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This original work discusses mathematical methods needed by undergraduates in the United States and Canada preparing for competitions at the level of the International Mathematical Olympiad (IMO) and the Putnam Competition. The six-part treatment covers counting methods, number theory, inequalities and the theory of equations, metrical geometry, analysis, and number representations and logic. Includes problems with solutions plus 1,000 problems for students to finish themselves.
Book Synopsis Concepts and Problems for Mathematical Competitors by : Alexander Sarana
Download or read book Concepts and Problems for Mathematical Competitors written by Alexander Sarana and published by Courier Dover Publications. This book was released on 2020-08-12 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This original work discusses mathematical methods needed by undergraduates in the United States and Canada preparing for competitions at the level of the International Mathematical Olympiad (IMO) and the Putnam Competition. The six-part treatment covers counting methods, number theory, inequalities and the theory of equations, metrical geometry, analysis, and number representations and logic. Includes problems with solutions plus 1,000 problems for students to finish themselves.
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.
Book Synopsis Concepts in Competitive Mathematics by : Zachary M. Boazman
Download or read book Concepts in Competitive Mathematics written by Zachary M. Boazman and published by Zachary Boazman. This book was released on 2010-05-27 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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, Bibliography, Index. What's new in the second edition? Larger figures Improved formatting More exmples New contests cited Updated information Bibliography Corrected errors And more!
Book Synopsis Concepts in Competitive Mathematics, Second Edition by : Zachary M. Boazman
Download or read book Concepts in Competitive Mathematics, Second Edition written by Zachary M. Boazman and published by CreateSpace. This book was released on 2014-08-13 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Bibliography, Index. What's new in the second edition? Larger figures Improved formatting More exmples New contests cited Updated information Bibliography Corrected errors And more!
A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.
Book Synopsis Problem-Solving Strategies by : Arthur Engel
Download or read book Problem-Solving Strategies written by Arthur Engel and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.
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.
Book Synopsis Putnam and Beyond by : Răzvan Gelca
Download or read book Putnam and Beyond written by Răzvan Gelca and published by Springer. This book was released on 2017-09-19 with total page 857 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
While the books in this series are primarily designed for AMC competitors, they contain the most essential and indispensable concepts used throughout middle and high school mathematics. Some featured topics include key concepts such as equations, polynomials, exponential and logarithmic functions in Algebra, various synthetic and analytic methods used in Geometry, and important facts in Number Theory. The topics are grouped in lessons focusing on fundamental concepts. Each lesson starts with a few solved examples followed by a problem set meant to illustrate the content presented. At the end, the solutions to the problems are discussed with many containing multiple methods of approach. I recommend these books to not only contest participants, but also to young, aspiring mathletes in middle school who wish to consolidate their mathematical knowledge. I have personally used a few of the books in this collection to prepare some of my students for the AMC contests or to form a foundation for others. By Dr. Titu Andreescu US IMO Team Leader (1995 - 2002) Director, MAA American Mathematics Competitions (1998 - 2003) Director, Mathematical Olympiad Summer Program (1995 - 2002) Coach of the US IMO Team (1993 - 2006) Member of the IMO Advisory Board (2002 - 2006) Chair of the USAMO Committee (1996 - 2004) I love this book! I love the style, the selection of topics and the choice of problems to illustrate the ideas discussed. The topics are typical contest problem topics: divisors, absolute value, radical expressions, Veita's Theorem, squares, divisibility, lots of geometry, and some trigonometry. And the problems are delicious. Although the book is intended for high school students aiming to do well in national and state math contests like the American Mathematics Competitions, the problems are accessible to very strong middle school students. The book is well-suited for the teacher-coach interested in sets of problems on a given topic. Each section begins with several substantial solved examples followed by a varied list of problems ranging from easily accessible to very challenging. Solutions are provided for all the problems. In many cases, several solutions are provided. By Professor Harold Reiter Chair of MATHCOUNTS Question Writing Committee. Chair of SAT II Mathematics committee of the Educational Testing Service Chair of the AMC 12 Committee (and AMC 10) 1993 to 2000.
