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MARC 21

The Art of Proof: Basic Training for Deeper Mathematics
Tag	Description
020	$a9781441970237
082	$a510
099	$aOnline Resource: Springer
100	$aBeck, Matthias.
245	$aThe Art of Proof$h[EBook]$bBasic Training for Deeper Mathematics$cby Matthias Beck, Ross Geoghegan.
260	$aNew York, NY$bSpringer$c2010.
300	$aXXII, 182 pages: 23 illus.$bonline resource.
336	$atext
338	$aonline resource
440	$aUndergraduate Texts in Mathematics,$x0172-6056 ;$v0
505	$aPreface -- Notes for the Student -- Notes for Instructors -- Part I: The Discrete -- 1 Integers -- 2 Natural Numbers and Induction -- 3 Some Points of Logic -- 4 Recursion -- 5 Underlying Notions in Set Theory -- 6 Equivalence Relations and Modular Arithmetic -- 7 Arithmetic in Base Ten -- Part II: The Continuous -- 8 Real Numbers -- 9 Embedding Z in R -- 10. Limits and Other Consequences of Completeness -- 11 Rational and Irrational Numbers -- 12 Decimal Expansions -- 13 Cardinality -- 14 Final Remarks -- Further Topics -- A Continuity and Uniform Continuity -- B Public-Key Cryptography -- C Complex Numbers -- D Groups and Graphs -- E Generating Functions -- F Cardinal Number and Ordinal Number -- G Remarks on Euclidean Geometry -- List of Symbols -- Index.
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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700	$aGeoghegan, Ross.$d1963-$eauthor.
710	$aSpringerLink (Online service)
830	$aUndergraduate Texts in Mathematics,$v0
856	$uhttp://dx.doi.org/10.1007/978-1-4419-7023-7