A History of Algebra
Author : Bartel L. van der Waerden
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 15,89 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3642515991
An Introduction to the History of Algebra
Author : Jacques Sesiano
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 19,14 MB
Release : 2009
Category : Mathematics
ISBN : 0821844733
Book Description
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.
Unknown Quantity
Author : John Derbyshire
Publisher : National Academies Press
Page : 391 pages
File Size : 19,35 MB
Release : 2006-06-02
Category : Science
ISBN : 030909657X
Book Description
Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages-and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics-it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.
Taming the Unknown
Author : Victor J. Katz
Publisher : Princeton University Press
Page : 504 pages
File Size : 18,3 MB
Release : 2014-07-21
Category : Mathematics
ISBN : 0691149054
Book Description
What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra’s remarkable growth through different epochs around the globe.
A History of Abstract Algebra
Author : Jeremy Gray
Publisher : Springer
Page : 412 pages
File Size : 37,82 MB
Release : 2018-08-07
Category : Mathematics
ISBN : 3319947737
Book Description
This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
A History of Abstract Algebra
Author : Israel Kleiner
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 45,67 MB
Release : 2007-10-02
Category : Mathematics
ISBN : 0817646841
Book Description
This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
الكتاب المختصر فى حساب الجبر والمقابلة
Author : Muḥammad ibn Mūsá Khuwārizmī
Publisher :
Page : 360 pages
File Size : 17,48 MB
Release : 1831
Category : Algebra
ISBN :
Book Description
Algebra in Ancient and Modern Times
Author : V. S. Varadarajan
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 46,3 MB
Release : 1998
Category : Mathematics
ISBN : 9780821809891
Book Description
The author uses an historical approach to show the advancement of algebra from its ancient beginnings to its modern usage.
Mathematics and Its History
Author : John Stillwell
Publisher : Springer Nature
Page : 400 pages
File Size : 26,47 MB
Release : 2020-11-07
Category : Mathematics
ISBN : 3030551938
Book Description
This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition
Greek Mathematical Thought and the Origin of Algebra
Author : Jacob Klein
Publisher : Courier Corporation
Page : 246 pages
File Size : 16,74 MB
Release : 2013-04-22
Category : Mathematics
ISBN : 0486319814
Book Description
Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography.
