Exploring mathematics : an engaging introduction to proof
Author(s)
Bibliographic Information
Exploring mathematics : an engaging introduction to proof
（Cambridge mathematical textbooks）
Cambridge University Press, 2017
- : hardback
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Note
Includes bibliographical references (p. 318-320) and index
Description and Table of Contents
Description
Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.
Table of Contents
- 1. Let's play!
- 2. Discovering and presenting mathematics
- 3. Sets
- 4. The integers and the fundamental theorem of arithmetic
- 5. Functions
- 6. Relations
- 7. Cardinality
- 8. The real numbers
- 9. Probability and randomness
- 10. Algebra and symmetry
- 11. Projects
- Appendix A. Solutions, answers, or hints to in-text exercises
- Index
- Bibilography.
by "Nielsen BookData"
