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Yet Another Introduction to Analysis [Paperback]

Victor Bryant
4.6 out of 5 stars  See all reviews (12 customer reviews)

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Book Description

September 28, 1990 052138835X 978-0521388351
Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well-motivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and well-motivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it.

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Editorial Reviews

Review

"Bryant's style is extremely leisurely, copiously illustrated, often intuitively appealing, chatty and unintimidating, in contrast to other treatments of similar material..." Choice

Product Details

  • Paperback: 300 pages
  • Publisher: Cambridge University Press (September 28, 1990)
  • Language: English
  • ISBN-10: 052138835X
  • ISBN-13: 978-0521388351
  • Product Dimensions: 9.1 x 5.9 x 0.8 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #819,862 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
73 of 75 people found the following review helpful
By Rahman
Format:Paperback
Mathematical analysis is a refinement of calculus, and a pathway into further branches of mathematics, including topology and advanced topics in algebra. Analysis, however, may not seem to be at all related to calculus at its initial stages. An introductory course on analysis can render an unprepared student, even with experience in other branches of mathematics, perplexed and challenged to an extreme. Only later in the analysis course are even the most basic topics of calculus introduced.
One of the most important considerations prior to taking an analysis course is the level of background and understanding of mathematical logic. Set theory, a branch of mathematical logic, is in fact the basis of calculus as well. Due to an emphasis upon computations, however, the highest grades in calculus are possible without understanding, or even knowing of, this underlying foundation.
This work is unique among those introducing analysis, in that it does not require a background in set theory. It in fact teaches numerous fundamental concepts of set theory, without stating that it is doing so. Examples provided are based on daily concrete experience, yet are altered for purposes of mathematical instruction. These descriptions are sufficiently general as to prepare the reader for when formal set theory is introduced in more rigorous textbooks.
In addition to being an extremely readable and accessible work, solutions and hints are provided for every review question for every section of the book. This is in stark contrast to textbooks on the subject, which, while costing several times more, are typically designed for a classroom setting, and so leave all questions unanswered.
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19 of 19 people found the following review helpful
5.0 out of 5 stars Great Introduction December 20, 2002
Format:Paperback
This is a text for Real Analysis at the Junior Level (American university level). It goes to extreme lengths to make analysis understandable to people who have no prior exposure. The organization is good. Completeness is introduced early as (the "piggy in the middle"). Proofs are written in detail with fill-in-the-blank spots to force the reader to follow the argument. It has good exercises making it an easy book to teach out of. Excellent for the absolute beginner. Good candidate for the classroom.
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18 of 20 people found the following review helpful
5.0 out of 5 stars Outstanding introduction to advanced mathematics August 26, 1999
Format:Paperback
While there have been countless introductions to mathematical analysis (calculus) this is my favorite. The author does a brilliant job of making the subject matter interesting and very understandable with excellent exercises along the way which have solutions in the back ! A must read for bright highschool seniors and college freshman that are taking calculus or will be.
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12 of 13 people found the following review helpful
5.0 out of 5 stars Basic Real Analysis unleashed October 21, 2001
Format:Paperback
Bryant builds the basic concepts of a first course in mathematical analysis upon the notion of numerical sequences. This approach gives an unified vision and amazing insights. Infinite series, limits, derivatives, Riemann integral are studied in an integrated vision. Clear ideas, illustrations and humor are found across all its pages. Good and illuminating exercises, too. An excellent introduction to basic real analysis.
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8 of 8 people found the following review helpful
Format:Paperback
Victor Bryant's informal, conversational text, Yet Another Introduction to Analysis, offers an engaging, well-motivated introduction to real analysis, but it is not a full substitute for a more formal, more axiomatically structured approach. However, Bryant's text is a great companion text, and is especially suitable for self-tutoring purposes, or as pre-read prior to taking that first rigorous analysis class. The reader need only be familiar with first year calculus.

As is so often said, mathematics is not a spectator sport, and Bryant clearly expects his readers to work the problem sets; the text frequently makes direct use of the results of previous problems. Bryant provides full solutions to nearly every problem, another reason why this book is so good for self-study. (The solutions section is 67 pages.) Bryant's problems were rarely difficult or overly time consuming, and are most notable for clarifying key points in the text.

Bryant begins with a brief examination of real numbers, looking at why the irrational numbers so out number the rational ones. (The completeness axiom is introduced in the short first chapter.) I particularly enjoyed the next section, Bryant's examination of whether a series converges or not and ways to determine the sum of an infinite series. (I had not previously been all that interested in the study of series, but Bryant's approach peaked my interest. I have now purchased a more advanced Dover reprint, Infinite Series by James M. Hyslop, for follow-up reading.)

A longer section examines the familiar concept of a function from various perspectives, using the inverse relationship between exp and the log as one of the key examples.
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5 of 5 people found the following review helpful
By P
Format:Paperback|Verified Purchase
I found this book an excellent introduction to real analysis. The math courses I took during my US undergraduate engineering degree (your standard Calc I - Calc III) focused more on computation than theory. This book gave me a deeper understanding of the real number line, sequences and series, functions, differentiation, and integration, as well as some much-needed practice in writing proofs.

I was a bit worried starting the book that it would be too difficult, but fortunately, the book started at just the right level for me and continued at a good pace. The book is written in a friendly and conversational style and all the concepts are well-explained, with lots of graphs to make things clear.

The exercises often have you proving some key theory that is referred to later on, which gives a strong motivation to work through all the exercises. For someone with little experience writing proofs like myself, the exercises were not overly difficult, but provided a good challenge. The book provides full, worked-out solutions to all the exercises, which makes it great for self-study (I used the book to get some background on analysis over summer before I started my master's).

Overall, I found this to be an excellent book. I highly recommend it for self-study or as a supplement to a course.
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Most Recent Customer Reviews
5.0 out of 5 stars American Universities are searching for this book!
If you're interested in "plug-in" the numbers and learning peculiar rules when to "plug-in, what numbers," then you'll never LEARN or appreciate the calculus. Read more
Published 12 months ago by G. Tomer
5.0 out of 5 stars Good book but cannot be used on its own for beginners to analysis.
Cannot be used on its own for beginner students to analysis. Recommend to use with other books on proofs.
Also, basic calculus is necessary.
Published 13 months ago by Liu J.
5.0 out of 5 stars Not too hot and not too cold, Not too hard and not too soft...
Just right!

This is the real analysis book for all us Goldie Locks out there.
Published on February 15, 2008 by A Reader
1.0 out of 5 stars A book without a table of content
Look inside the book! This book has a table of content, with only 5 entries. You you want to look up a thema to repeat it, or to learn a special thing you are interested in, you... Read more
Published on December 27, 2005 by Mathematik-Freak
5.0 out of 5 stars Accessible book gets to the heart of analysis
Bryant's book on analysis is a great illustration of what a textbook should be. He takes what many upper level college mathematics students consider to be the most tedious and... Read more
Published on December 17, 2005 by calvinnme
4.0 out of 5 stars Analysis Lite
Unlike many of the other reviewers of this work, I found Dr. Bryant's informal writing style a hassle. Read more
Published on October 4, 2005 by Aaron Rutledge
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