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 on the WWW.

• 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 and its associated scoring site (Washington, United States)
  • 2002 IMO (Glasgow, United Kingdom)
  • 2003 IMO (Tokyo, Japan)
  • 2004 IMO (Athens, Greece)
• 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 on the WWW.
• 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 and Mandelbrot Midlevels competitions.
• 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

• 20,000 Problems Under the Sea (formerly MathPro Online) has a searchable directory of math problems.
• 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).