東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Proof patterns

Joshi, Mark.

FindBook

Google Book

Amazon

博客來

Proof patterns

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Proof patterns/ by Mark Joshi.
作者:	Joshi, Mark.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	xiii, 190 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Proof theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-16250-8
ISBN:	9783319162508 (electronic bk.)

Proof patterns
Joshi, Mark.

Proof patterns[electronic resource] /by Mark Joshi. - Cham :Springer International Publishing :2015. - xiii, 190 p. :ill., digital ;24 cm.

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 (electronic bk.)

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

543782
Proof theory.

LC Class. No.: QA9.54

Dewey Class. No.: 511.36

Proof patterns
LDR:02353nmm a2200313 a 4500 001 1998083
003 DE-He213
005 20151029101912.0
006 m d
007 cr nn 008maaau
008 151112s2015 gw s 0 eng d
020 $a 9783319162508 (electronic bk.)
020 $a 9783319162492 (paper)
024 7 $a 10.1007/978-3-319-16250-8 $2 doi
035 $a 978-3-319-16250-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA9.54
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
082 0 4 $a 511.36 $2 23
090 $a QA9.54 $b .J83 2015
100 1 $a Joshi, Mark. $3 2139594
245 1 0 $a Proof patterns $h [electronic resource] / $c by Mark Joshi.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xiii, 190 p. : $b ill., digital ; $c 24 cm.
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 Proof theory. $3 543782
650 0 $a Number theory. $3 515832
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Geometry. $3 517251
650 2 4 $a Combinatorics. $3 895617
650 2 4 $a Analysis. $3 891106
650 2 4 $a Topology. $3 522026
650 2 4 $a Mathematics Education. $3 637497
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-16250-8
950 $a Mathematics and Statistics (Springer-11649)