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Transition to Analysis with Proof de Steven Krantz

Transition to Analysis with Proof: Textbooks in Mathematics

Autor Steven Krantz
en Limba Engleză Hardback – 8 noi 2017
Transition to Real Analysis with Proof provides undergraduate students with an introduction to analysis including an introduction to proof. The text combines the topics covered in a transition course to lead into a first course on analysis. This combined approach allows instructors to teach a single course where two were offered.
The text opens with an introduction to basic logic and set theory, setting students up to succeed in the study of analysis. Each section is followed by graduated exercises that both guide and challenge students. The author includes examples and illustrations that appeal to the visual side of analysis. The accessible structure of the book makes it an ideal refence for later years of study or professional work.
 
  • Combines the author’s previous works Elements of Advanced Mathematics with Foundations of Analysis
  • Combines logic, set theory and other elements with a one-semester introduction to analysis.
  • Author is a well-known mathematics educator and researcher
  • Targets a trend to combine two courses into one
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Specificații

ISBN-13: 9781138064140
ISBN-10: 1138064149
Pagini: 362
Ilustrații: 43
Dimensiuni: 156 x 234 mm
Greutate: 0.45 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics

Cuprins

Chapter 1 Basic Logic; Chapter 2 Methods of Proof; Chapter 3 Set TheoryChapter 4 Relations and Functions; Chapter 5 Essential Number Systems Chapter 6 Sequences; Chapter 7 Series of Numbers; Chapter 8 Basic Topology Open and Closed Sets; Chapter 9 Limits and Continuity of Functions; Chapter 10 Differentiation of Functions; Chapter 11 The Integral; APPENDIX: Construction of The Weierstrass Nowhere Differentiable Function; Chapter 12 Sequences and Series of Functions; APPENDIX: Proof of the Weierstrass Approximation Theorem; Chapter 13 Elementary Transcendental Functions APPENDIX I Elementary Number Systems Table NotationGlossary Bibliography, Index

Recenzii

This book is designed for undergraduate students and provides an introduction to analysis including an introduction to proofs. Namely, it starts with basic logic along with set theory and suggests plenty of instructive examples on how to do a correct mathematical reasoning. Then, he moves to functions, sequences, basic topology, differentiation, and integration. The text ends with power series and elementary transcendental functions. Each section of the book has a clear and convenient structure. It opens with "Preliminary remarks", which in a few sentences explain what the following passage is about. Then, the main text follows in which every statement is equipped with an instructive proof. Examples and exercises help master the material of the topic. \A look back" blocks consist of a few simple questions (like "What is a monotone sequence?") and serve as a test if you understand the basics.
General remarks. The language of the book is quite vivid and lively, at the same time it is available for non-native students. The text has useful navigation tools like glossary, index, and the table of notations. The only disadvantage, in my opinion, is the lack of solutions and answers to the exercises.
Nikita Evseev (Novosibirsk)

Descriere

Transition to Real Analysis with Proof provides undergraduate students with an introduction to analysis including an introduction to proof. The text combines the topics covered in a transition course to lead into a first course on analysis. This combined approach allows instructors to teach a single course where two were offered.