Mark Joshi: Proof Patterns | Taschenbuch

Cover: 9783319162492 | Proof Patterns | Mark Joshi | Taschenbuch | xiii | Englisch | 2015

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Mark Joshi, a leading mathematician in analysis and financial mathematics, published several successful textbooks and over sixty research papers in mathematics. He is known for his innovative viewpoints and intuitive style.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

Induction and complete induction.- Double Counting.- The pigeonhole principle.- Divisions.- Contrapositive and contradiction.- Intersection-enclosure and Generation.- Difference of invariants.- Linear dependence, fields and transcendence.- Formal equivalence.- Equivalence extension.- Proof by classification.- Specific-generality.- Diagonal tricks and cardinality.- Connectedness and the Jordan curve theorem.- The Euler characteristic and the classification of regular polyhedra.- Discharging.- The matching problem.- Games.- Analytical patterns.- Counterexamples.

Details

Erscheinungsjahr:	2015
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiii 190 S. 24 s/w Illustr. 190 p. 24 illus.
ISBN-13:	9783319162492
ISBN-10:	3319162497
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Joshi, Mark
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 12 mm
Von/Mit:	Mark Joshi
Erscheinungsdatum:	30.03.2015
Gewicht:	0,318 kg

Artikel-ID: 104894169