The Art of Proof: Basic Training for Deeper Mathematics (Undergraduate Texts in Mathematics). [Neubuch].
Beck, Matthias und Ross Geoghegan:
Language: English
Published by Springer, 2010
- First Edition
- Hardcover
- New
Seller: ANTIQUARIAT Franke BRUDDENBOOKS, Lübeck, GermanyANTIQUARIAT Franke BRUDDENBOOKS
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203 S. Buch ist neu, aus priv. Vorbesitz, ungelesen. -----Inhalt. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. 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 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. 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. ISBN: 9781441970220 Due to new EU packaging regulations, we are currently unable to ship to many EU countries. Shipping to Germany, the Netherlands, Ireland, Finland, and the Baltic states is possible. Deliveries to border-based parcel lockers or cross-border parcel forwarding services remain possible. Shipping to all countries outside the EU also remains possible. Sprache: Englisch Gewicht in Gramm: 567.…
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- Title
- The Art of Proof: Basic Training for Deeper Mathematics (Undergraduate Texts in Mathematics). [Neubuch].
- Author
- Beck, Matthias und Ross Geoghegan:
- Publisher
- Springer
- Publication year
- 2010
- Condition
- Neu
- Binding
- Gebundene Ausgabe, Gr. 8°
- Language
- English
- ISBN 10
- 1441970223
- ISBN 13
- 9781441970220
- Edition
- 2010.
- Item weight
- 567 grams
- Series
- Book 39 of 170: Undergraduate Texts in Mathematics
- Seller catalogs
- Bildende Kunst
"Synopsis" may belong to another edition of this title.
About the Author
Matthias Beck received his initial training in mathematics in Würzburg, Germany, received his Ph.D. in mathematics from Temple University, and is now associate professor of mathematics at San Francisco State University. He is the recipient of the 2013 MAA Haimo Award for Distinguished College or University Teaching of Mathematics. He is the author of a previously published Springer book, Computing the Continuous Discretely (with Sinai Robins).
Ross Geoghegan received his initial training in mathematics in Dublin, Ireland, received his Ph.D. in mathematics from Cornell University, and is now professor of mathematics at the State University of New York at Binghamton. He is the author of a previously published Springer book, Topological Methods in Group Theory.
"About the title" may belong to another edition of this title.
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