Download or read book Titu Andreescu and Mark Saul written by Titu Andreescu and published by American Mathematical Soc.. This book was released on 2016-12-19 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not “linear”. The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. There are also “secret” pathways through the book. Each chapter has a subtext, a theme which prepares the student for learning other mathematical topics, concepts, or habits of mind. For example, the early chapters on the arithmetic mean/geometric mean inequality show how very simple observations can be leveraged to yield useful and interesting results. Later chapters give examples of how one can generalize a mathematical statement. The chapter on the Cauchy-Schwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discover—and follow. 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.
Download or read book A Festival of Mathematics written by Alice Peters and published by American Mathematical Society, Mathematical Sciences Research Institute. This book was released on 2022-04-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, inspired by the Julia Robinson Mathematics Festival, aims to engage students in mathematical discovery through fun and approachable problems that reveal deeper mathematical ideas. Each chapter starts with a gentle on-ramp, such as a game or puzzle requiring no more than simple arithmetic or intuitive concepts of symmetry. Follow-up problems and activities require intuitive logic and reveal more sophisticated notions of strategy and algorithms. Projects are designed so that progress is more important than any end goal, ensuring that students will learn something significant no matter how far they get. The process of understanding the questions and how they build on one another becomes an exhilarating ride, revealing serious mathematics before the reader is aware of the transition. This book can be used in classrooms, math clubs, after school activities, homeschooling, and parent/student gatherings and is appropriate for students of age 8 to 18, as well as for teachers wanting to hone their skills. 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.
Download or read book Mathematical Olympiad Challenges written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems. Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops.
Download or read book Mathematics via Problems written by Mikhail B. Skopenkov and published by American Mathematical Society, Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI). This book was released on 2023-11-17 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation from Russian of Part III of the book Mathematics via Problems: From Olympiads and Math Circles to Profession. Part I, Algebra, and Part II, Geometry, have been published in the same series. The main goal of this book is to develop important parts of mathematics through problems. The authors tried to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover such topics in combinatorics as counting, graphs, constructions and invariants in combinatorics, games and algorithms, probabilistic aspects of combinatorics, and combinatorial geometry. Definitions and/or references for material that is not standard in the school curriculum are included. To help students that might be unfamiliar with new material, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions. The book is based on classes taught by the authors at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, SLMath (formerly 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.
Download or read book Math Out Loud An Oral Olympiad Handbook written by Steven Klee and published by American Mathematical Soc.. This book was released on 2021-09-30 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics via Problems written by Arkadiy Skopenkov and published by American Mathematical Society, Mathematical Sciences Research Institute. This book was released on 2021-02-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation from Russian of Part I of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. The other two parts, Geometry and Combinatorics, will be published soon. The main goal of this book is to develop important parts of mathematics through problems. The author tries to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover and recreate much of elementary mathematics and start edging into the sophisticated world of topics such as group theory, Galois theory, and so on, thus building a bridge (by showing that there is no gap) between standard high school exercises and more intricate and abstract concepts in mathematics. Definitions and/or references for material that is not standard in the school curriculum are included. However, many topics in the book are difficult when you start learning them from scratch. To help with this, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions The book is based on classes taught by the author at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. 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.
Download or read book Inspiring Mathematics Lessons from the Navajo Nation Math Circles written by Dave Auckly and published by American Mathematical Soc.. This book was released on 2019-12-05 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The people of the Navajo Nation know mathematics education for their children is essential. They were joined by mathematicians familiar with ways to deliver problems and a pedagogy that, through exploration, shows the art, joy and beauty in mathematics. This combined effort produced a series of Navajo Math Circles—interactive mathematical explorations—across the Navajo Reservation. This book contains the mathematical details of that effort. Between its covers is a thematic rainbow of problem sets that were used in Math Circle sessions on the Reservation. The problem sets are good for puzzling over and exploring the mathematical ideas within. They will help nurture curiosity and confidence in students. The problems come with suggestions for pacing, for adjusting the problems to be more or less challenging, and for different approaches to solving them. This book is a wonderful resource for any teacher wanting to enrich the mathematical lives of students and for anyone curious about mathematical thinking outside the box. 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.
Download or read book How Round Is a Cube And Other Curious Mathematical Ponderings written by James Tanton and published by American Mathematical Soc.. This book was released on 2019-07-12 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general math enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking. The essays are self-contained and rely only on tools from high-school mathematics (with only a few pieces that ever-so-briefly brush up against high-school calculus). The gist of each essay is easy to pick up with a cursory glance—the reader should feel free to simply skim through some essays and dive deep into others. This book is an invitation to play with mathematics and to explore its wonders. Much joy awaits! 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.
Download or read book Math Circle by the Bay written by Laura Givental and published by American Mathematical Soc.. This book was released on 2018-12-14 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on selected topics that the authors taught in math circles for elementary school students at the University of California, Berkeley; Stanford University; Dominican University (Marin County, CA); and the University of Oregon (Eugene). It is intended for people who are already running a math circle or who are thinking about organizing one. It can be used by parents to help their motivated, math-loving kids or by elementary school teachers. We also hope that bright fourth or fifth graders will be able to read this book on their own. The main features of this book are the logical sequence of the problems, the description of class reactions, and the hints given to kids when they get stuck. This book tries to keep the balance between two goals: inspire readers to invent their own original approaches while being detailed enough to work as a fallback in case the teacher needs to prepare a lesson on short notice. It introduces kids to combinatorics, Fibonacci numbers, Pascal's triangle, and the notion of area, among other things. The authors chose topics with deep mathematical context. These topics are just as engaging and entertaining to children as typical “recreational math” problems, but they can be developed deeper and to more advanced levels. 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.
