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Yet Another Introduction to Analysis Paperback – September 28, 1990

ISBN-13: 978-0521388351 ISBN-10: 052138835X

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Editorial Reviews

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

  • Paperback: 300 pages
  • Publisher: Cambridge University Press (September 28, 1990)
  • Language: English
  • ISBN-10: 052138835X
  • ISBN-13: 978-0521388351
  • Product Dimensions: 6 x 0.7 x 9 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: #651,176 in Books (See Top 100 in Books)

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See all 12 customer reviews
Proofs are written in detail with fill-in-the-blank spots to force the reader to follow the argument.
James M. Cargal
One of the most important considerations prior to taking an analysis course is the level of background and understanding of mathematical logic.
Rahman
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.
P

Most Helpful Customer Reviews

73 of 75 people found the following review helpful By Rahman on July 8, 2001
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 By James M. Cargal on 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 By Carl F. Mclaren Jr. on 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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8 of 8 people found the following review helpful By Michael Wischmeyer on March 7, 2008
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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12 of 13 people found the following review helpful By Amazon Customer on 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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5 of 5 people found the following review helpful By P on July 11, 2008
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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