Softcover ISBN:  9781470453381 
Product Code:  MCL/28 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Electronic ISBN:  9781470469559 
Product Code:  MCL/28.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 

Book DetailsMSRI Mathematical Circles LibraryVolume: 28; 2022; 208 ppMSC: Primary 97;
This book, inspired by the Julia Robinson Mathematics Festival, aims to engage students in mathematical discovery through fun and approachable problems that reveal deeper mathematical ideas.
Each chapter starts with a gentle onramp, such as a game or puzzle requiring no more than simple arithmetic or intuitive concepts of symmetry. Followup problems and activities require intuitive logic and reveal more sophisticated notions of strategy and algorithms. Projects are designed so that progress is more important than any end goal, ensuring that students will learn something significant no matter how far they get. The process of understanding the questions and how they build on one another becomes an exhilarating ride, revealing serious mathematics before the reader is aware of the transition.
This book can be used in classrooms, math clubs, after school activities, homeschooling, and parent/student gatherings and is appropriate for students of age 8 to 18, as well as for teachers wanting to hone their skills.
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.ReadershipThis book is for facilitators interested in running Math Circles or Julia Robinson Math Festivals.

Table of Contents

Foreword

Preface

Acknowledgements

Part 1. Activity Guides

Chapter 1. Color Triangle Challenge

Some Initial Explorations

Toward a Generalization

Further Generalizations

Applying Arithmetic

Connection to the Binomial Coefficients

Historical Notes

Chapter 2. Magic Squares and Algebra

Constructing a Magic Square

The Geometry of Magic Squares

Some Facts about Groups

Uniqueness of the Magic Square: Some Combinatoric Results

New Magic Squares from Old

The Vector Space of a Magic Square

Magic Squares and Tictactoe

Historical Notes

Chapter 3. Nim

OneRow Nim

Nim Variants

TwoRow Nim

Historical Notes

Chapter 4. Palindrome Grab!

The Basic Game

The Greedy Game

The Patient Game

Historical Notes

Chapter 5. To Twos, Too! Two Twos? More?

SDP2 Representations

SP2 Representations

S2P2 Representations

Some Extensions

Historical Notes

Chapter 6. Prisoner Puzzle

Last Man Sitting

Lucky 7?

Changing of the Guard

Historical Notes

Chapter 7. Broken Calculators

Calculator 1

Calculator 2

Calculator 3

Calculator 4

Calculator 5

Historical Notes

Chapter 8. Dominoes and Checkerboards

Constructing Tilings

Counting Tilings

Historical Notes

Chapter 9. Fair Division

Rectangles, Triangles, Squares

Quadrilaterals and Squares

Historical Notes

Chapter 10. Jumping Julia

Mazes and Graph Theory

Make Your Own Maze

Historical Notes

Part 2. Activity Handouts

Chapter 1. Color Triangle Challenge

Some Initial Explorations

Toward a Generalization

Applying Arithmetic

Chapter 2. Magic Squares and Algebra

Constructing a Magic Square

The Geometry of Magic Squares

Uniqueness of the Magic Square: Some Combinatoric Results

New Magic Squares from Old

Chapter 3. Nim

OneRow Nim

Nim Variants

TwoRow Nim

Chapter 4. Palindrome Grab!

The Basic Game

The Greedy Game

The Patient Game

Chapter 5. To Twos, Too! Two Twos? More?

SDP2 Representations

SP2 Representations

S2P2 Representations

Some Extensions

Chapter 6. Prisoner Puzzle

Last Man Sitting

Lucky 7?