Download or read book The Cauchy Schwarz Master Class written by J. Michael Steele and published by Cambridge University Press. This book was released on 2004-04-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.
Download or read book USA and International Mathematical Olympiads 2005 written by Zuming Feng and published by MAA. This book was released on 2006 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually by the MAA American Mathematics Competitions since 1976. This collection of excellent problems and beautiful solutions is a valuable companion for students who wish to develop their interest in mathematics.
Download or read book USA and International Mathematical Olympiads 2004 written by Titu Andreescu and published by MAA. This book was released on 2005 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olypiad (IMO), have been published annually since 1976. The IMO is the world mathematics championship for high school students. It takes place every year in a different country. The IMO competitions help to discover, challenge, and encourage mathematically gifted young people all over the world. In addition to presenting their own carefully written solutions to the problems presented here, the editors have provided remarkable solutions developed by the examination committees, contestants, and experts, during and after the contests. They also provide a comprehensive guide to other materials on advances problem-solving. This collection of excellent problems and beautiful solutions is a valuable companion for students who wish to develop their interest in mathematics outside the school curriculum and to deepen their knowledge of mathematics.
Download or read book The William Lowell Putnam Mathematical Competition written by Gerald L. Alexanderson and published by American Mathematical Soc.. This book was released on 2018-12-05 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Putnam Competition has been providing a challenge to gifted college mathematics students since 1928. 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.
Download or read book The William Lowell Putnam Mathematical Competition written by A. M. Gleason and published by American Mathematical Soc.. This book was released on 2019-07-24 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: Back by popular demand, we are pleased to reissue this outstanding collection of problems and solutions from the Putnam Competitions covering the years 1938-1964. Problemists the world over, including all past and future Putnam Competitors, will revel in mastering the difficulties posed by this collection of problems from the first 25 William Lowell Putnam Competitions. Solutions to all 347 problems are given. In some cases multiple solutions are included, some which contestants could reasonably be expected to find under examination conditions, and others which are more elegant or utilize more sophisticated techniques. Valuable references and historical comments on many of the problems are presented. The book concludes with four articles on the Putnam competition written by G. Birkhoff, L. E. Bush, L. J. Mordell, and L. M. Kelly which are reprinted from the American Mathematical Monthly. There is great appeal here for all; teachers, students, and all those who love good problems and see them as an entree to beautiful and powerful ideas.
Download or read book The Contest Problem Book IX written by David Wells and published by American Mathematical Society. This book was released on 2021-02-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the ninth book of problems and solutions from the American Mathematics Competitions (AMC) contests. It chronicles 325 problems from the thirteen AMC 12 contests given in the years between 2001 and 2007. The authors were the joint directors of the AMC 12 and the AMC 10 competitions during that period. The problems have all been edited to ensure that they conform to the current style of the AMC 12 competitions. Graphs and figures have been redrawn to make them more consistent in form and style, and the solutions to the problems have been both edited and supplemented. A problem index at the back of the book classifies the problems into subject areas of Algebra, Arithmetic, Complex Numbers, Counting, Functions, Geometry, Graphs, Logarithms, Logic, Number Theory, Polynomials, Probability, Sequences, Statistics, and Trigonometry. A problem that uses a combination of these areas is listed multiple times. The problems on these contests are posed by members of the mathematical community in the hope that all secondary school students will have an opportunity to participate in problem-solving and an enriching mathematical experience.
Download or read book The Contest Problem Book VIII written by J. Douglas Faires and published by American Mathematical Society. This book was released on 2022-02-25 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 50 years, the Mathematical Association of America has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools. The problems for these contests are constructed in the hope that all high school students interested in mathematics will have the opportunity to participate in the contests and will find the experience mathematically enriching. These contests are intended for students at all levels, from the average student at a typical school who enjoys mathematics to the very best students at the most special school. In the year 2000, the Mathematical Association of America initiated the American Mathematics Competitions 10 (AMC 10) for students up to grade 10. The Contest Problem Book VIII is the first collection of problems from that competition covering the years 2001–2007. J. Douglas Faires and David Wells were the joint directors of the AMC 10 and AMC 12 during that period, and have assembled this book of problems and solutions. There are 350 problems from the first 14 contests included in this collection. A Problem Index at the back of the book classifies the problems into the following major subject areas: Algebra and Arithmetic, Sequences and Series, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, Solid Geometry, Discrete Probability, Statistics, Number Theory, and Logic. The major subject areas are then broken down into subcategories for ease of reference. The problems are cross-referenced when they represent several subject areas.
Download or read book First Steps for Math Olympians Using the American Mathematics Competitions written by J. Douglas Faires and published by American Mathematical Soc.. This book was released on 2020-10-26 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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!
