The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series.

Author: Roger B. Nelsen

Publisher: MAA

ISBN: 0883857006

Category: Mathematics

Page: 152

View: 896

Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series.

Author: Roger B. Nelsen

Publisher: American Mathematical Soc.

ISBN: 9781470451868

Category: Education

Page: 152

View: 345

Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

Publisher: The Mathematical Association of America

ISBN: 9780883857908

Category: Mathematics

Page: 187

View: 433

Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs. The proofs in the book are divided by topic into five chapters: Geometry & Algebra; Trigonometry, Calculus & Analytic Geometry; Inequalities; Integers & Integer Sums; and Infinite Series & Other Topics. The proofs in the book are intended primarily for the enjoyment of the reader, however, teachers will want to use them with students at many levels: high school courses from algebra through precalculus and calculus; college level courses in number theory, combinatorics, and discrete mathematics; and pre-service and in-service courses for teachers.

Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one could begin to go about proving it.

Author: Roger B. Nelsen

Publisher: American Mathematical Soc.

ISBN: 9781470451882

Category: Mathematics

Page: 130

View: 573

Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integer sums; and sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

There are many sources for such proofs. The books Proofs without Words: Exercises in Visual Thinking (Classroom Resource Materials) (v. 1, 2, 3) by
Roger Nelsen is one source of similar materials. Proofs Without Words and
Beyond ...

Author: Dave Auckly

Publisher: American Mathematical Soc.

ISBN: 9781470453879

Category: Education

Page: 281

View: 203

The people of the Navajo Nation know mathematics education for their children is essential. They were joined by mathematicians familiar with ways to deliver problems and a pedagogy that, through exploration, shows the art, joy and beauty in mathematics. This combined effort produced a series of Navajo Math Circles—interactive mathematical explorations—across the Navajo Reservation. This book contains the mathematical details of that effort. Between its covers is a thematic rainbow of problem sets that were used in Math Circle sessions on the Reservation. The problem sets are good for puzzling over and exploring the mathematical ideas within. They will help nurture curiosity and confidence in students. The problems come with suggestions for pacing, for adjusting the problems to be more or less challenging, and for different approaches to solving them. This book is a wonderful resource for any teacher wanting to enrich the mathematical lives of students and for anyone curious about mathematical thinking outside the box. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

The Pythagoreans were the first to be intrigued by the triangular numbers n ( n + 1 ) / 2 , the squares n2 , and polygonal numbers in general . ... A good exercise or
project for a number theory class might be to understand and explain the
geometry of the set of triples in the paper . ... of squares VIII , in Proofs Without Words II : More Exercises in Visual Thinking , MAA , Classroom Resource Materials , p .

Author: Arthur T. Benjamin

Publisher: American Mathematical Soc.

ISBN: 9780883853405

Category: Mathematics

Page: 311

View: 503

In Biscuits of Number Theory, the editors have chosen articles that are exceptionally well-written and that can be appreciated by anyone who has taken (or is taking) a first course in number theory. This book could be used as a textbook supplement for a number theory course, especially one that requires students to write papers or do outside reading. The editors give examples of some of the possibilities. The collection is divided into seven chapters: Arithmetic; Primes; Irrationality and Continued Fractions; Sums of Squares and Polygonal Numbers; Fibonacci Numbers; Number-Theoretic Functions; and Elliptic Curves, Cubes and Fermat's Last Theorem. As with any anthology, you don't have to read the Biscuits in order. Dip into them anywhere: pick something from the table of contents that strikes your fancy, and have at it. If the end of an article leaves you wondering what happens next, then by all means dive in and do some research. You just might discover something new!

Author: Caren L. DiefenderferPublish On: 2010-02-18

Reader collecting articles from MAA journals between 1977 and 2007, selected for usefulness to high school calculus teachers.

