The Art of Proof [electronic resource] :Basic Training for Deeper Mathematics / by Matthias Beck, Ross Geoghegan.
by Beck, Matthias [author.]; Geoghegan, Ross [author.]; SpringerLink (Online service).
Material type:
BookSeries: Undergraduate Texts in Mathematics: 0Publisher: New York, NY : Springer New York, 2010.Description: XXII, 182 p. 23 illus. online resource.ISBN: 9781441970237.Subject(s): Mathematics | Mathematics | Mathematics, generalDDC classification: 510 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA1-939 (Browse shelf) | Available |
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| RM1-950 Post-Transcriptional Regulation by STAR Proteins | QA401-425 Sparse and Redundant Representations | RC648-665.2 Hormone Use and Abuse by Athletes | QA1-939 The Art of Proof | QR251-255 Biomphalaria Snails and Larval Trematodes | R856-857 Design and Use of Assistive Technology | RC648-665.2 Obesity Before Birth |
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.
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