Putnam preparation

BOOKS

Here are books that were recommended to me.

• 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.

You can find other similar books in the QA43.* area of the library.

SIMILAR COMPETITIONS

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
  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
  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: http://www.clubs.psu.edu/up/math/

OTHER NEWS

• 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.

PROBLEMS AND SOLUTIONS

ORGANIZATION:

• By default, there are two windows that will pop-up: one for problems and solutions, and one for hints.
  You can open more windows, as described below:

  To open a link in a new window, check the menu provided by the right mouse button (when it is over the link).
  Often the middle button is a shortcut.

COMMENTS:

• 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 I can take a look.
  Of course, checking could go faster if you have also time to explain the solution on the blackboard.
  Let me know if you would like to see me.
• You might have already worked through these problems - I will add more as we go along.

• Putnam problems and solutions (link to Univ. of Nebraska, Lincoln).
  Many other problems were posted there (see row of links below title).

• 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.

• 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.