Proof Patterns

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Joshi, Mark (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Temas:
Number theory.
Geometry.
Discrete mathematics.
Mathematical analysis.
Topology.
Mathematics-Study and teaching .
Number Theory.
Discrete Mathematics.
Analysis.
Mathematics Education.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Proof Patterns  |h [electronic resource] /  |c by Mark Joshi. 
250 |a 1st ed. 2015. 
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300 |a XIII, 190 p. 24 illus.  |b online resource. 
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505 0 |a 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. 
520 |a 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. 
650 0 |a Number theory. 
650 0 |a Geometry. 
650 0 |a Discrete mathematics. 
650 0 |a Mathematical analysis. 
650 0 |a Topology. 
650 0 |a Mathematics-Study and teaching . 
650 1 4 |a Number Theory. 
650 2 4 |a Geometry. 
650 2 4 |a Discrete Mathematics. 
650 2 4 |a Analysis. 
650 2 4 |a Topology. 
650 2 4 |a Mathematics Education. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319162515 
776 0 8 |i Printed edition:  |z 9783319162492 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-319-16250-8  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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