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Yet Another Introduction to Analysis Paperback – 28 Jun 1990

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Product details

  • Paperback: 300 pages
  • Publisher: Cambridge University Press (28 Jun 1990)
  • Language: English
  • ISBN-10: 052138835X
  • ISBN-13: 978-0521388351
  • Product Dimensions: 15.2 x 1.7 x 22.8 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 306,394 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Product Description


"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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Analysis is an extension of school calculus. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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3 of 5 people found the following review helpful By Jamie B. on 2 Nov 2009
Format: Paperback
This book introduces you in a non-confrontational, yet challenging way to the basic concepts of analysis. The author has refrained from making it too easy, (not that it would be) by helping you fill in pieces of proofs as you go along, and providing a wide array of exercises. Thoroughly foog book.
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Most Helpful Customer Reviews on (beta) 12 reviews
73 of 75 people found the following review helpful
Exposes Mathematical Analysis Without Set Theory Background 9 July 2001
By Rahman - Published on
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. This self-testing of the understanding of each section is crucial for subject matter requiring such attention to detail and precision.
The numerous illustrations throughout the book are rendered clearly and with instructional purpose, yet are often drawn by hand, adding to the sense of familiarity with the author. All of the basic subject matter for a course on analysis is provided, yet has been specifically tailored for a reader in the stages of preparation, of review after completion, or one who is simply inquisitive as to what is required to comprehend analysis successfully.
The softcover edition is durable and portable, and the book remains in excellent condition through numerous readings, which it will almost certainly go through.
If you have been required to take an analysis class but left it with only a vague sense of its underpinnings, you may wish to go through this work when time permits. For the price of the book, the information and instruction provided is truly outstanding. This text receives the highest marks in all categories.
19 of 19 people found the following review helpful
Great Introduction 21 Dec 2002
By James M. Cargal - Published on
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.
18 of 20 people found the following review helpful
Outstanding introduction to advanced mathematics 27 Aug 1999
By Carl Mclaren - Published on
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.
8 of 8 people found the following review helpful
Yet Another Good Text from Victor Bryant - Great for Self-Tutorial Purposes 7 Mar 2008
By Michael Wischmeyer - Published on
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. The final two chapters focus on a primary topic of analysis, the basic theorems of differentiation and integration. Familiarity with partial differentiation and multiple integration is not needed.

Some readers may find Bryant's conversational approach to be too wordy and occasionally digressive, but I personally enjoy his leisurely style. I also recommend Bryant's short text titled Metric Spaces, Iteration and Application, published by Cambridge University Press.

Another good choice is Maxwell Rosenlicht's Introduction to Analysis, available in an inexpensive Dover edition. It offers a more traditional, structured approach to analysis that is suitable either as follow-up to Yet Another Introduction to Analysis, or as a stand-alone self-tutorial text. Although Rosenlicht's text emphasizes generality and abstraction to a greater extent, it is still more concrete and less terse than many standard texts on real analysis.
12 of 13 people found the following review helpful
Basic Real Analysis unleashed 22 Oct 2001
By Amazon Customer - Published on
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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