The Beginnings and Evolution of Algebra

The Beginnings and Evolution of Algebra
Author: Isabella Bashmakova
Publisher: American Mathematical Soc.
Total Pages: 199
Release: 2000-01-15
Genre: Mathematics
ISBN: 1470457229

The elements of algebra were known to the ancient mesopotamians at least 4000 years ago. Today, algebra stands as one of the cornerstones of modern mathematics. How then did the subject evolve? An illuminating read for historians of mathematics and working algebraists looking into the history of their subject.

The Beginnings and Evolution of Algebra

The Beginnings and Evolution of Algebra
Author: I. G. Bashmakova
Publisher: Cambridge University Press
Total Pages: 200
Release: 2000-04-27
Genre: Mathematics
ISBN: 9780883853290

An examination of the evolution of one of the cornerstones of modern mathematics.

Unknown Quantity

Unknown Quantity
Author: John Derbyshire
Publisher: National Academies Press
Total Pages: 391
Release: 2006-06-02
Genre: Science
ISBN: 030909657X

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.

Episodes in the History of Modern Algebra (1800-1950)

Episodes in the History of Modern Algebra (1800-1950)
Author: Jeremy J. Gray
Publisher: American Mathematical Soc.
Total Pages: 346
Release: 2011-08-31
Genre: Mathematics
ISBN: 0821869043

Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.

Taming the Unknown

Taming the Unknown
Author: Victor J. Katz
Publisher: Princeton University Press
Total Pages: 504
Release: 2014-07-21
Genre: Mathematics
ISBN: 0691149054

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 Algebra

A History of Algebra
Author: Bartel L. van der Waerden
Publisher: Springer Science & Business Media
Total Pages: 279
Release: 2013-06-29
Genre: Mathematics
ISBN: 3642515991

A History of Vector Analysis

A History of Vector Analysis
Author: Michael J. Crowe
Publisher: Courier Corporation
Total Pages: 306
Release: 1994-01-01
Genre: Mathematics
ISBN: 0486679101

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

Modern Algebra and the Rise of Mathematical Structures

Modern Algebra and the Rise of Mathematical Structures
Author: Leo Corry
Publisher: Birkhäuser
Total Pages: 463
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034879172

This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.

Mathematical Thought From Ancient to Modern Times, Volume 1

Mathematical Thought From Ancient to Modern Times, Volume 1
Author: Morris Kline
Publisher: Oxford University Press
Total Pages: 434
Release: 1990-03-01
Genre: Mathematics
ISBN: 0199770468

The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.