A Gateway to Higher Mathematics

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Jones & Bartlett Learning, 2005 - Computers - 309 pages
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A Gateway to Higher Mathematics integrates the process of teaching students how to do proofs into the framework of displaying the development of the real number system. The text eases the students into learning how to construct proofs, while preparing students how to cope with the type of proofs encountered in the higher-level courses of abstract algebra, analysis, and number theory. After using this text, the students will not only know how to read and construct proofs, they will understand much about the basic building blocks of mathematics. The text is designed so that the professor can choose the topics to be emphasized, while leaving the remainder as a reference for the students.
 

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Contents

Logic and Techniques for Proofs
2
Elementary Set Theory
21
The Development of the Integers
71
Properties and Application of Integers
139
Fields and the Rational Numbers
197
The Development of the Real Numbers
223
Some Additional Properties
259
Proof of the CantorSchroderBernstein
287
References
305
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