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Writing proofs in analysis

Kane, Jonathan M.

Writing proofs in analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Writing proofs in analysisby Jonathan M. Kane.
Author:	Kane, Jonathan M.
Published:	Cham :Springer International Publishing :2016.
Description:	xx, 347 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Proof theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-30967-5
ISBN:	9783319309675$q(electronic bk.)

Writing proofs in analysis
Kane, Jonathan M.

Writing proofs in analysis[electronic resource] /by Jonathan M. Kane. - Cham :Springer International Publishing :2016. - xx, 347 p. :ill., digital ;24 cm.

What Are Proofs, And Why Do We Write Them? -- The Basics of Proofs -- Limits -- Continuity -- Derivatives -- Riemann Integrals -- Infinite Series -- Sequences of Functions -- Topology of the Real Line -- Metric Spaces.

This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.

ISBN: 9783319309675$q(electronic bk.)

Standard No.: 10.1007/978-3-319-30967-5doiSubjects--Topical Terms:

190840
Proof theory.

LC Class. No.: QA9.54

Dewey Class. No.: 511.36

Writing proofs in analysis
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100 1 $a Kane, Jonathan M. $3 747921
245 1 0 $a Writing proofs in analysis $h [electronic resource] / $c by Jonathan M. Kane.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xx, 347 p. : $b ill., digital ; $c 24 cm.
505 0 $a What Are Proofs, And Why Do We Write Them? -- The Basics of Proofs -- Limits -- Continuity -- Derivatives -- Riemann Integrals -- Infinite Series -- Sequences of Functions -- Topology of the Real Line -- Metric Spaces.
520 $a This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.
650 0 $a Proof theory. $3 190840
650 0 $a Mathematical analysis. $3 186133
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Fourier Analysis. $3 273776
650 2 4 $a Mathematical Logic and Foundations. $3 274479
710 2 $a SpringerLink (Online service) $3 273601
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856 4 0 $u http://dx.doi.org/10.1007/978-3-319-30967-5
950 $a Mathematics and Statistics (Springer-11649)