Changing of the Guard

Chapter 7. Broken Calculators

Calculator 1

Calculator 2

Calculator 3

Calculator 4

Calculator 5

Chapter 8. Dominoes and Checkerboards

Constructing Tilings

Counting Tilings

Chapter 9. Fair Division

Rectangles, Triangles, Squares

Quadrilaterals and Squares

Chapter 10. Jumping Julia

Mazes and Graph Theory

Make Your Own Maze


Additional Material

Reviews

There are a number of books available with intriguing problems for students (and others) to puzzle over, but you will want to make room in your bookshelf for one more.
Steve Benson, Lesley University


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 Book Details
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This book, inspired by the Julia Robinson Mathematics Festival, aims to engage students in mathematical discovery through fun and approachable problems that reveal deeper mathematical ideas.
Each chapter starts with a gentle onramp, such as a game or puzzle requiring no more than simple arithmetic or intuitive concepts of symmetry. Followup problems and activities require intuitive logic and reveal more sophisticated notions of strategy and algorithms. Projects are designed so that progress is more important than any end goal, ensuring that students will learn something significant no matter how far they get. The process of understanding the questions and how they build on one another becomes an exhilarating ride, revealing serious mathematics before the reader is aware of the transition.
This book can be used in classrooms, math clubs, after school activities, homeschooling, and parent/student gatherings and is appropriate for students of age 8 to 18, as well as for teachers wanting to hone their skills.
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.
This book is for facilitators interested in running Math Circles or Julia Robinson Math Festivals.

Foreword

Preface

Acknowledgements

Part 1. Activity Guides

Chapter 1. Color Triangle Challenge

Some Initial Explorations

Toward a Generalization

Further Generalizations

Applying Arithmetic

Connection to the Binomial Coefficients

Historical Notes

Chapter 2. Magic Squares and Algebra

Constructing a Magic Square

The Geometry of Magic Squares

Some Facts about Groups

Uniqueness of the Magic Square: Some Combinatoric Results

New Magic Squares from Old

The Vector Space of a Magic Square

Magic Squares and Tictactoe

Historical Notes

Chapter 3. Nim

OneRow Nim

Nim Variants

TwoRow Nim

Historical Notes

Chapter 4. Palindrome Grab!

The Basic Game

The Greedy Game

The Patient Game

Historical Notes

Chapter 5. To Twos, Too! Two Twos? More?

SDP2 Representations

SP2 Representations

S2P2 Representations

Some Extensions

Historical Notes

Chapter 6. Prisoner Puzzle

Last Man Sitting

Lucky 7?

Changing of the Guard

Historical Notes

Chapter 7. Broken Calculators

Calculator 1

Calculator 2

Calculator 3

Calculator 4

Calculator 5

Historical Notes

Chapter 8. Dominoes and Checkerboards

Constructing Tilings

Counting Tilings

Historical Notes

Chapter 9. Fair Division

Rectangles, Triangles, Squares

Quadrilaterals and Squares

Historical Notes

Chapter 10. Jumping Julia

Mazes and Graph Theory

Make Your Own Maze

Historical Notes

Part 2. Activity Handouts

Chapter 1. Color Triangle Challenge

Some Initial Explorations

Toward a Generalization

Applying Arithmetic

Chapter 2. Magic Squares and Algebra

Constructing a Magic Square

The Geometry of Magic Squares

Uniqueness of the Magic Square: Some Combinatoric Results

New Magic Squares from Old

Chapter 3. Nim

OneRow Nim

Nim Variants

TwoRow Nim

Chapter 4. Palindrome Grab!

The Basic Game

The Greedy Game

The Patient Game

Chapter 5. To Twos, Too! Two Twos? More?

SDP2 Representations

SP2 Representations

S2P2 Representations

Some Extensions

Chapter 6. Prisoner Puzzle

Last Man Sitting

Lucky 7?

Changing of the Guard

Chapter 7. Broken Calculators

Calculator 1

Calculator 2

Calculator 3

Calculator 4

Calculator 5

Chapter 8. Dominoes and Checkerboards

Constructing Tilings

Counting Tilings

Chapter 9. Fair Division

Rectangles, Triangles, Squares

Quadrilaterals and Squares

Chapter 10. Jumping Julia

Mazes and Graph Theory

Make Your Own Maze

There are a number of books available with intriguing problems for students (and others) to puzzle over, but you will want to make room in your bookshelf for one more.
Steve Benson, Lesley University