Proof Patterns

2015 | ISBN: 9783319162492 | English | 189 pages | True PDF | 4,27 MB

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
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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