A Transition to Abstract Mathematics~tqw~ darksiderg

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A Transition to Abstract Mathematics

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Type.................: Ebook

Part Size............: 1,971,198 bytes



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Posted by............: ~tqw~



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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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