Math Hour Olympiads is a non-standard method of training middle- and high-school students interested in mathematics where students spend several hours thinking about a few difficult and unusual problems. When a student solves a problem, the solution is presented orally to a pair of friendly judges. Discussing the solutions with the judges creates a personal and engaging mathematical experience for the students and introduces them to the true nature of mathematical proof and problem solving. This book recounts the authors' experiences from the first ten years of running a Math Hour Olympiad at the University of Washington in Seattle. The major part of the book is devoted to problem sets and detailed solutions, complemented by a practical guide for anyone who would like to organize an oral olympiad for students in their community. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Olympiad problems help able school students flex their mathematical muscles. Good Olympiad problems are unpredictable: this makes them worthwhile but it also makes them seem hard and even unapproachable. The Mathematical Olympiad Handbook contains some of the problems and solutions from the British Mathematical Olympiads from 1965 to 1996 in a form designed to help bright students overcome this barrier.

This updated printing of the first edition of Colorado Mathematical Olympiad: the First Twenty Years and Further Explorations gives the interesting history of the competition as well as an outline of all the problems and solutions that have been created for the contest over the years. Many of the essay problems were inspired by Russian mathematical folklore and written to suit the young audience; for example, the 1989 Sugar problem was written in a pleasant Lewis Carroll-like story. Some other entertaining problems involve olde Victorian map colourings, King Authur and the knights of the round table, rooks in space, Santa Claus and his elves painting planes, football for 23, and even the Colorado Springs subway system.

See also A SECOND STEP TO MATHEMATICAL OLYMPIAD PROBLEMS The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the first 8 of 15 booklets originally produced to guide students intending to contend for placement on their country's IMO team. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A First Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.

This Manual was primarily written to assist Irish secondary-school students who are preparing to compete in the Irish Mathematical Olympiad (held in May each year) or the International Mathematical Olympiad (held each July). It has also proved useful in other countries, and is popular among people who simply enjoy mathematics. The Mathematical Olympiads are written examinations, based on what is called "second--level mathematics". There are significant variations between countries in the content of second--level programmes in Mathematics. Thus, Irish competitors find themselves faced with problems that require background knowledge that is not covered in the Senior Cycle programme for Irish schools. In order to have a reasonable chance of success, they need to master this material. The authors are academics who have many years experience as voluntary trainers of Olympiad contestants and in other mathematical enrichment activities for young people. The selection of material is based on this experience.

This book is intended as a teacher's manual and a self-study handbook for high-school or college students, and mathematical competitors. It consists mainly of problems created by the authors, with author-prepared-solutions, which were used in different national and international Mathematical Olympiads from 1984 to 2019. The book is arranged by topic and difficulty level. The book gives a broad view of mathematics and goes well beyond the elementary mathematics by providing deeper treatments of the following topics: Geometry and Trigonometry, Number theory, Algebra, Combinatorics and Calculus.