A Concise Introduction to Pure Mathematics, Second Edition

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CRC Press, Mar 24, 2000 - Mathematics - 176 pages
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For many students interested in pursuing - or required to pursue - the study of mathematics, a critical gap exists between the level of their secondary school education and the background needed to understand, appreciate, and succeed in mathematics at the university level. A Concise Introduction to Pure Mathematics provides a robust bridge over this gap. In nineteen succinct chapters, it covers the range of topics needed to build a strong foundation for the study of the higher mathematics.

Sets and proofs Inequalities
Real numbers Decimals
Rational numbers Introduction to analysis
Complex numbers Polynomial equations
Induction Integers and prime numbers
Counting methods Countability
Functions Infinite sets
Platonic Solids Euler's Formula

Written in a relaxed, readable style, A Concise Introduction to Pure Mathematics leads students gently but firmly into the world of higher mathematics. It demystifies some of the perceived abstractions, intrigues its readers, and entices them to continue their exploration on to analysis, number theory, and beyond.
 

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Contents

Sets and Proofs
1
Number Systems
11
Decimals
17
Inequalities
23
nh Roots and Rational Powers
29
Complex Numbers
33
Polynomial Equations
45
Induction
55
The Integers
87
Prime Factorization
95
More on Prime Numbers
103
Congruence of Integers
107
Counting and Choosing
115
Vlll
127
Infinity
145
Index
159

Eulers Formula and Platonic Solids
69
Introduction to Analysis
79

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