000			03153nam a22004215i 4500
001			u371806
003			SIRSI
005			20160812080149.0
007			cr nn 008mamaa
008			100825s2010 xxu| s |||| 0|eng d
020			_a9781441970237 _9978-1-4419-7023-7
040			_cMX-MeUAM
050		4	_aQA1-939
082	0	4	_a510 _223
100	1		_aBeck, Matthias. _eauthor.
245	1	4	_aThe Art of Proof _h[recurso electrónico] : _bBasic Training for Deeper Mathematics / _cby Matthias Beck, Ross Geoghegan.
264		1	_aNew York, NY : _bSpringer New York, _c2010.
300			_aXXII, 182 p. 23 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUndergraduate Texts in Mathematics, _x0172-6056 ; _v0
505	0		_aThe Discrete -- Integers -- Natural Numbers and Induction -- Some Points of Logic -- Recursion -- Underlying Notions in Set Theory -- Equivalence Relations and Modular Arithmetic -- Arithmetic in Base Ten -- The Continuous -- Real Numbers -- Embedding Z in R -- Limits and Other Consequences of Completeness -- Rational and Irrational Numbers -- Decimal Expansions -- Cardinality -- Final Remarks -- Further Topics -- Continuity and Uniform Continuity -- Public-Key Cryptography -- Complex Numbers -- Groups and Graphs -- Generating Functions -- Cardinal Number and Ordinal Number -- Remarks on Euclidean Geometry.
520			_aThe Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. Some of the proofs are presented in detail, while others (some with hints) may be assigned to the student or presented by the instructor. The authors recommend that the two parts of the book -- Discrete and Continuous -- be given equal attention. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.
650		0	_aMathematics.
650	1	4	_aMathematics.
650	2	4	_aMathematics, general.
700	1		_aGeoghegan, Ross. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441970220
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056 ; _v0
856	4	0	_zLibro electrónico _uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-1-4419-7023-7
596			_a19
942			_cLIBRO_ELEC
999			_c199686 _d199686