عنوان

Algebra

0816049548 (hardcover)

IR

E-2891

انگلیسی

IR

Algebra

[Book]

:sets, symbols, and the language of thought

/ John Tabak

New York

: Facts On File,

, c2004.

xiv, 224 p. , ill. , 24 cm.

(History of mathematics.)

Print

Includes bibliographical references (p. 203-212) and index.

Discusses the history, progress, and applications of algebra, as well as its usefulness to science and society, and includes a timeline of notable events. Algebra developed independently in several places around the world, with Hindu, Greek, and Arabic ideas and problems arising at different points in history. Mostly rhetorical in its early forms, the symbolic form of algebra used today was formalized in the 17th century and later. In the past two centuries, algebra has taken two diverging paths. One is toward increasingly higher levels of abstraction, and the other is toward more concrete computational methods. Both paths are greatly influenced by past theories and developments in algebra. Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.

Introduction: Algebra as language -- First Algebras: Mesopotamia: Beginnings of Algebra -- Mesopotamians and second-degree equations -- Mesopotamians and indeterminate equations -- Clay tablets and electronic calculators -- Egyptian algebra -- Chinese algebra -- Rhetorical algebra Greek algebra: Discovery of the Pythagoreans -- Incommensurability of [radical]2 -- Geometric algebra -- Algebra made visible -- Diophantus of Alexandria -- Algebra from India to Northern Africa: -- Brahmagupta and the new algebra -- Mahavira -- Bhaskara and the end of an era -- Islamic mathematics -- Poetry and algebra -- Al-Khwarizmi and a new concept of algebra -- Problem and a solution -- Omar Khayyam, Islamic algebra at its best -- Leonardo of Pisa -- Algebra as a theory of equations: -- New algorithms -- Algebra as a tool in science -- Francois Viete, algebra as a symbolic language -- Thomas Harriot -- Albert Girard and the fundamental theorem of algebra -- Further attempts at a proof -- Using polynomials -- Algebra in geometry and analysis: Rene Descartes -- Descartes on multiplication -- Pierre de Fermat -- Fermat's last theorem -- New approach -- Search for new structures: Niels Henrik Abel -- Evariste Galois -- Galois theory and the doubling of the cube -- Doubling the cube with a straightedge and compass is impossible -- Solution of algebraic equations -- Group theory in chemistry -- Laws of thought: Aristotle -- Gottfried Leibniz -- George Boole and the laws of thought -- Boolean algebra -- Aristotle and Boole -- Refining and extending Boolean algebra -- Boolean algebra and computers -- Theory of matrices and determinants: Early ideas -- Spectral theory -- Theory of matrices -- Matrix multiplication -- Computational application of matrix algebra -- Matrices in ring theory -- Chronology -- Glossary -- Further reading -- Index.

Tabak, John.History of mathematics

Algebra, History

Tabak, John.

ایران

۰۹۱۷

عادی

عادی

E-2891.PDF

5084222

مدیر

متن

0

E-2891

old catalog

p

BL

1

a

Y