Book Synopsis Fifty Lectures for American Mathematics Competitions by : Jane Chen
Download or read book Fifty Lectures for American Mathematics Competitions written by Jane Chen and published by Createspace Independent Publishing Platform. This book was released on 2013-01-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the books in this series are primarily designed for AMC competitors, they contain the most essential and indispensable concepts used throughout middle and high school mathematics. Some featured topics include key concepts such as equations, polynomials, exponential and logarithmic functions in Algebra, various synthetic and analytic methods used in Geometry, and important facts in Number Theory. The topics are grouped in lessons focusing on fundamental concepts. Each lesson starts with a few solved examples followed by a problem set meant to illustrate the content presented. At the end, the solutions to the problems are discussed with many containing multiple methods of approach. I recommend these books to not only contest participants, but also to young, aspiring mathletes in middle school who wish to consolidate their mathematical knowledge. I have personally used a few of the books in this collection to prepare some of my students for the AMC contests or to form a foundation for others. By Dr. Titu Andreescu US IMO Team Leader (1995 - 2002) Director, MAA American Mathematics Competitions (1998 - 2003) Director, Mathematical Olympiad Summer Program (1995 - 2002) Coach of the US IMO Team (1993 - 2006) Member of the IMO Advisory Board (2002 - 2006) Chair of the USAMO Committee (1996 - 2004) I love this book! I love the style, the selection of topics and the choice of problems to illustrate the ideas discussed. The topics are typical contest problem topics: divisors, absolute value, radical expressions, Veita's Theorem, squares, divisibility, lots of geometry, and some trigonometry. And the problems are delicious. Although the book is intended for high school students aiming to do well in national and state math contests like the American Mathematics Competitions, the problems are accessible to very strong middle school students. The book is well-suited for the teacher-coach interested in sets of problems on a given topic. Each section begins with several substantial solved examples followed by a varied list of problems ranging from easily accessible to very challenging. Solutions are provided for all the problems. In many cases, several solutions are provided. By Professor Harold Reiter Chair of MATHCOUNTS Question Writing Committee. Chair of SAT II Mathematics committee of the Educational Testing Service Chair of the AMC 12 Committee (and AMC 10) 1993 to 2000.
This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.
Book Synopsis The William Lowell Putnam Mathematical Competition 1985-2000 by : Kiran Sridhara Kedlaya
Download or read book The William Lowell Putnam Mathematical Competition 1985-2000 written by Kiran Sridhara Kedlaya and published by MAA. This book was released on 2002 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.
This text opens with the theory of 2-person zero-sum games, 2-person non-zero sum games, and n-person games, at a level between non-mathematical introductory books and technical mathematical game theory books. Includes introductory explanations of gaming and meta games. Includes numerous exercises anbd problems with solutions and over 30 illustrations. 1986 edition.
Book Synopsis Games, Theory and Applications by : L. C. Thomas
Download or read book Games, Theory and Applications written by L. C. Thomas and published by Courier Corporation. This book was released on 2012-12-13 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text opens with the theory of 2-person zero-sum games, 2-person non-zero sum games, and n-person games, at a level between non-mathematical introductory books and technical mathematical game theory books. Includes introductory explanations of gaming and meta games. Includes numerous exercises anbd problems with solutions and over 30 illustrations. 1986 edition.
Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.
Book Synopsis Mathematics as Problem Solving by : Alexander Soifer
Download or read book Mathematics as Problem Solving written by Alexander Soifer and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.
The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years.
Book Synopsis Mathematical Problem Posing by : Florence Mihaela Singer
Download or read book Mathematical Problem Posing written by Florence Mihaela Singer and published by Springer. This book was released on 2015-06-12 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years.
