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Proof Patterns

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Proof Patterns/ by Mark Joshi.
Author:	Joshi, Mark.
Description:	XIII, 190 p. 24 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Number theory. -
Online resource:	https://doi.org/10.1007/978-3-319-16250-8
ISBN:	9783319162508

Proof Patterns
Joshi, Mark.

Proof Patterns[electronic resource] /by Mark Joshi. - 1st ed. 2015. - XIII, 190 p. 24 illus.online resource.

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.

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.

ISBN: 9783319162508

Standard No.: 10.1007/978-3-319-16250-8doiSubjects--Topical Terms:

527883
Number theory.

LC Class. No.: QA241-247.5

Dewey Class. No.: 512.7

Proof Patterns
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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.
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