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Contests in Higher Mathematics
One of the most effective ways to stimulate students to enjoy intellectual efforts is the scientific competition. In 1894 the Hungarian Mathematical and Physical Society introduced a mathematical competition for high school students. The success of high school competitions led the Mathematical Society to found a college level contest, named after Miklós Schweitzer. The problems of the Schweitzer Contests are proposed and selected by the most prominent Hungarian mathematicians. This book collects the problems posed in the contests between 1962 and 1991 which range from algebra, combinatorics, theory of functions, geometry, measure theory, number theory, operator theory, probability theory, topology, to set theory. The second part contains the solutions. The Schweitzer competition is one of the most unique in the world. The experience shows that this competition helps to identify research talents. This collection of problems and solutions in several fields in mathematics can serve as a guide for many undergraduates and young mathematicians. The large variety of research level problems might be of interest for more mature mathematicians and historians of mathematics as well.
Imo Problems, Theorems, And Methods: Combinatorics
The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics.In the combinatorics volume, the IMO combinatorics problems are organized into six chapters: 'Enumerative Combinatorics Problems,' 'Existence Problems,' 'Extremal Combinatorial Problems,' 'Operation and Logical Reasoning Problems,' 'Combinatorial Geometry Problems,' an...
Surveys in Combinatorics 2005
This volume provides an up-to-date overview of current research across combinatorics.
Imo Problems, Theorems, And Methods (In 4 Volumes)
The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics. These volumes are collectively titled 'IMO Problems, Theorems, and Methods'.
Imo Problems, Theorems, And Methods: Number Theory
The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics.In the number theory volume, the IMO number theory problems are organized into three chapters: 'Divisibility of Integers,' 'Modular Arithmetic,' and 'Indeterminate Equations.' Each chapter begins with an introduction to the relevant foundational knowledge and methods, followed by a reclassification and reorganization of past IMO problems. Multiple elegant solutions are provided for some of the problems, along with a statistical analysis of their difficulty.The book concludes with a record of past IMO participation and award information, as well as an index of number theory problems, facilitating further study and convenient reference. This series is suitable for researchers in mathematical competitions, mathematics educators, and contestants.
Imo Problems, Theorems, And Methods: Algebra
The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics.In the algebra volume, the IMO algebra problems are organized into five chapters: 'Equation Problems,' 'Function Problems,' 'Sequence Problems,' 'Inequality Problems,' and 'Other Algebra Problems.' Each chapter begins with an introduction to the relevant foundational knowledge and methods, followed by a reclassification and reorganization of past IMO problems. Multiple elegant solutions are provided for some of the problems, along with a statistical analysis of their difficulty.The book concludes with a record of past IMO participation and award information, as well as an index of algebra problems, facilitating further study and convenient reference. This series is suitable for researchers in mathematical competitions, mathematics educators, and contestants.
