.
    Can attend one or both sessions.
  • Note that you should only submit those notes that are useful for the solutions - may lose points for incorrect statements.
• The rules (see http://math.scu.edu/putnam/rulescJan.html):

  RULES
  
  The competition is open only to regularly enrolled undergraduates, in colleges and universities of the United States and Canada, who have not yet received a college degree. No individual may participate in the competition more than four times. An eligible entrant who is also a high school student must be informed of this four time limit.
  A college or university with at least three registered entrants obtains a team rank through the positions achieved by three designated individual contestants.
  No collaboration or outside assistance is permitted during the examination. Each contestant, even if designated as a team member, must work independently on the examination questions.
  
  Please note that there are no provisions for "unofficial" entrants.
  
  The local supervisor must be a regular faculty member.