Author: Caren L. Diefenderfer

Publisher: MAA

ISBN: 0883857618

Category: Juvenile Nonfiction

Page: 507

View: 661

The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.The MAA has twice previously issued a calculus reader, collecting articles on calculus from its journals: Selected Papers in Calculus, published in 1969 and reprinted as Part I of A Century of Calculus, and Part II published in 1992. In a sense The Calculus Collection is the third volume in that series, but different in that it is a collection chosen for its usefulness to those who teach first-year calculus in high schools as well as colleges and universities.

As the reader shall see, a given mathematical idea or relation may have many
different images that justify it, so that ... Proofs Without Words: Exercises in Visual Thinking Classroom Resource Materials • Catalog Code: PWW - 160 pp., ...

Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory.

Author: Roger B. Nelsen

Publisher: American Mathematical Soc.

ISBN: 9781470448462

Category: Mathematics

Page: 153

View: 625

Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. [Author]; Roger Nelsen is a long-time contributor of ``Proofs Without Words'' in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.

The frequent use of examples is beneficial to the reader , as are the large exercise sets . ... and exposing enough detail , without getting bogged down ( or
bogging down the reader ) with minute details . ... Mathematics 31 - 6101 93 -
86388 Orig Nelsen , Roger B . Proofs without words : exercises in visual thinking .
... 152p ( Classroom resource materials , 1 ) index ISBN 0 - 88385 - 700 - 6 pbk ,
$ 23 .

Including Related Teaching Materials K-12. M M. Calculus ... 1997 . Vol . 1.
Fractals for the Classroom : Strategic Activities ... Classroom Resource Materials
Series . ... 1998 . pap , text 27.95 ( 0-88385-708-1 , CMB ) Proofs Without Words Exercises in Visual Thinking . Roger B. ... Diana V. Lambdin , et al , eds . ( Illus . )
.

Camille DEBIÈVE R.B. NELSEN . Proofs without Words . Exercices in Visual Thinking . Classroom Resource Materials , vol . 1. The Mathematical Association
of America , Washington ( 1993 ) . vii + 152 pages . Broché , ISBN 0-88385-700-6
.

Author: R.R. Bowker Company. Department of BibliographyPublish On: 1995

Pronounce It Perfectly in English , No . 1 . LC 95 - 12841 . ( Pronounce It Perfectly
in . . . Ser . ) . Jul . 1995 . audio write for info . ... Yedlin , Jane & Raupp , Magdale .
Passport to English : Grammar Exercises in Context , Vol . 1 . 2nd ed . Aug . ...
Collaboration Module 5 : Providing Support in the Classroom ( Facilitator Guide )
( A Staff Development Series for General ... There is so much love pouring into
our world that LIGHTSHIPS had to be written as visible proof of the Illumined
Ones ...

Author: R.R. Bowker Company. Department of Bibliography

Well - educated people may be better able to comprehend visuals which require
some level of interpretation or extend beyond ... a variety of creative techniques ,
the lack of creativity in educational materials is a noted reason for their
ineffectiveness . ... To examine their application to the visual communication
media arts such as film and television , this paper : ( 1 ) ... The classroom exercise
and software present methods for expanding visual thinking and helping students
recognize the ...

If the primary school library fund has some spare cash , a copy of this on the
shelves would not be left unread . ... colourful and inviting book for younger time -
travellers with a serious historical purpose and many uses in the classroom . ... O
7502 2355 3 ; 2356 1 Advertised as ' young , friendly and funny ' these Sam ' s
Science Books ' are exuberant ... The rest of the book is devoted to instruction ,
beginning with the basic equipment needed and exercises to minimise the risk of
injury .

WINDSINGER'S prose, photos, drawings and lyrics late visual. rational pathways;
the music evokes intuitive, rhythmic and ... Gary Smith P.O. Box 1/ -4030 I
Vanguard Stereo Album – $6.95 - - Wellsville, Utah 84.339 I Stereo Cassette
Tapes — $6.95 ... l I TOTAL ENCLOSED - City State Zip I l t See Materials/
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women who sing songs about things like lollipop trees and use words like bunny,
tummy, and horsie.