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Author: Serge Tabachnikov
Publisher: American Mathematical Soc.
Published: 2001
Total Pages: 148
ISBN-13: 9780821821718
DOWNLOAD EBOOKThis volume is a collection of articles translated from Russian editions of the journal "Kvant"--T.p. verso.
Author: Titu Andreescu
Publisher: MAA
Published: 2004
Total Pages: 106
ISBN-13: 9780883858172
DOWNLOAD EBOOKThe Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually since 1976. This is the fourth volume in that series. The IMO is a world mathematics competition for high school students that takes place each year in a different country. Students from all over the world participate in this competition. These Olympiad style exams consist of several challenging essay-type problems. Although a correct and complete solution to an Olympiad problem often requires deep analysis and careful argument, the problems require no more than a solid background in high school mathematics coupled with a dose of mathematical ingenuity. There are helpful hints provided for each of the problems. These hints often help lead the student to a solution of the problem. Complete solutions to each of the problems is also included, and many of the problems are presented together with a collection of remarkable solutions developed by the examination committees, contestants and experts, during or after the contest. For each problem with multiple solutions, some common crucial results are presented at the beginning of these solutions.
Author: Zuming Feng
Publisher: MAA
Published: 2006
Total Pages: 100
ISBN-13: 9780883858233
DOWNLOAD EBOOKThe 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.
Author: Titu Andreescu
Publisher: MAA
Published: 2005
Total Pages: 130
ISBN-13: 9780883858196
DOWNLOAD EBOOKThe 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.
Author: Arkadiy Skopenkov
Publisher: American Mathematical Society, Mathematical Sciences Research Institute
Published: 2021-02-11
Total Pages: 196
ISBN-13: 1470448785
DOWNLOAD EBOOKThis 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.
Author: Kenji Ueno
Publisher: American Mathematical Society
Published: 2023-07-13
Total Pages: 149
ISBN-13: 1470475545
DOWNLOAD EBOOKThis is the first of three volumes originated from a series of lectures in mathematics given by professors of Kyoto University in Japan for high school students. The main purpose of the lectures was to show the listeners the beauty and liveliness of mathematics using the material that is accessible to people with little preliminary knowledge. The first chapter of the book talks about the geometry and topology of surfaces. Among other topics the authors discuss the Poincar‚?Hopf theorem about critical points of vector fields on surfaces and the Gauss?Bonnet theorem about the relation between the curvature and topology (Euler characteristics). The second chapter addresses various aspects of the concept of dimension, including the Peano curve and the Poincar‚ approach to dimension. It also discusses the structure of three-dimensional manifolds, proving, in particular, that the three-dimensional sphere is the union of two doughnuts.
Author: Margaret Cozzens
Publisher: American Mathematical Soc.
Published: 2013-09-05
Total Pages: 355
ISBN-13: 0821883216
DOWNLOAD EBOOKHow quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.
Author: Jacques Sesiano
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 187
ISBN-13: 0821844733
DOWNLOAD EBOOKOffers a basic introduction to the types of problems that illustrate the earliest forms of algebra. This book presents some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. It analyzes various examples of problems, with their typical solution methods.
Author: Kenneth R. Davidson
Publisher: American Mathematical Society
Published: 2023-10-30
Total Pages: 200
ISBN-13: 1470473321
DOWNLOAD EBOOKThis book is a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as Unique Factorization, arithmetic over quadratic number fields, the RSA encryption scheme, and finite fields. In addition to introducing students to the rigorous foundations of mathematical proofs, the authors cover several specialized topics, giving proofs of the Fundamental Theorem of Algebra, the transcendentality of $e$, and Quadratic Reciprocity Law. The book is aimed at incoming undergraduate students with a strong passion for mathematics.
Author: Timothy G. Feeman
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 141
ISBN-13: 0821832557
DOWNLOAD EBOOK``Every map is a tool, a product of human effort and creativity, that represents some aspects of our world or universe ... [This] course was powered by the belief that by exploring the mathematical ideas involved in creating and analyzing maps, students would see how mathematics could help them to understand and explain their world.'' -from the Preface Portraits of the Earth exemplifies the AMS's mission to bring the power and vitality of mathematical thought to the nonexpert. It isdesigned to teach students to think logically and to analyze the technical information that they so readily encounter every day. Maps are exciting, visual tools that we encounter on a daily basis: from street maps to maps of the world accompanying news stories to geologic maps depicting theunderground structure of the earth. This book explores the mathematical ideas involved in creating and analyzing maps, a topic that is rarely discussed in undergraduate courses. It is the first modern book to present the famous problem of mapping the earth in a style that is highly readable and mathematically accessible to most students. Feeman's writing is inviting to the novice, yet also interesting to readers with more mathematical experience. Through the visual context of maps andmapmaking, students will see how contemporary mathematics can help them to understand and explain the world. Topics explored are the shape and size of the earth, basic spherical geometry, and why one can't make a perfect flat map of the planet. The author discusses different attributes that maps can have anddetermines mathematically how to design maps that have the desired features. The distortions that arise in making world maps are quantitatively analyzed. There is an in-depth discussion on the design of numerous map projections-both historical and contemporary-as well as conformal and equal-area maps. Feeman looks at how basic map designs can be modified to produce maps with any center, and he indicates how to generalize methods to produce maps of arbitrary surfaces of revolution. Also includedare end-of-chapter exercises and laboratory projects. Particularly interesting is a chapter that explains how to use MapleR add-on software to make maps from geographic data points. This book would make an excellent text for a basic undergraduate mathematics or geography course and would beespecially appealing to the teacher who is interested in exciting visual applications in the classroom. It would also serve nicely as supplementary reading for a course in calculus, linear algebra, or differential geometry. Prerequisites include a solid grasp of trigonometry and basic calculus. RWaterloo Maple, Inc., Ontario, Canada.
