MARC 主機 00000nam a2200457 i 4500 
001    978-3-319-30967-5 
003    DE-He213 
005    20161102095523.0 
006    m     o  d         
007    cr nn 008maaau 
008    160528s2016    gw      s         0 eng d 
020    9783319309675|q(electronic bk.) 
020    9783319309651|q(paper) 
024 7  10.1007/978-3-319-30967-5|2doi 
040    GP|cGP|erda|dAS 
041 0  eng 
050  4 QA9.54 
082 04 511.36|223 
100 1  Kane, Jonathan M.,|eauthor 
245 10 Writing proofs in analysis /|cby Jonathan M. Kane 
264  1 Cham :|bSpringer International Publishing :|bImprint: 
300    1 online resource (xx, 347 pages) :|billustrations, 
       digital ;|c24 cm 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
347    text file|bPDF|2rda 
505 0  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    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 Proof theory 
650  0 Mathematical analysis 
650 14 Mathematics 
650 24 Functional Analysis 
650 24 Fourier Analysis 
650 24 Mathematical Logic and Foundations 
710 2  SpringerLink (Online service) 
773 0  |tSpringer eBooks 
856 40 |u