國立虎尾科技大學 |

Writing Proofs in Analysis

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Writing Proofs in Analysis/ by Jonathan M. Kane.
作者:	Kane, Jonathan M.
面頁冊數:	XX, 347 p. 79 illus., 75 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Functional analysis. -
電子資源:	https://doi.org/10.1007/978-3-319-30967-5
ISBN:	9783319309675

Writing Proofs in Analysis
Kane, Jonathan M.

Writing Proofs in Analysis[electronic resource] /by Jonathan M. Kane. - 1st ed. 2016. - XX, 347 p. 79 illus., 75 illus. in color.online resource.

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

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

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Writing Proofs in Analysis
LDR:02866nam a22003975i 4500 001 981735
003 DE-He213
005 20200630040006.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319309675 $9 978-3-319-30967-5
024 7 $a 10.1007/978-3-319-30967-5 $2 doi
035 $a 978-3-319-30967-5
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a Kane, Jonathan M. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1109375
245 1 0 $a Writing Proofs in Analysis $h [electronic resource] / $c by Jonathan M. Kane.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XX, 347 p. 79 illus., 75 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Functional analysis. $3 527706
650 0 $a Fourier analysis. $3 639284
650 0 $a Mathematical logic. $2 bicssc $3 810627
650 1 4 $a Functional Analysis. $3 672166
650 2 4 $a Fourier Analysis. $3 672627
650 2 4 $a Mathematical Logic and Foundations. $3 669393
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319309651
776 0 8 $i Printed edition: $z 9783319309668
776 0 8 $i Printed edition: $z 9783319809311
856 4 0 $u https://doi.org/10.1007/978-3-319-30967-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)