Putnam preparation

BOOKS

• Loren C. Larson: Problem solving through problems, Springer-Verlag 1983 or 1992, 332 pages.
  See a selection of problems from the first chapter of the 1983 edition.
• Titu Andreescu, Razvan Gelca: Mathematical Olympiad challenges, Birkhauser 2000, 260 pages.
• Titu Andreescu, Razvan Gelca: Putnam and beyond, 2010, 814 pages; this is the library copy, there is an electronic version at UHD.
  Here is the list of corrections.
• The classical How to solve it (library copy) by George Polya (there are newer editions too).
  Here is a summary (via Univ. of Utah)

SIMILAR COMPETITIONS

Garden State Undergraduate Mathematics Conference (and competition)

International Student Competition in Europe.

Virginia Tech Regional Mathematics Contest.

• There are seven problems for two hours and a half.
• This competition has problems of a different type. I am told that they often have a relatively "quick" solution (if you find the right idea/method).

Mathematical Contest in Modeling and Interdisciplinary Contest in Modeling

• The Mathematical Contest in Modeling (MCM) is a contest where teams of undergraduates use mathematical modeling to present their solutions to real world problems.
• The Interdisciplinary Contest in Modeling (ICM) is an extension of MCM designed to develop and advance interdisciplinary problem-solving skills as well as competence in written communication. ICM is a part of MCM.

WEB RESOURCES

• MIT OpenCourseWare, Problem Solving Seminar, Fall 2002 [as of Sep 2015, link not working]
  http://aka-ocw.mit.edu/OcwWeb/Mathematics/18-S34Problem-Solving-SeminarFall2002/CourseHome/index.htm

  Information from the web-site:
  Highlights of this Course: This seminar is geared toward Freshmen. The course website features extensive problem sets and supplementary problems. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.
  Course Description This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

• MIT OpenCourseWare, The Art of Counting, Spring 2003 [as of Sep 2015, link not working]
  http://aka-ocw.mit.edu/OcwWeb/Mathematics/18-S66The-Art-of-CountingSpring2003/CourseHome/index.htm

  Information from the web-site:
  Highlights of this Course: This undergraduate subject on "The Art of Counting" features a comprehensive set of 233 problems for students to solve. The course is structured with one lecture session per week, and student presentations to report on their work in one problem session per week.
  Course Description The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2^n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

• Penn State Math Club: https://orgcentral.psu.edu/organization/mathclub
• Univ. of Maryland Putnam (4th place in 2022 out of 456 competing institutions, 8th place in 2023): https://www.putnam.math.umd.edu/

OTHER NEWS

• "Math Club" at UH (as of 2019):
  • See MENTOR, Multi-Science Enrichment for Networking, Training, and Opportunities in Research
  • To contact other students involved with MENTOR, join the MENTOR groupme
• There is (or used to be?) a Mathematics club on campus, called UHME. To reach it try the e-mail UHME@math.uh.edu or the Phi Mu Epsilon chapter at UH.
• A piece of UH news about the Science Club and other undergraduate math/science activities, see here.

PROBLEMS AND SOLUTIONS

• Putnam problems and solutions
  • Here is the "official" link with problems, solutions and scores; https://kskedlaya.org/putnam-archive/ and comments about its history (and future).
  • For the problems with comments/solutions/etc., see this link at Art of problem solving. Search the web for "art of problem solving putnam".
    Thanks to Nikhil for this link.
  • American Mathematical Competitions site, via the Mathematical Association of America.
    [As of Nov. 2013, does not contain much material about Putnam.]
  
  
• The problems A1 from recent competitions. These are the first problems, and it is said that in general they are simpler.
  
• The problems B1 from recent competitions. These are the first problems of the afternoon session.
  
• The problems A2 and problems B2 from recent competitions.
  
• A link to math competition material, courtesy of Prof. Ed Barbeau, U. Toronto (added Oct. 2012)
  • Putnam problems sorted by type
  • this Links for undergraduate students contains, in addition to the above list, also theory
  
  
• OTHER PROBLEMS:
  • Can find challenging discussing problems in the American Mathematical Monthly; here is the online version in the UH library.

ORGANIZATION for problems/hints below:

• By default, there are two windows that will pop-up: one for problems and solutions, and one for hints.
• The hints are only a suggestion. You could find many other solutions following your own ideas.
  Sometimes the posted solutions also offer more ways to solve a given problem.
• I suggest that you write (at least a sketch of) your solution, so that we can take a look.

• Zachary's problem and its solution.
  
• Putnam 1999
  • The problems.
  • The solutions to all 12 problems (from the UN, Lincoln link).
  • Hints: problems A1, A2, A3 seem easier to handle.
    • Problem A1: hint 1, hint 2, hint 3, hint 4, hint 5; answer.
    • Problem A2: hint 1, hint 2, hint 3, hint 4.
    • Problem A3: hint 1, hint 2, hint 3, hint 4, hint 5.
• Putnam 2002
  • The problems.
  • The solutions to all 12 problems (from the UN, Lincoln link).
  • Hints: problems A1, A2 seem easier to handle. Maybe A6 too.
    Problem A3 looks "complicated", but only until the good idea emerges!
  • Problem A1: hint 1.
  • Problem A2: hint 1, hint 2, hint 3, hint 4, hint 5, hint 6.
  • Problem A3: hint 1, hint 2, hint 3, hint 4, hint 5, hint 6, hint 7.