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Author : Tabachnikov
Publisher : Universities Press
Page : 192 pages
File Size : 41,6 Mb
Release : 2024-07-04
Category : Electronic
ISBN : 8173714185
Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 169 pages
File Size : 55,5 Mb
Release : 1999-08-03
Category : Algebra
ISBN : 9780821810026
This volume and Kvant Selecta: Algebra and Analysis, II (MAWRLD/15) are the first volumes of articles published from 1970 to 1990 in the Russian journal, Kvant. The influence of this magazine on mathematics and physics education in Russia is unmatched. This collection represents the Russian tradition of expository mathematical writing at its best. Articles selected for these two volumes are written by leading Russian mathematicians and expositors. Some articles contain classical mathematical gems still used in university curriculae today. Others feature cutting-edge research from the 20th Century. The articles in these books are written so as to present genuine mathematics in a conceptual, entertaining, and accessible way. The volumes are designed to be used by students and teachers who love mathematics and want to study its various aspects, thus deepening and expanding the school curriculum. The articles in the first volume are mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra.
Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 41,7 Mb
Release : 1999
Category : Mathematics
ISBN : 0821819151
This volume contains translated articles originally published from 1970 to 1990 in the Russian journal "Kvant." The influence of this magazine on mathematics and physics education in Russia is unmatched. This volume initiates a collection that represents the Russian tradition of expository mathematical writing at its best. Written by leading Russian mathematicians and expositors, these articles present mathematics in a conceptual, entertaining, and accessible way. This volume is designed for students and teachers who love mathematics, and can expand on local school curriculum subjects. This second volume addresses diverse aspects of analysis and algebra.
Author : Serge Tabachnikov
Publisher : Universities Press
Page : 176 pages
File Size : 50,5 Mb
Release : 1999
Category : Algebra
ISBN : 8173714177
Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 42,7 Mb
Release : 1999-08-03
Category : Mathematics
ISBN : 0821810022
This volume contains translated articles originally published from 1970 to 1990 in the Russian journal "Kvant." The influence of this magazine on mathematics and physics education in Russia is unmatched. This volume initiates a collection that represents the Russian tradition of expository mathematical writing at its best. Written by leading Russian mathematicians and expositors, these articles present mathematics in a conceptual, entertaining, and accessible way. This volume is designed for students and teachers who love mathematics, and can expand on local school curriculum subjects. This first volume addresses various topics in number theory.
Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 55,7 Mb
Release : 2001
Category : Mathematics
ISBN : 0821821717
This volume is a collection of articles translated from Russian editions of the journal "Kvant"--T.p. verso.
Author : Kenji Ueno,Kōji Shiga,Shigeyuki Morita
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 42,8 Mb
Release : 2003
Category : Functions
ISBN : 9780821832837
Three volumes originating from a series of lectures in mathematics given by professors of Kyoto University in Japan for high school students.
Author : Jacques Sesiano
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 51,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821844731
Offers 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,Matthew Satriano
Publisher : American Mathematical Society
Page : 200 pages
File Size : 49,5 Mb
Release : 2023-10-30
Category : Mathematics
ISBN : 9781470473327
This 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 : Koji Shiga,Toshikazu Sunada
Publisher : American Mathematical Society
Page : 141 pages
File Size : 55,6 Mb
Release : 2005-07-18
Category : Mathematics
ISBN : 9780821832844
This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. The first chapter talks about the theory of manifolds. It includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form).The second chapter discusses the notion of the area of a figure on the plane and the volume of a solid body in space. It includes the proof of the Bolyai-Gerwien theorem about scissors-congruent polynomials and Dehn's solution of the Third Hilbert Problem. This is the third volume originating from a series of lectures given at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first and second volumes are available as Volume 19 and Volume 20 in the AMS series, ""Mathematical World"".
Author : Radmila Bulajich Manfrino,José Antonio Gómez Ortega,Rogelio Valdez Delgado
Publisher : Birkhäuser
Page : 311 pages
File Size : 44,8 Mb
Release : 2015-02-09
Category : Mathematics
ISBN : 9783319119465
The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world. In the first four chapters the authors cover material for competitions at high school level. The level advances with the chapters. The topics explored include polynomials, functional equations, sequences and an elementary treatment of complex numbers. The final chapters provide a comprehensive list of problems posed at national and international contests in recent years, and solutions to all exercises and problems presented in the book. It helps students in preparing for national and international mathematical contests form high school level to more advanced competitions and will also be useful for their first year of mathematical studies at the university. It will be of interest to teachers in college and university level, and trainers of the mathematical Olympiads.
Author : Margaret Cozzens, Steven J. Miller
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 50,9 Mb
Release : 2013-09-05
Category : Business & Economics
ISBN : 9780821883211
How 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 : Jonathan K. Hodge,Richard E. Klima
Publisher : American Mathematical Soc.
Page : 238 pages
File Size : 40,6 Mb
Release : 2018-10-01
Category : Elections
ISBN : 9781470442873
The Mathematics of Voting and Elections: A Hands-On Approach, Second Edition, is an inquiry-based approach to the mathematics of politics and social choice. The aim of the book is to give readers who might not normally choose to engage with mathematics recreationally the chance to discover some interesting mathematical ideas from within a familiar context, and to see the applicability of mathematics to real-world situations. Through this process, readers should improve their critical thinking and problem solving skills, as well as broaden their views of what mathematics really is and how it can be used in unexpected ways. The book was written specifically for non-mathematical audiences and requires virtually no mathematical prerequisites beyond basic arithmetic. At the same time, the questions included are designed to challenge both mathematical and non-mathematical audiences alike. More than giving the right answers, this book asks the right questions. The book is fun to read, with examples that are not just thought-provoking, but also entertaining. It is written in a style that is casual without being condescending. But the discovery-based approach of the book also forces readers to play an active role in their learning, which should lead to a sense of ownership of the main ideas in the book. And while the book provides answers to some of the important questions in the field of mathematical voting theory, it also leads readers to discover new questions and ways to approach them. In addition to making small improvements in all the chapters, this second edition contains several new chapters. Of particular interest might be Chapter 12 which covers a host of topics related to gerrymandering.
Author : Kenji Ueno,Kōji Shiga,Shigeyuki Morita
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 41,7 Mb
Release : 2003
Category : Mathematics
ISBN : 0821832824
Three volumes originating from a series of lectures in mathematics given by professors of Kyoto University in Japan for high school students.
Author : Timothy G. Feeman
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 51,6 Mb
Release : 2024-07-04
Category : Mathematics
ISBN : 0821872613
''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.