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

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Courier Corporation, 2004 - Mathematics - 274 pages
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"Makes the reader feel the inspiration that comes from listening to a great mathematician." "Bulletin, " American Mathematical Society
A distinguished mathematician and educator enlivens abstract discussions of arithmetic, algebra, and analysis by means of graphical and geometrically perceptive methods. His three-part treatment begins with topics associated with arithmetic, including calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers. Algebra-related subjects constitute the second part, which examines real equations with real unknowns and equations in the field of complex quantities. The final part explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 edition. 125 figures."
 

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Contents

Arithmetic
6
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
HI Concerning Infinitesimal Calculus Proper
207
Transcendence of the Numbers e and n
237
The Theory of Assemblages
250
Index of Names
269
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About the author (2004)

1862-1953

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