The Art of Proof, Softcover reprint of the original 1st ed. 2010
Basic Training for Deeper Mathematics
Undergraduate Texts in Mathematics Series

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Language: English

Approximative price 42.15 €

In Print (Delivery period: 15 days).

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The Art of Proof
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Support: Print on demand

Approximative price 42.15 €

In Print (Delivery period: 15 days).

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The art of proof: basic training for deeper mathematics (hardback) (series: undergraduate texts in mathematics)
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182 p. · 17.8x25.4 cm · Hardback
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. 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.
Preface.- 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.

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.

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