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Contemporary mathematics is often extremely abstract, and the important questions mathematicians concern themselves with can sometimes be difficult to describe to the interested non-specialist. Perhaps this is one reason that so many histories of mathematics give little attention to the last hundred years of discovery—despite the fact that this period has probably been the most productive in the history of mathematics. Now in full color, The History of Mathematics set features five revised editions and one new volume that cover a significant portion of recent mathematical history as well as its origins. From the in-depth interviews with prominent mathematicians (one per volume), readers will develop an appreciation for current work in mathematics as well as an interest in the future of this remarkable subject. This set will be invaluable to anyone interested in this fascinating topic and how it applies to everyday situations.
Algebra, Revised Edition
Sets, Symbols, and the Language of Thought
Algebra, Revised Edition describes the history of both strands of algebraic thought. This updated resource describes some of the earliest progress in algebra as well as some of the mathematicians in Mesopotamia, Egypt, China, and Greece who contributed to this early period. It goes on to explore the many breakthroughs in algebraic techniques as well as how letters were used to represent numbers. New material has been added to the chapter on “modern” algebra, a type of mathematical research that continues to occupy the attention of many mathematicians today.
Contents: Introduction • The First Algebras • Greek Algebra • Algebra from India to Northern Africa • Algebra as a Theory of Equations • Algebra in Geometry and Analysis • The Search for New Structures • The Laws of Thought • The Theory of Matrices and Determinants • Conclusion • Afterword • Chronology • Glossary • Further Resources • Index
Beyond Geometry, Revised Edition
A New Mathematics of Space and Form
Beyond Geometry describes how set-theoretic topology developed and why it now occupies a central place in mathematics. Describing axiomatic method as well as providing a definition of what a geometric property is, this new resource examines how early analysts incorporated geometric thinking into their development of the calculus. It also looks at the various mathematicians who struggled to develop a new conceptual framework for mathematics and examines one of the sub-disciplines of set-theoretic topology called dimension theory.
Contents: Introduction • Topology: A Prehistory • A Failure of Intuition • A New Mathematical Landscape • The First Topological Spaces • The Standard Axioms and Three Topological Properties • Schools of Topology • Dimension Theory • Topology and the Foundations of Modern Mathematics • Afterword • Chronology • Glossary • Further Resources • Index
Geometry, Revised Edition
The Language of Space and Form
Geometry, Revised Edition describes geometry in antiquity. Beginning with a brief description of some of the geometry that preceded the geometry of the Greeks, it takes up the story of geometry during the European Renaissance as well as the significant mathematical progress in other areas of the world. It also discusses the analytic geometry of René Descartes and Pierre Fermat, the alternative coordinate systems invented by Isaac Newton, and the solid geometry of Leonhard Euler. Also included is an overview of the geometry of one of the most successful mathematicians of the 19th century, Bernhard Riemann, who created both higher dimensional geometry and geometry that is intrinsic to surfaces. The theory of relativity is also examined in great detail in this full-color resource.
Contents: Introduction • Part One: Geometry in Antiquity • Geometry before the Greeks • Early Greek Geometry • Major Mathematical Works of Greek Geometry • Part Two: New Geometries • Mathematics and Art during the Renaissance • The First Theorems • Projective Geometry Rediscovered • A Non-Euclidean Geometry • Part Three: Coordinate Geometry • The Beginnings of Analytic Geometry • Calculus and Analytic Geometry • Differential Geometry • The Shape of Space and Time • Infinite-Dimensional Geometries • Conclusion • Afterword • Chronology • Glossary • Further Resources • Index ISBN - 9788130925622
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Pages : 1582
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