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Year: 1950 Publisher: Basel: Birkhäuser,
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ISBN: 287647073X 287647073X Year: 1992 Publisher: Sceaux : Jacques Gabay,
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Abel, Niels Henrik, 1802-1829 --- Mathematics --- Collected works
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ISBN: 0828402744 9780828402743 Year: 1974 Publisher: New York (N.Y.): Chelsea,
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Abel, Niels Henrik --- Abel, Niels Henrik, --- Abel, Niels Henrik, - 1802-1829
ISBN: 0262162164 0262661829 9780262661829 9780262162166 Year: 2003 Publisher: Cambridge (Mass.): MIT Press,
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The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra-which even Newton resisted-and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof. [Publisher]
Equations, Roots of --- Abel, Niels Henrik, --- Equations, Roots of. --- Algebra --- Équations, Racines des --- Algèbre --- History --- Histoire --- Abel, Niels Henrik --- Équations, Racines des. --- Histoire. --- Abel, Niels Henrik, - 1802-1829 --- Équations, Racines des. --- Algèbre
ISBN: 3540438262 3642623506 3642189083 Year: 2004 Publisher: Berlin : Springer,
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Abel's influence on modern mathematics is substantial. This is seen in many ways, but maybe clearest in the number of mathematical terms containing the adjective Abelian. In algebra, algebraic and complex geometry, analysis, the theory of differential and integral equations, and function theory there are terms like Abelian groups, Abelian varieties, Abelian integrals, Abelian functions. A number of theorems are attributed to Abel. The famous Addition Theorem of Abel, proved in his Paris Mémoire, stands out, even today, as a mathematical landmark. This book, written by some of the foremost specialists in their fields, contains important survey papers on the history of Abel and his work in several fields of mathematics. The purpose of the book is to combine a historical approach to Abel with an overview of his scientific legacy as perceived at the beginning of the 21st century.
Differential equations --- Geometry, Algebraic --- Equations différentielles --- Congresses --- Congresses. --- Congrès --- Abel, Niels Henrik, --- Abel, Niels Henrik (1802-1829) --- Abel, Niels Henrik --- Algebraic geometry. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Mathematics. --- History. --- Differential equations. --- Partial differential equations. --- Algebraic Geometry. --- Analysis. --- Functional Analysis. --- History of Mathematical Sciences. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Partial differential equations --- 517.91 Differential equations --- Annals --- Auxiliary sciences of history --- Math --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Algebraic geometry --- Geometry
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