說明 
1 online resource (xx, 347 pages) : illustrations, digital ; 24 cm 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 

text file PDF rda 
附註 
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 wellwritten 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 fullcolor diagrams to elucidate the topics at hand 
Host Item 
Springer eBooks

主題 
Proof theory


Mathematical analysis


Mathematics


Functional Analysis


Fourier Analysis


Mathematical Logic and Foundations

Alt Author 
SpringerLink (Online service)

