LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512.7
Title	Proof Patterns ([EBook]) / by Mark Joshi.
Author	Joshi, Mark
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2015.
Physical Details	XIII, 190 p. 24 illus. : online resource.
ISBN	9783319162508
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-16250-8
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Combinatorics . Geometry . Mathematical analysis . Mathematics . Mathematics Education . Number Theory . Topology . Authors: Joshi, Mark . Corporate Authors: SpringerLink (Online service) . Classification: 512.7 . 512.7 (DDC 23) .

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