**Classroom Resource Materials**

Volume: 39;
2011;
207 pp;
Softcover

Print ISBN: 978-0-88385-780-9

Product Code: CLRM/39

List Price: $35.00

AMS Member Price: $26.25

MAA member Price: $26.25

**Electronic ISBN: 978-0-88385-912-4
Product Code: CLRM/39.E**

List Price: $35.00

AMS Member Price: $26.25

MAA member Price: $26.25

# Rediscovering Mathematics: You Do the Math

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*Shai Simonson*

MAA Press: An Imprint of the American Mathematical Society

Rediscovering Mathematics is aimed at
a general audience and addresses the question of how best to teach and
study mathematics. The book attempts to bring the exciting and
dynamic world of mathematics to a non-technical audience. With so
much focus today on how best to educate the new generation and make
mathematics less rote and more interactive, this book is an
eye-opening experience for many people who suffered with dull math
teachers and curricula.

Rediscovering Mathematics is an
eclectic collection of mathematical topics and puzzles aimed at
talented youngsters and inquisitive adults who want to expand their
view of mathematics. By focusing on problem solving, and discouraging
rote memorization, the book shows how to learn and teach mathematics
through investigation, experimentation, and
discovery. Rediscovering Mathematics is also an excellent
text for training math teachers at all levels. Topics range in
difficulty and cover a wide range of historical periods, with some
examples demonstrating how to uncover mathematics in everyday life,
including: number theory and its application to secure communication
over the Internet, the algebraic and combinatorial work of a medieval
mathematician Rabbi, and applications of probability to sports,
casinos, and gambling.

Rediscovering Mathematics provides a
fresh view of mathematics for those who already like the subject, and
offers a second chance for those who think they don't.

#### Reviews & Endorsements

This very nice book provides mathematics teachers with a valuable resource of mathematical puzzles designed to challenge, motivate, educate and entertain students helping them to discover the internal elegance and beauty of mathematics..The book is written in a precise and clear manner; all explanations are made transparent and easy to follow. In the end of the book, resources for "rediscovering mathematics," suggestions for further reading, and a helpful index are provided. This lovely book unostentatiously promotes mathematical discovery and creativity combining the features of a useful educational tool and a very entertaining recreational reading. It will bring many joyful moments to the readers irrelevant to their mathematical background and previous experience with the subject.

-- Yuri V. Rogovchenko, zbMATH

[S]econdary math teachers...could use this text as a journey to personal professional development. Shai Simonson's "Rediscovering Mathematics: You Do the Math" is a fun text to guide this journey...To support my suggestion for using this text as one guide to a professional development journey, I also refer to Simonson's claim that it offers 'a fresh view of mathematics for those who already like the subject and offers a second chance for those who think they don't.. In fact, the book can fit the same claim if used with students.

-- MathNEXUS

The book would be a captivating resource for two main audiences: teachers and gifted students. First, the author passionately advocates that teachers represent mathematics as an interactive enterprise that creates inquisitive students rather than memorizers. The problems and explanations serve as exemplary resources for teachers to act as a 'conductor of a symphony" always probing students to dig deeper into generalizations. Second, the book could serve as a supplementary textbook for gifted students driven to explore nontraditional mathematical topics. The prose and detailed explanations make this book a must-have for the mathematically curious.

-- Chris Bolognese, Mathematics Teacher

How can we encourage students to get beyond a mindless approach to mathematics and become active learners who will strive for insight, understanding and creativity? This book, whose author teaches computer science at Stonehill College in Easton, MA, addresses this question explicitly.

-- Edward Barbeau, Crux Mathematicorum

The book is intended for teachers, in particular, preservice teachers. It will be enjoyed by curious young fans of all ages.

-- Alexander Bogomolny, Cut the Knot

“Rediscovering Mathematics: You Do the Math”, by Shai Simonson is a great book. It starts with his piece on "How to Read Mathematics," which I love, and wends its way through lots of mathematical problems, and lots of ideas about how to teach and learn math. … Simonson includes a number of problems I haven't seen before, which is quite a feat after all the grazing I've done online in the past few years. And the problems are at lots of levels, so there is much to chew on whatever your mathematical sophistication.

-- Math Mama

What a mix of problems! Simonson (Stonehill College) has provided a unique collection of problems intended for a wide range of readers. They seem to be all the fun and interesting problems that one finds as supplements and extras in a variety of textbooks. This reviewer has used many of the familiar problems in this work to generate interest or to motivate students on the need to learn what they might think are the more mundane topics in a textbook. … The author provides some theoretical background, but on the whole, the book is really a plug-and-chug look at problems.

-- M.D. Sanford, Felician College, CHOICE Magazine

# Table of Contents

## Rediscovering Mathematics: You Do the Math

- cover cover11
- Copyright page ii3
- Title page iii4
- Acknowledgements vii8
- A Guide for the Reader xiii14
- Introduction: How to Read Mathematics xvii18
- Mathematical Discovery in the Classroom 134
- Don't Reach for Your Calculator (Yet) 1346
- Have Another Piece of Pie, Zeno? 3164
- Thinking Like a Mathematician---Lessons from a Medieval Rabbi 4174
- What is Mathematics Good For? 6396
- Three Averages 77110
- Algorithms---The Unexpected Role of Pure Mathematics 93126
- A Solution to the Two Jug Puzzle 94127
- Euclid's Algorithm 96129
- Other Methods for Calculating Greatest Common Divisors 99132
- The Efficiency (or Speed) of an Algorithm 99132
- The Egyptian Multiplication Algorithm 101134
- The Fast Modular Exponentiation Algorithm 103136
- Greatest Common Divisors, Algorithms, and E-Commerce 105138
- E-Commerce and Cryptography 106139
- The Rest of the Story---The RSA Algorithm 108141
- Challenges 109142

- Pythagoras' Theorem and Math by Pictures 113146
- Memorizing Versus Understanding 129162
- Games and Gambling 143176
- Soccer Balls and Counting Tricks 159192
- Pizza Pi and Area 169202
- Back to the Classroom 185218
- Resources for Rediscovering Mathematics 195228
- Further Reading 199232
- Index 201234
- About the Author 207240