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eBook The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics) epub

by John Stillwell

eBook The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics) epub
  • ISBN: 3319015761
  • Author: John Stillwell
  • Genre: Science
  • Subcategory: Mathematics
  • Language: English
  • Publisher: Springer; 2013 edition (October 16, 2013)
  • Pages: 244 pages
  • ePUB size: 1214 kb
  • FB2 size 1770 kb
  • Formats txt mbr lrf mobi


This book is an interesting introduction to set theory and real analysis embedded in properties of the real .

This book is an interesting introduction to set theory and real analysis embedded in properties of the real numbers. The 300-plus problems are frequently challenging and will interest both upper-level undergraduate students and readers with a strong mathematical background. While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure.

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Undergraduate Texts in Mathematics Stillwell, John (2013). The Real Numbers: An Introduction to Set Theory and Analysis.

Undergraduate Texts in Mathematics. Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. There is no Springer-Verlag numbering of the books like in the Graduate Texts in Mathematics series. The books are numbered here by year of publication. Stillwell, John (2013). ISBN 978-3-319-01576-7. Conway, John B. (2014). A Course in Point Set Topology.

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real . John Stillwell is a professor of mathematics at the University of San Francisco.

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. He is also an accomplished author, having published several books with Springer, including Mathematics and Its History; The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the . Undergraduate Texts in Mathematics. But these seemingly simple requirements lead to deep issues of set y, the axiom of choice, and large cardinals. The Real Numbers An Introduction to Set Theory and Analysis.

Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to. .

Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis.

Real Numbers by John Stillwell While most texts on real analysis are content to assume the real .

Real Numbers by John Stillwell. Author John Stillwell.

Электронная книга "The Real Numbers: An Introduction to Set Theory and Analysis", John Stillwell

Электронная книга "The Real Numbers: An Introduction to Set Theory and Analysis", John Stillwell. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "The Real Numbers: An Introduction to Set Theory and Analysis" для чтения в офлайн-режиме.

The typical undergraduate real analysis course, which is supposed to explain.

An introduction to set theory and analysis. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar.

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory―uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.

By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis―the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics.

Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

Comments: (3)
Wnex
Very well done. A good balance of a concise mathematical treatment combined with both philosophical and historical context, which makes it highly readable. Considering that in just over 200 pages it spans from "What Are Numbers?" to Dedekind cuts to cardinalities to Borel sets to ZF axioms to AC & CH and more, this book is more about the overall fabric that reaches across these concepts rather than an intense treatment of the details. This may leave some wanting more in various areas, but to do that in one book would turn this into an 800-page tome. This book actually delivers on the back cover description.
Darksinger
Definitely, you get what a Dedekind Cut is visually that is why I purchased the book. Doing the problem exercises shall put the meat on the bones of the exposition to be a completely filled in body of work. This is a book of in need of Elementary Number Theory to go with it. I recommend Burton's Elementary Number Theory to accompany this book then some other books to fill in between the lines because the author relies more on the exercise problems to fill in the details than had I wished for a more detailed exposition and more clarity, or more compacted amounts of information per page, then this is not the case here. There is space to be filled in here, on some pages, there are jumps that makes it awkward to see where the author is trying to say.
LoboThommy
The devotee of Landau's "Foundations of Analysis" should get a copy of Elliot Mendelson's "Number Systems and the Foundations of Analysis". After 1973, Landau is the stone age, a rigorous treatment using very bad notation. Now, nobody needs to be subjected to Landau's treatment of natural numbers which is antique and mathematically poor by today's standards. People interested in the natural numbers should consult Leon Henkin's 1960 article "On mathematical induction", American Mathematical Monthly, 67. Any college math library should have it. After reading Mendelson's book, there are two excellent enrichment books. One is "Retracing Elementary Mathematics" by Leon Henkin and 3 others. The other is the book in question, John Stillwell's "The Real Numbers, An Introduction to Set Theory and Analysis". Everyone interested in arithmetic and analysis should read this book! It describes the historical sequence from ancient times of theoretical problems and how they were solved. One sees the real numbers from a new angle, one that is enlightening and charming. And two angles are far better than one, especially in mathematics. I cannot recommend this book too highly.
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