What is the IMC?
The International Mathematics Competition is a mathematics contest for undergraduate students, taking place every summer at the American University in Blagoevgrad, Bulgaria.
Over a two-day period, participants solve 10 problems based on the material that is typically seen during an undergraduate mathematics programme (especially linear and abstract algebra, real and complex analysis, differential equations, combinatorics and number theory).
While higher year students are more likely to have had the exposure needed to compete successfully, students at all levels can participate.
If you enjoy the challenge of tackling difficult problems and the satisfaction of solving them, you will enjoy the process of preparing for, and competing in, the IMC!
IMC Preparation at Durham
During Epiphany term 2026, the Durham MPSS will meet weekly on Wednesdays (time and place given below) to have tea/coffee, eat biscuits and solve maths problems. Each week we will focus on a different problem sheet dealing with a specific topic/theme. Depending on interest, some (informal) discussion of the theme will be provided.
We are meeting as a group because despite the format of maths contests, problem solving is most fruitfully accomplished as a collective effort. In particular, group solving and discussion is definitely encouraged!
Below, you will find problem sheets (and, eventually, their solutions) that will be useful in preparing for the IMC:
(January 14, 2-5 PM, W007) Proof techniques, Induction and the Pigeonhole Principle: Problems Hints Solutions
(January 21, 2-5 PM, W007) Inequalities: Problems Hints Solutions
(January 28, 2-5 PM, W007) Linear Algebra: Problems Hints Solutions
(February 4, 2-5 PM, W007) Polynomials: Problems Hints Solutions
(February 11, 2-5 PM, W007) Sequences and Series: Problems Hints Solutions
(February 18, 2-5 PM, W007) Number Theory: Problems Hints Solutions
(February 25, 2-5 PM, W007) Set Theory and Combinatorics: Problems Hints Solutions
(March 4, 2-5 PM, W007) Real Analysis and Integration: Problems Hints Solutions
(March 11, 2-5 PM, W007) Miscellaneous (e.g. abstract algebra, complex analysis, geometry):
(Complex analysis:) Problems Hints Solutions (Abstract Algebra:) Problems Hints Solutions
(March 18, 2-5 PM, W007) TBA
Last year, the team selection test took place on June 9th.
Additional Resources:
Recommended problem books:
Putnam and Beyond, by Titu Andreescu and Razvan Gelca
Problem Solving through Problems, by Loren Larson
Challenging Mathematical Problems with Elementary Solutions, vol. I and II, by A.M. Yaglom and I.M. Yaglom
Berkeley Problems in Mathematics, by Paulo Ney de Souza and Jorge-Nuno Silva
In North America, the William Lowell Putnam Competition is the preeminent mathematics contest for undergraduate students. While sometime more challenging than IMC problems, they serve as useful preparatory material for students eager to participate in the IMC.
An archive devoted to all of the Putnam problems since 1985 can be found here.
A broad, useful collection of olympiad-type problems can be found here.
A large collection of IMC preparatory material, including problems by topic, by Mike Daas, can be found here.
Each of the past IMC contest webpages has links to the problems from past years, as here.