Over and Over Again (Anneli Lax New Mathematical Library) 1st Edition

by Gengzhe Chang (Author), Thomas W. Sederberg (Author)

4 customer reviews

ISBN-13: 978-0883856413

ISBN-10: 0883856417

Why is ISBN important?

Have one to sell? Sell on Amazon

More Buying Choices

9 New from $59.90 11 Used from $25.23

20 used & new from $25.23

See All Buying Options

Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student

Iterations, that is transformations that are applied to objects over and over again, are the subject of this book. Three types of iteration are considered. The first, smoothing, is the process by which geometrical shapes can be transformed into standard types. Functional iteration is a way of describing the phenomenon of chaos. Finally, iterations involving curves and surfaces play an important role in computer aided design and graphics. These themes are explored and developed with no more background required than high school mathematics and a little calculus. Several basic strategies are highlighted which unlock solutions to problems involving iteration, and these are then applied to solve problems drawn from International Mathematical Olympiads.

Over and Over Again (Anneli Lax New Mathematical Library)

Available from these sellers.

Customers Who Bought This Item Also Bought

Page 1 of 1 Start overPage 1 of 1

This shopping feature will continue to load items. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

C. D. Olds

4

Paperback
Arthur Engel

1

Paperback
Edward Packel

3

Paperback
George Pólya

3

Paperback
Ross Honsberger

2

Paperback
$23.00
Max Schiffer
Paperback

Customers Viewing This Page May Be Interested In These Sponsored Links

(What's this?)

1. Mathematical Libraries	-	Leader in Management Software! Get the most from your cluster hardware	www.brightcomputing.com/
2. IMSL Numerical Libraries	-	High performance, precise libraries you can rely on. Get started today.	www.roguewave.com/

Ad feedback

NO_CONTENT_IN_FEATURE

Product Details

Series: Anneli Lax New Mathematical Library (Book 38)
Paperback: 324 pages
Publisher: The Mathematical Association of America; 1 edition (December 1997)
Language: English
ISBN-10: 0883856417
ISBN-13: 978-0883856413
Product Dimensions: 5.4 x 0.7 x 8.5 inches
Shipping Weight: 14.9 ounces
Average Customer Review: 4.2 out of 5 stars See all reviews (4 customer reviews)
Amazon Best Sellers Rank: #2,750,526 in Books (See Top 100 in Books)
- #1239 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #1614 in Books > Textbooks > Science & Mathematics > Mathematics > Geometry
- #3089 in Books > Science & Math > Mathematics > Geometry & Topology

Would you like to update product info or give feedback on images?

Customer Reviews

4.3 out of 5 stars

5 star		75%
4 star		0%
3 star		0%
2 star		25%
1 star		0%

See all 4 customer reviews

Share your thoughts with other customers

Write a customer review

Most Helpful Customer Reviews

6 of 7 people found the following review helpful

Enriching Material for High School Students

By A Customer on June 3, 2002

Format: Paperback

Over and Over Again is ideal for high school students preparing for national olympiads such as the USAMO or for students trying to enrich their knowledge of mathematics. Many interesting topics are adressed such as Sharkovskii's theorem which is presented at a high school level, even though it is not typically encountered in college until junior level classes on chaos theory. There is also a well written section on complex numbers in geometry which shows how complex numbers can be used to prove both classical theorems in geometry as well as more contemporary theorems such as Clifford's Circle theorem.

Comment Was this review helpful to you? Yes No Sending feedback...

Thank you for your feedback.

Sorry, we failed to record your vote. Please try again

Report abuse

8 of 10 people found the following review helpful

Good for computer programmers, too.

By Bryan Z. Wagstaff on August 22, 2003

Format: Paperback Verified Purchase

This book, like so many of their papers, can help clarify topics that you feel you should understand, but don't. It covers topics that many college math graduates don't understand well, with much of it at a high-school math level. For the self-taught computer programmer, it will cover many math topics that will help you in your career. As both authors have extensive backgrounds in computer graphics, you will notice that this book is slanted toward those ideas and algorithms. As a reference book, it explains the algorithms in clear language. It is well worth the money.
Dr. Sederberg, one of the authors, has been said to make mathematics speak like poetry. He has written many papers in Computer Science and has had several publications in SIGGRAPH, the world's most impressive computer graphics conference. Having just SIGGRAPH paper one is considered an accomplishment -- he has 10 to date. Gengzhe Chang, I believe, was one of his Ph.D. students. Of their joint publications, I feel this is the most useful.

Comment Was this review helpful to you? Yes No Sending feedback...

Thank you for your feedback.

Sorry, we failed to record your vote. Please try again

Report abuse

2 of 2 people found the following review helpful

Generally elementary overview of one of the most foundational mathematical techniques

By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on January 30, 2011

Format: Paperback

Repeated operations provide much of the foundations of mathematics, one has only to look at the positive integers and the process of repeatedly adding one to realize that. From these earliest beginnings of mathematics to the present where repeated operations are used to solve problems using computers there is a broad swath of transformations that have been repeated and used to answer questions.
The book is constructed from a set of chapters where a foundational topic is introduced, one or more problems is stated and then an operation is applied several times to solve the problems. Proof techniques such as induction and infinite descent are covered. Many of the problems are taken or modified from those appearing in Mathematical Olympiad (MO) examinations. While some of the problems in the last chapters require a background in calculus the others could be used to prepare teams for the MO exams and towards that end, a set of exercises is given at the end of each chapter.
Given the significance of iterative techniques in mathematics, it is unfortunate that they are not made a more fundamental component of mathematics education. Towards that end I strongly recommend that math teachers at all levels read this book and use some of the ideas in their classes.

Comment Was this review helpful to you? Yes No Sending feedback...

Thank you for your feedback.

Sorry, we failed to record your vote. Please try again

Report abuse

0 of 23 people found the following review helpful

As mathematics books go, don't spend your money!

By Roger Bagula on April 7, 2000

Format: Paperback

There is a bright light in the iteration theory chapter, but overall it is pretty badly written and dull. The mathematics is all very good, but tastes like old soda crackers!

Comment Was this review helpful to you? Yes No Sending feedback...

Thank you for your feedback.

Sorry, we failed to record your vote. Please try again

Report abuse

See all 4 customer reviews (newest first)

Write a customer review