An edition of The elements of advanced mathematics
(1995)
The elements of advanced mathematics
2nd ed.
by Steven G. Krantz
- 0 Ratings
- 0 Want to read
- 0 Currently reading
- 0 Have read
Share
×Close
This edition doesn't have a description yet. Can you add one?
Check nearby libraries
Buy this book
Previews available in: English
Subjects
MathematicsShowing 2 featured editions. View all 2 editions?
| Edition | Availability |
|---|---|
1
The elements of advanced mathematics
2002, Chapman & Hall
in English
- 2nd ed.
1584883030 9781584883036
|
aaaa
Libraries near you:
WorldCat
|
2
|
eeee
|
Book Details
Table of Contents
Machine generated contents note: 1 Basic Logic 1
1.1 Principles of Logic1
1.2 Truth2
1.3 "And" and "Or" 3 3
1.4 "Not"6
1.5 "If- Then"7
1.6 Contrapositive, Converse, and "Iff"10
1.7 Quantifiers13
1.8 Truth and Provability17
Exercises21
2 Methods of Proof 27
2.1 What is a Proof?27
2.2 Direct Proof28
2.3 Proof by Contradiction33
2.4 Proof by Induction36
2.5 Other Methods of Proof40
Exercises43
3 Set Theory 47
3.1 Undefinable Terms47
3.2 Elements of Set Theory48
3.3 Venn Diagrams52
3.4 Further Ideas in Elementary Set Theory53
3.5 Indexing and Extended Set Operations55
Exercises57
4 Relations and Functions 61
4.1 Relations61
4.2 Order Relations 64
4.3 Functions 66
4.4 Combining Functions 69
4.5 Cantor's Notion of Cardinality 73
Exercises 85
5 Axioms of Set Theory, Paradoxes, and Rigor 91
5.1 Axioms of Set Theory91
5.2 The Axiom of Choice 94
5.2.1 Well Ordering94
5.2.2 The Continuum Hypothesis95
5.2.3 Zorn's Lemma95
5.2.4 The Hausdorff Maximality Principle96
5.2.5 The Banach-Tarski Paradox97
5.3 Independence and Consistency97
5.4 Set Theory and Arithmetic 99
Exercises101
6 Number Systems 105
6.0 Preliminary Remarks105
6.1 The Natural Number System106
6.2 The Integers111
6.3 The Rational Numbers117
6.4 The Real Number System124
6.5 The Non-Standard Real Number System133
6.5.1 The Need for Non-Standard Numbers133
6.5.2 Filters and Ultrafilters133
6.5.3 A Useful Measure133
6.5.4 An Equivalence Relation134
6.5.5 An Extension of the Real Number System134
6.6 The Complex Numbers135
6.7 The Quaternions, the Cayley Numbers, and Beyond139
Exercises141
7 More on the Real Number System 147
7.0 Introduction 147
7.1 Sequences147
7.2 Open Sets and Closed Sets149
7.3 Compact Sets151
7.4 The Cantor Set152
7.4.1 Construction of a Remarkable Compact Set153
Exercises156
8 Examples of Axiomatic Theories 159
8.0 Introductory Remarks159
8.1 Group Theory159
8.2 Euclidean and Non-Euclidean Geometry168
Exercises180.
Edition Notes
Includes bibliographical references (p. 209-210) and index.
Classifications
External Links
The Physical Object
ID Numbers
Source records
Community Reviews (0)
Feedback?
History
- Created April 1, 2008
- 10 revisions
Wikipedia citation
×CloseCopy and paste this code into your Wikipedia page. Need help?
| February 7, 2024 | Edited by ImportBot | import existing book |
| September 15, 2021 | Edited by ImportBot | import existing book |
| December 3, 2020 | Edited by MARC Bot | import existing book |
| April 16, 2010 | Edited by bgimpertBot | Added goodreads ID. |
| April 1, 2008 | Created by an anonymous user | Imported from Scriblio MARC record |