Writing Proofs in Analysis

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Writing Proofs in Analysis by Jonathan M. Kane, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jonathan M. Kane ISBN: 9783319309675
Publisher: Springer International Publishing Publication: May 28, 2016
Imprint: Springer Language: English
Author: Jonathan M. Kane
ISBN: 9783319309675
Publisher: Springer International Publishing
Publication: May 28, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Qualitative Methodologies in Organization Studies by Jonathan M. Kane
Cover of the book The Palgrave Handbook of Race and the Arts in Education by Jonathan M. Kane
Cover of the book Protein Kinase CK2 Cellular Function in Normal and Disease States by Jonathan M. Kane
Cover of the book Mathematical Software – ICMS 2016 by Jonathan M. Kane
Cover of the book Higher Education: Handbook of Theory and Research by Jonathan M. Kane
Cover of the book Environmental Archaeology by Jonathan M. Kane
Cover of the book Automotive Electronics Design Fundamentals by Jonathan M. Kane
Cover of the book The Legal Regime Applicable to Private Military and Security Company Personnel in Armed Conflicts by Jonathan M. Kane
Cover of the book PTSD and Forensic Psychology by Jonathan M. Kane
Cover of the book Intellectual Capital Management as a Driver of Sustainability by Jonathan M. Kane
Cover of the book Emerging Markets from a Multidisciplinary Perspective by Jonathan M. Kane
Cover of the book Linear Regression by Jonathan M. Kane
Cover of the book Religious Education in a Global-Local World by Jonathan M. Kane
Cover of the book The World Disorder by Jonathan M. Kane
Cover of the book L2-Gain and Passivity Techniques in Nonlinear Control by Jonathan M. Kane
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy