LEADER 04222nam  22008175  450 
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010   $a3-319-16250-0
024 7 $a10.1007/978-3-319-16250-8
035   $a(CKB)3710000000379634
035   $a(SSID)ssj0001465680
035   $a(PQKBManifestationID)11859799
035   $a(PQKBTitleCode)TC0001465680
035   $a(PQKBWorkID)11487076
035   $a(PQKB)11199516
035   $a(DE-He213)978-3-319-16250-8
035   $a(MiAaPQ)EBC6312865
035   $a(MiAaPQ)EBC5577975
035   $a(Au-PeEL)EBL5577975
035   $a(OCoLC)905596430
035   $a(PPN)184889790
035   $a(EXLCZ)993710000000379634
100   $a20150317d2015      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aProof Patterns /$fby Mark Joshi
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (XIII, 190 p. 24 illus.) 
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-16249-7 
327   $aInduction 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.
330   $aThis 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.
606   $aNumber theory
606   $aGeometry
606   $aCombinatorial analysis
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aTopology
606   $aMathematics?Study and teaching 
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000
606   $aMathematics Education$3https://scigraph.springernature.com/ontologies/product-market-codes/O25000
615  0$aNumber theory.
615  0$aGeometry.
615  0$aCombinatorial analysis.
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aTopology.
615  0$aMathematics?Study and teaching .
615 14$aNumber Theory.
615 24$aGeometry.
615 24$aCombinatorics.
615 24$aAnalysis.
615 24$aTopology.
615 24$aMathematics Education.
676   $a511.6
700   $aJoshi$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755573
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299776103321
996   $aProof Patterns$91522593
997   $aUNINA