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.

Download or read book A Primer for Mathematics Competitions written by Alexander Zawaira and published by OUP Oxford. This book was released on 2008-10-31 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.

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.

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.

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.

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.

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Download or read book Count Down written by Steve Olson and published by Houghton Mifflin Harcourt. This book was released on 2004 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each summer six math whizzes selected from nearly a half-million American teens compete against the world's best problem solvers at the International Mathematical Olympiad.Steve Olson followed the six 2001 contestants from the intense tryouts to the Olympiad's nail-biting final rounds to discover not only what drives these extraordinary kids but what makes them both unique and typical.In the process he provides fascinating insights into the science of intelligence and learning and, finally, the nature of genius.Brilliant, but defying all the math-nerd stereotypes, these teens want to excel in whatever piques their curiosity, and they are curious about almost everything - music, games, politics, sports, literature.One team member is ardent about both water polo and creative writing. Another plays four musical instruments.For fun and entertainment during breaks, the Olympians invent games of mind-boggling difficulty.Though driven by the glory of winning this ultimate math contest, they are in many ways not so different from other teenagers, finding pure joy in indulging their personal passions. Beyond the the Olympiad, Olson sheds light on many questions, from why Americans feel so queasy about math, to why so few girls compete in the subject, to whether or not talent is innate.Inside the cavernous gym where the competition takes place, Count Down uncovers a fascinating subculture and its engaging, driven inhabitants.

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.

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.

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. ​​

Download or read book A Mathematical Mosaic written by Ravi Vakil and published by Brendan Kelly Publishing Inc.. This book was released on 1996 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Powerful problem solving ideas that focus on the major branches of mathematics and their interconnections.

Download or read book 104 Number Theory Problems written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

Download or read book Competition Math for Middle School written by Jason Batteron and published by . This book was released on 2011-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The William Lowell Putnam Mathematical Competition written by Gerald L. Alexanderson and published by Cambridge University Press. This book was released on 2003 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Putnam Competition has since 1928 been providing a challenge to gifted college mathematics students. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions. In 1980, the MAA published the first William Lowell Putnam Mathematical Competition book, covering the contest from 1938 to 1964. In 2002 the third of the Putnam problem books appeared, covering the years 1985 through 2000. All three of these books belong on the bookshelf of students, teachers, and all interested in problem solving.

Download or read book Breakthrough Problem Solving with Action Learning written by Michael Marquardt and published by Stanford University Press. This book was released on 2012-05-16 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Breakthrough Problem Solving with Action Learning explores why and how action learning groups have been so successful and creative in solving complex problems. The text begins by briefly reviewing the theories that undergird the effectiveness of action learning, philosophically situating readers and pointing them in the direction of related academic works that they may wish to explore. It then turns to stories of how organizations have employed action learning in solving specific, often-encountered business problems. These cases not only serve as real-world models for how action learning can be successfully employed, but also offer inspiration and potential starting points and guidelines for other businesses that face similar problems. The book concludes with a cross-case analysis that pinpoints the ingredients necessary for breakthrough problem solving via action learning.

Download or read book A Primer for the Mathematics of Financial Engineering written by Dan Stefanica and published by . This book was released on 2011 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: