Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis

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Cosimo, Inc., Jan 1, 2009 - Mathematics - 284 pages
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When the mathematician Felix Klein first went to university, he was surprised at just how little what he had learned up to that point was relevant to his new studies. Professors had their own interests, and these they conveyed without regard for the math students of the future that these prospective secondary schoolteachers would one day instruct. Elementary Mathematics from an Advanced Standpoint was written to help remedy that problem. Though highly regarded as one of the finest mathematical minds of his day, Professor Klein took a great deal of interest in guiding teachers and "reducing the gap between the school and the university." Readers will come away impressed at the clarity of Klein's writing, and the ease with which he conveys complex mathematical ideas. Divided into three parts-arithmetic, algebra, and analysis-and covering such topics as complex numbers, real equations, and logarithmic and exponential functions, Klein's classic is essential reading for math instructors and students planning to become math instructors. German mathematician FELIX KLEIN (1849-1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Geometry and Famous Problems of Elementary Geometry.
 

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Contents

Introduction
1
The First Extension of the Notion of Number
22
Concerning Special Properties of Integers
37
Real Equations with Real Unknowns
87
Equations in the field of complex quantities
101
Logarithmic and Exponential Functions
144
The Goniometric Functions
162
Concerning Infinitesimal Calculus Proper
207
Transcendence of the Numbers e and as
237
The Theory of Assemblages
250
Index of Names
269

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