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  • Introduction to Analysis (Pure and Applied Undergraduate Texts)

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Introduction to Analysis (Pure and Applied Undergraduate Texts) 5th Revised edition

4.2 out of 5 stars (64)

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Introduction to Analysis is designed to bridge the gap between the intuitive calculus usually offered at the undergraduate level and the sophisticated analysis courses the student encounters at the graduate level. In this book the student is given the vocabulary and facts necessary for further study in analysis. The course for which it is designed is usually offered at the junior level, and it is assumed that the student has little or no previous experience with proofs in analysis. A considerable amount of time is spent motivating the theorems and proofs and developing the reader's intuition. Of course, that intuition must be tempered with the realization that rigorous proofs are required for theorems. The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section. Also, at the end of each section, one finds several Projects. The purpose of a Project is to give the reader a substantial mathematical problem and the necessary guidance to solve that problem. A Project is distinguished from an exercise in that the solution of a Project is a multi-step process requiring assistance for the beginner student.
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Editorial Reviews

About the Author

Ph.D., University of Kansas

Product details

  • Publisher ‏ : ‎ American Mathematical Society
  • Publication date ‏ : ‎ January 13, 2009
  • Edition ‏ : ‎ 5th Revised edition
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 240 pages
  • ISBN-10 ‏ : ‎ 0821847872
  • ISBN-13 ‏ : ‎ 978-0821847879
  • Item Weight ‏ : ‎ 1.01 pounds
  • Dimensions ‏ : ‎ 7.17 x 0.67 x 10.47 inches
  • Best Sellers Rank: #442,007 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.2 out of 5 stars (64)

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Customer reviews

4.2 out of 5 stars
64 global ratings
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Customers say

Customers have mixed opinions about the book's content, with some finding it a good textbook while others note it focuses too much on function proofs. The readability receives mixed feedback, with some customers finding it easy to use and understand, while others find it difficult to read.
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14 customers mention content, 9 positive, 5 negative
Customers have mixed opinions about the content of the textbook, with some finding it a good textbook while others report issues with unclear explanations and insufficient visual aids.
...I received it exactly on time! It is a good book, hard subject, but it helps a lot.Read more
Difficult to read; hard to understand; examples are not helpful; using terminology not in the norm of upper level math classes.Read more
Good textbook. Not expensive, and easy to read. Not enough pictures and explanation thoughRead more
...It gives the reader a gentle introduction to the subject. The proofs are rigorous and easy to follow....Read more
7 customers mention readability, 3 positive, 4 negative
Customers have mixed opinions about the book's readability, with some finding it easy to use and understand, while others report it being difficult to read.
...The book, therefore, is probably going to be hard to understand, and with a book that's so concise about it's explanations really can only be used...Read more
Good textbook. Not expensive, and easy to read. Not enough pictures and explanation thoughRead more
This book is absolutely impossible to read....Read more
...The proofs are rigorous and easy to follow. Before embarking upon an analysis class, a person should take an introduction to proof class....Read more

Top reviews from the United States

  • 5 out of 5 stars
    A Good Place to Start
    Reviewed in the United States on March 14, 2012
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    This book broke me into analysis. It gives the reader a gentle introduction to the subject. The proofs are rigorous and easy to follow. Before embarking upon an analysis class, a person should take an introduction to proof class. Without such a class, the language of analysis will make no sense to the reader. For example, if you do not know how to do proof by induction, then you will struggle in analysis. The negative reviews for this book likely stem from readers who did not take such a class. Thanks to this book and Munkres' topology, I am now able to read and enjoy Baby Rudin. Baby Rudin is good, but I would not have liked it without first using Munkres and Gaughan. Note that Gaughan is not a complete substitute for Rudin. Rudin is general whereas Gaughan focuses mainly on the real line. Albeit, Gaughan is much easier on a reader who is new to the subject. Gaughan's treatment of sequences sets the stage for the book. He then goes into continuity and uniform continuity. The definitions and theorems are lucid. Gaughan then delves into differentiation, integration, and power series. The ordering of the topics allows the reader to move from topic to topic without having to flip back and forth through the book.

    16 people found this helpful
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  • 5 out of 5 stars
    Excellent
    Reviewed in the United States on March 1, 2014
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    This book has been beneficial to me in the Real Analysis course I am taking. It is good for any math real analysis course.

    2 people found this helpful
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  • 4 out of 5 stars
    Well organized
    Reviewed in the United States on December 20, 2013
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    I greatly appreciate the fluency of the logic and discussion found in this book. It was fantastic. I've attempted this course at another school using the professors notes (it was death). This book is so much easy to use and understand; it was a night and day difference. There seem to be a lot of different methods for proving these basic theorems inherent to the concepts and principles underlying calculus and this book is very clear and smart about accomplishing this task. I would recommend this book and I am not going to sell it. It is great.

    5 people found this helpful
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  • 5 out of 5 stars
    Gaughn's revolution
    Reviewed in the United States on December 28, 2013
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    anyone getting into mathematics needs to have this book on there shelf! it is probably the greatest abstract algebra (modern Algebra) in history. for those taking a class that deals with algebra theory, you have to use this book!

    One person found this helpful
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  • 5 out of 5 stars
    Nice book
    Reviewed in the United States on February 23, 2020
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    Fast delivery and good.

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  • 5 out of 5 stars
    Five Stars
    Reviewed in the United States on September 26, 2014
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    It is really in a good condition though it is not a new book.

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  • 3 out of 5 stars
    Depends on your class and teacher.
    Reviewed in the United States on June 14, 2014
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    Though I don't like bringing in the atmosphere in which the book is used, intro to analysis really suggests that this is going to be a students first exposure to rigorously enforced proofs. The book, therefore, is probably going to be hard to understand, and with a book that's so concise about it's explanations really can only be used in a setting where the teacher is going to provide the foundations of understanding the symbols and logic behind the proofs the book tends to breeze through. The class I was in took so long to understand the concepts we hardly made it anywhere in this book. So in a class where you're lectures expose you to the terminology and general shape of the proofs so that you can decipher the book I'm sure this could be used. If you're not getting that in your class maybe you'll want to find some additional reference material that will walk through it a bit slower.

    Mindless complaint: Really wish authors wouldn't start with a Chapter 0. It makes it feel so unimportant.

    3 people found this helpful
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  • 1 out of 5 stars
    Difficult
    Reviewed in the United States on July 17, 2013
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    Difficult to read; hard to understand; examples are not helpful; using terminology not in the norm of upper level math classes.

    2 people found this helpful
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