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Proof and the art of mathematics : examples and extensions / Joel David Hamkins.
- Format:
- Book
- Author/Creator:
- Hamkins, Joel David, author.
- Language:
- English
- Subjects (All):
- Proof theory--Textbooks.
- Proof theory.
- Logic, Symbolic and mathematical--Textbooks.
- Logic, Symbolic and mathematical.
- Genre:
- Textbooks.
- Physical Description:
- 1 online resource (viii, 123 pages) : illustrations
- Place of Publication:
- Cambridge, Massachusetts : The MIT Press, [2021]
- [Place of publication not identified] : [publisher not identified], [2021]
- System Details:
- text file
- Summary:
- How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.
- Contents:
- 1 A Classical Beginning p. 1
- 2 Multiple Proofs p. 9
- 3 Number Theory p. 15
- 4 Mathematical Induction p. 21
- 5 Discrete Mathematics p. 31
- 6 Proofs without Words p. 41
- 7 Theory of Games p. 49
- 8 Pick's Theorem p. 57
- 9 Lattice-Point Polygons p. 63
- 10 Polygonal Dissection Congruence Theorem p. 75
- 11 Functions and Relations p. 83
- 12 Graph Theory p. 93
- 13 Infinity p. 103
- 14 Order Theory p. 111
- 15 Real Analysis p. 117.
- Notes:
- Electronic reproduction. Ann Arbor, MI Available via World Wide Web.
- Description based on print version record.
- ISBN:
- 9780262362566
- 0262362562
- Publisher Number:
- 99989176733
- Access Restriction:
- Restricted for use by site license.
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