The Art of Proof Basic Training for Deeper Mathematics /
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on sol...
| Main Authors: | , |
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| Corporate Author: | |
| Format: | Electronic |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
2010.
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| Series: | Undergraduate Texts in Mathematics,
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| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4419-7023-7 |
Table of Contents:
- Preface
- Notes for the Student
- Notes for Instructors
- Part I: The Discrete
- 1 Integers
- 2 Natural Numbers and Induction
- 3 Some Points of Logic
- 4 Recursion
- 5 Underlying Notions in Set Theory
- 6 Equivalence Relations and Modular Arithmetic
- 7 Arithmetic in Base Ten
- Part II: The Continuous
- 8 Real Numbers
- 9 Embedding Z in R
- 10. Limits and Other Consequences of Completeness
- 11 Rational and Irrational Numbers
- 12 Decimal Expansions
- 13 Cardinality
- 14 Final Remarks
- Further Topics
- A Continuity and Uniform Continuity
- B Public-Key Cryptography
- C Complex Numbers
- D Groups and Graphs
- E Generating Functions
- F Cardinal Number and Ordinal Number
- G Remarks on Euclidean Geometry
- List of Symbols
- Index.