Transition to Analysis with Proof

1. Auflage 2017
ISBN: 978-1-138-06406-5
Verlag: Chapman and Hall/CRC

Buch, Englisch, 362 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 553 g

Reihe: Textbooks in Mathematics

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

Autoren/Hrsg.

Krantz, Steven

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mengenlehre
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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

Über Autor(innen)

Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He received his Ph.D. from Princeton University and since then has taught at UCLA, Princeton University, and Pennsylvania State University. Dr. Krantz has written over 175 scholarly papers and more than 65 books. He is the founding editor of the Journal of Geometric Analysis. He was named a fellow of the American Mathematical Society and has received the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize.