Authors:
- Equips students to recognise proof patterns across fields in pure mathematics
- Reinforces each technique with end of chapter problems
- Supports further research with extensive additional reading suggestions
- Includes supplementary material: sn.pub/extras
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Table of contents (20 chapters)
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Front Matter
About this book
This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity.
The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.
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Authors and Affiliations
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Centre for Actuarial Studies, University of Melbourne, Melbourne, Australia
Mark Joshi
About the author
Bibliographic Information
Book Title: Proof Patterns
Authors: Mark Joshi
DOI: https://doi.org/10.1007/978-3-319-16250-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-16249-2Published: 30 March 2015
eBook ISBN: 978-3-319-16250-8Published: 17 March 2015
Edition Number: 1
Number of Pages: XIII, 190
Number of Illustrations: 24 b/w illustrations
Topics: Number Theory, Geometry, Combinatorics, Analysis, Topology, Mathematics Education