Contests in Higher Mathematics

Contests in Higher Mathematics PDF

Author: Gabor J. Szekely

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 576

ISBN-13: 1461207339

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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.

First Steps for Math Olympians: Using the American Mathematics Competitions

First Steps for Math Olympians: Using the American Mathematics Competitions PDF

Author: J. Douglas Faires

Publisher: American Mathematical Soc.

Published: 2020-10-26

Total Pages: 307

ISBN-13: 1470451263

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Any high school student preparing for the American Mathematics Competitions should get their hands on a copy of this book! A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability. As students' problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians!

Laboratories in Mathematical Experimentation

Laboratories in Mathematical Experimentation PDF

Author: Mount Holyoke College

Publisher: Springer Science & Business Media

Published: 1997-03

Total Pages: 308

ISBN-13: 9780387949222

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The text is composed of a set of sixteen laboratory investigations which allow the student to explore rich and diverse ideas and concepts in mathematics. The approach is hands-on, experimental, an approach that is very much in the spirit of modern pedagogy. The course is typically offered in one semester, at the sophomore (second year) level of college. It requires completion of one year of calculus. The course provides a transition to the study of higher, abstract mathematics. The text is written independent of any software. Supplements will be available on the projects' web site.

Solving Mathematical Problems

Solving Mathematical Problems PDF

Author: Terence Tao

Publisher: OUP Oxford

Published: 2006-07-28

Total Pages: 116

ISBN-13: 0191568694

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Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.

Putnam and Beyond

Putnam and Beyond PDF

Author: Răzvan Gelca

Publisher: Springer

Published: 2017-09-19

Total Pages: 857

ISBN-13: 3319589881

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This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

Euclidean Geometry in Mathematical Olympiads

Euclidean Geometry in Mathematical Olympiads PDF

Author: Evan Chen

Publisher: American Mathematical Soc.

Published: 2021-08-23

Total Pages: 311

ISBN-13: 1470466201

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This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.

The Stanford Mathematics Problem Book

The Stanford Mathematics Problem Book PDF

Author: George Polya

Publisher: Courier Corporation

Published: 2013-04-09

Total Pages: 80

ISBN-13: 048631832X

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Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Concepts in Competitive Mathematics

Concepts in Competitive Mathematics PDF

Author: Zachary M. Boazman

Publisher: Zachary Boazman

Published: 2010-05-27

Total Pages: 96

ISBN-13:

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This short reference book contains fundamental concepts crucial to solving math competition problems such as those found on the Mathematical Association of America's AMC 10, AMC 12, and AIME, as well as those found in local or regional competitions. Full of formulas as well as examples and solutions, this book shows how specific problems can be best solved in order to succeed in math competitions. Content is organized by mathematical topic and has been selected for its diversity. Topics include Number Theory, Combinatorics, Probability, Statistics, Sequences and Series, Algebra, Geometry, Trigonometry, and Coordinate Mathematics. The book even contains a section containing the author's own tips from past experience in math competitions. All in all, this is a must buy for math competition participants and teachers alike. Contains: Nine Chapters, Table of Contents, Index.

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