Problems

Contests

International Mathematical Olympiad

The International Mathematical Olympiad (IMO) is an international competition for pre-college students held every July. Up to six participants from each country, selected using national olympiad-type exams (see below), attempt to solve 6 problems in 2 sessions of 4.5 hours. The top scorers are honored with gold, silver and bronze medals.

The following list catalogs just some of the vast amount of IMO information available online:

• The problems and solutions from all of the IMOs, in HTML, can be found here.
• The following IMOs have their own home pages:
  • 1995 IMO (Toronto, Canada)
  • 1996 IMO (Mumbai, India)
  • 1997 IMO (Mar del Plata, Argentina)
  • 1998 IMO (Taipei, Taiwan)
  • 1999 IMO (Bucharest, Romania)
  • 2000 IMO (Seoul and Taejon, South Korea)
  • 2001 IMO (Washington, United States)
  • 2002 IMO (Glasgow, United Kingdom)
  • 2003 IMO (Tokyo, Japan)
  • 2004 IMO (Athens, Greece)
  • 2005 IMO (Merida, Mexico)
  • 2006 IMO (Ljubljana, Slovania)
  • 2007 IMO (Hanoi, Vietnam)
  • 2008 IMO (Madrid, Spain)
  • 2009 IMO (Bremen, Germany)
  • 2010 IMO (Astana, Kazakhstan)
  • 2011 IMO (Amsterdam, Netherlands)
  • 2012 IMO (Mar del Plata, Argentina)
• The Canadian Mathematical Society has information about several recent IMOs and other national olympiads.
• American Math Competitions has the IMO problems from 1986 to 1999 in LaTeX, PostScript and PDF.
• Joseph Myers has score tables from some recent IMOs (dating back to 1993).
• Tom Verhoeff (who also maintains the IOI home page mentioned below) keeps a comprehensive directory of Olympiad information online.
• Hans Vernaeve mirrors problem files from various Olympiad sites.

National Math Olympiads

Most nations that participate in the International Mathematical Olympiad have some sort of IMO-style exam of their own as a qualifier for the IMO. The links below lead to olympiad resources for the indicated countries or groups. (I have explicitly marked pages not in English.)

• Asian Pacific (in English/French; unofficial); see also here (thanks to David Radcliffe)
• Australia (no problems)
• Belgium (in English/Dutch)
• Canada (in English/French)
• Estonia (in Estonian)
• Iberoamerican (in Spanish)
• Ireland
• Norway (in English/Norwegian)
• Peru (in English/Spanish)
• Romania (in Romanian)
• Singapore (unofficial; no problems)
• South Africa
• Spain (in Spanish)
• Sweden
• USA

Other Contests

These are for high-school students unless otherwise specified.

• For those in the San Francisco area, the Bay Area Mathematical Olympiad began in the spring of 1999.
• The Colorado Mathematical Olympiad.
• The 15th Korean Undergraduate Math Competition, from the USENET group sci.math.
• The home page of the Mandelbrot competition.
• The USA Mathematical Talent Search and International Mathematical Talent Search.
• Thanks to Andreas Blass (via Bill Correll), I have several years of the University of Michigan Undergraduate Mathematics Competition (UMUMC) in TeX:
  • ?th UMUMC (unknown year)
  • 12th UMUMC (1995)
  • 13th UMUMC (1996)
  • 14th UMUMC (1997) with results.
  • 16th UMUMC (1999) with results.
  • 17th UMUMC (2000) with results.
• Regarding the Putnam exam (a North American undergraduate contest), see American Math Competitions' USAMO/IMO/Putnam archive.
• Douglas Zare is running an undergraduate math competition over the Internet.

Other Problem Sources

Publications

• Crux Mathematicorum
• Kömal
• Mathematics and Informatics Quarterly

Miscellaneous

• BarcodesInc has a listing of several math and logic problems for reference that you might find helpful.
• Naoki Sato has a math competitions page covering, among other things, the Canadian Mathematical Olympiad and the Asian Pacific Mathematical Olympiad.

Related Subjects

I don't actively maintain this directory for related subjects, but here are a few links I have found useful or interesting.

General

• The IOI Secretariat maintains information on all of the major international science olympiads.

Programming Contests

• The definitive catalog of programming problems on the WWW is the tasks archive of Daniel Marx.
• The American Computer Science League sponsors a programming competition for high school students.
• The ACM international collegiate programming competition.
• The Duke Internet Programming Contest, based on the ACM contest but held over the Internet.
• A home page for the International Olympiad in Informatics. Also contains information on other science Olympiads, including the IMO.

Physics Contests

• The misnamed Boston Area Undergraduate Physics Competition is based at Harvard but held at several North American universities.
• Tom Verhoeff has a few links concerning the International Physics Olympiad (IPhO).