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The Art of Proof

Basic Training for Deeper Mathematics
BuchGebunden
182 Seiten
Englisch
Springererschienen am31.08.2010
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.mehr
Verfügbare Formate
BuchGebunden
EUR54,99
BuchKartoniert, Paperback
EUR42,75
E-BookPDF1 - PDF WatermarkE-Book
EUR39,99

Produkt

KlappentextThe 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.
Zusammenfassung
Presents fundamental mathematics, integers and real numbers, in a way that asks for student participation, while teaching how mathematics is done

Provides students with methods and ideas they can use in future courses

Primarily for: undergraduates who have studied calculus or linear algebra; mathematics teachers and teachers-in-training; scientists and social scientists who want to strengthen their command of mathematical methods

Extra topics in appendices give instructor flexibility

Includes supplementary material: sn.pub/extras

Request lecturer material: sn.pub/lecturer-material
Details
ISBN/GTIN978-1-4419-7022-0
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2010
Erscheinungsdatum31.08.2010
Seiten182 Seiten
SpracheEnglisch
Gewicht566 g
IllustrationenXXI, 182 p.
Artikel-Nr.11396191

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

Autor

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.