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＜電子ブック＞
The Art of Proof : Basic Training for Deeper Mathematics / by Matthias Beck, Ross Geoghegan
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2010.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2010
大きさ	XXI, 182 p : online resource
著者標目	*Beck, Matthias author Geoghegan, Ross author SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Algebra LCSH:Mathematical analysis LCSH:Mathematics FREE:Mathematical Logic and Foundations FREE:Algebra FREE:Analysis FREE:Mathematics
一般注記	The 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 The 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 HTTP:URL=https://doi.org/10.1007/978-1-4419-7023-7

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