Kvant Selecta
Author: Serge Tabachnikov
Publisher: Universities Press
Published: 1999
Total Pages: 176
ISBN-13: 9788173714177
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Kvant Selecta: Algebra and Analysis, I
Author: Serge Tabachnikov
Publisher: American Mathematical Soc.
Published: 1999-08-03
Total Pages: 172
ISBN-13: 9780821810026
DOWNLOAD EBOOK →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.
Kvant Selecta - Algebra And Analysis - Ii
Author: Tabachnikov
Publisher: Universities Press
Published:
Total Pages: 192
ISBN-13: 9788173714184
DOWNLOAD EBOOK →Kvant Selecta: Algebra and Analysis, II
Author: Serge Tabachnikov
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 188
ISBN-13: 9780821819159
DOWNLOAD EBOOK →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.
Kvant Selecta: Combinatorics, I
Author: Serge Tabachnikov
Publisher: American Mathematical Soc.
Published: 2001
Total Pages: 148
ISBN-13: 9780821821718
DOWNLOAD EBOOK →This volume is a collection of articles translated from Russian editions of the journal "Kvant"--T.p. verso.
Integer and Polynomial Algebra
Author: Kenneth R. Davidson
Publisher: American Mathematical Society
Published: 2023-10-30
Total Pages: 200
ISBN-13: 1470473321
DOWNLOAD EBOOK →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.
An Introduction to the History of Algebra
Author: Jacques Sesiano
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 187
ISBN-13: 0821844733
DOWNLOAD EBOOK →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.
The Mathematics of Encryption
Author: Margaret Cozzens
Publisher: American Mathematical Soc.
Published: 2013-09-05
Total Pages: 355
ISBN-13: 0821883216
DOWNLOAD EBOOK →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.
The Mathematics of Voting and Elections: A Hands-On Approach
Author: Jonathan K. Hodge
Publisher: American Mathematical Soc.
Published: 2018-10-01
Total Pages: 238
ISBN-13: 1470442876
DOWNLOAD EBOOK →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.
A Mathematical Gift, III
Author: Koji Shiga
Publisher: American Mathematical Society
Published: 2005-07-18
Total Pages: 141
ISBN-13: 0821832840
DOWNLOAD EBOOK →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"".
