Yet Another Introduction to Analysis [Paperback]

Victor Bryant (Author)

Book Description

ISBN-10: 052138835X | ISBN-13: 978-0521388351 | Publication Date: September 28, 1990

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.

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: 8.9 x 6 x 0.9 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #312,353 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

72 of 74 people found the following review helpful:

5.0 out of 5 stars Exposes Mathematical Analysis Without Set Theory Background, July 8, 2001

By 

Rahman (CA, USA) - See all my reviews

This review is from: Yet Another Introduction to Analysis (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:

5.0 out of 5 stars Great Introduction, December 20, 2002

By 

James M. Cargal (Montgomery, AL USA) - See all my reviews
(REAL NAME)   

This review is from: Yet Another Introduction to Analysis (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:

5.0 out of 5 stars Outstanding introduction to advanced mathematics, August 26, 1999

By 

Carl F. Mclaren Jr. (Haines City, Florida USA) - See all my reviews
(REAL NAME)   

This review is from: Yet Another Introduction to Analysis (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.