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A Transition to Abstract Mathematics
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General Information
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Type.................: Ebook
Part Size............: 1,971,198 bytes
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Posted by............: ~tqw~
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Release Notes
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A Transition to Abstract Mathematics was written under the assumption that
students do not yet know how to read upper level mathematics texts. Since the
primary purpose of the book is to teach students to write with formal rigor, and
since I naturally presume they do not yet appreciate exposition written in that
form, two overriding features of style defined the first edition: a loose and
informal
expository style of writing, and an airtight composition and organization of
the logic, so that no student could ever say that any necessary detail had been
overlooked or omitted. Consequently, the scope of the first edition was rather
narrow and forward focused, where every exercise had an important role in the
story and there were no characters too peripheral to the plot.
Table Of Contents
Why Read This Book? xiii
Preface xv
Preface to the First Edition xvii
Acknowledgments xxi
0 Notation and Assumptions 1
I Foundations of Logic and Proof Writing 9
1 Language and Mathematics 11
2 Properties of Real Numbers 45
3 Sets and Their Properties 63
4 Functions 119
II Basic Principles of Analysis 163
5 The Real Numbers 165
6 Sequences of Real Numbers 185
7 Functions of a Real Variable 207
III Basic Principles of Algebra 241
8 Groups 243
9 Rings 287
Index 345
Product Details
* ISBN: 0123744806
* ISBN-13: 9780123744807
* Format: Hardcover, 384pp
* Publisher: Elsevier Science & Technology Books
* Pub. Date: September 2008
* Edition Number: 2
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