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Festival of Mathematics: A Sourcebook [Pehme köide]

  • Formaat: Paperback / softback, 188 pages, kõrgus x laius: 254x178 mm, kaal: 405 g
  • Sari: MSRI Mathematical Circles Library
  • Ilmumisaeg: 30-Jun-2022
  • Kirjastus: American Mathematical Society
  • ISBN-10: 147045338X
  • ISBN-13: 9781470453381
Teised raamatud teemal:
  • Formaat: Paperback / softback, 188 pages, kõrgus x laius: 254x178 mm, kaal: 405 g
  • Sari: MSRI Mathematical Circles Library
  • Ilmumisaeg: 30-Jun-2022
  • Kirjastus: American Mathematical Society
  • ISBN-10: 147045338X
  • ISBN-13: 9781470453381
Teised raamatud teemal:
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 on-ramp, such as a game or puzzle requiring no more than simple arithmetic or intuitive concepts of symmetry. Follow-up 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.
Foreword   xi  
Preface   xv  
Acknowledgements   xix  
  Part 1 Activity Guides
  1 (166)
  Chapter 1 Color Triangle Challenge
  3 (20)
  Some Initial Explorations
  4 (5)
  Toward a Generalization
  9 (4)
  Further Generalizations
  13 (3)
  Applying Arithmetic
  16 (2)
  Connection to the Binomial Coefficients
  18 (3)
  Historical Notes
  21 (2)
  Chapter 2 Magic Squares and Algebra
  23 (30)
  Constructing a Magic Square
  23 (8)
  The Geometry of Magic Squares
  31 (3)
  Some Facts about Groups
  34 (2)
  Uniqueness of the Magic Square: Some Combinatoric Results
  36 (1)
  New Magic Squares from Old
  37 (4)
  The Vector Space of a Magic Square
  41 (8)
  Magic Squares and Tic-tac-toe
  49 (1)
  Historical Notes
  50 (3)
  Chapter 3 Nim
  53 (14)
  One-Row Nim
  53 (8)
  Nim Variants
  61 (2)
  Two-Row Nim
  63 (1)
  Historical Notes
  64 (3)
  Chapter 4 Palindrome Grab!
  67 (10)
  The Basic Game
  67 (2)
  The Greedy Game
  69 (2)
  The Patient Game
  71 (3)
  Historical Notes
  74 (3)
  Chapter 5 To Twos, Too! Two Twos? More?
  77 (16)
  SDP2 Representations
  77 (4)
  SP2 Representations
  81 (4)
  S2P2 Representations
  85 (4)
  Some Extensions
  89 (1)
  Historical Notes
  90 (3)
  Chapter 6 Prisoner Puzzle
  93 (10)
  Last Man Sitting
  93 (3)
  Lucky 7?
  96 (3)
  Changing of the Guard
  99 (2)
  Historical Notes
  101 (2)
  Chapter 7 Broken Calculators
  103 (10)
  Calculator 1
  103 (2)
  Calculator 2
  105 (3)
  Calculator 3
  108 (1)
  Calculator 4
  109 (1)
  Calculator 5
  110 (2)
  Historical Notes
  112 (1)
  Chapter 8 Dominoes and Checkerboards
  113 (18)
  Constructing Tilings
  114 (7)
  Counting Tilings
  121 (8)
  Historical Notes
  129 (2)
  Chapter 9 Fair Division
  131 (22)
  Rectangles, Triangles, Squares
  131 (5)
  Quadrilaterals and Squares
  136 (15)
  Historical Notes
  151 (2)
  Chapter 10 Jumping Julia
  153 (14)
  Mazes and Graph Theory
  153 (8)
  Make Your Own Maze
  161 (3)
  Historical Notes
  164 (3)
  Part 2 Activity Handouts
  167 (36)
  Chapter 1 Color Triangle Challenge
  169 (6)
  Some Initial Explorations
  170 (1)
  Toward a Generalization
  171 (1)
  Applying Arithmetic
  171 (4)
  Chapter 2 Magic Squares and Algebra
  175 (6)
  Constructing a Magic Square
  175 (2)
  The Geometry of Magic Squares
  177 (1)
  Uniqueness of the Magic Square: Some Combinatoric Results
  178 (1)
  New Magic Squares from Old
  179 (2)
  Chapter 3 Nim
  181 (2)
  One-Row Nim
  181 (1)
  Nim Variants
  182 (1)
  Two-Row Nim
  182 (1)
  Chapter 4 Palindrome Grab!
  183 (2)
  The Basic Game
  183 (1)
  The Greedy Game
  184 (1)
  The Patient Game
  184 (1)
  Chapter 5 To Twos, Too! Two Twos? More?
  185 (4)
  SDP2 Representations
  185 (1)
  SP2 Representations
  185 (1)
  S2P2 Representations
  186 (1)
  Some Extensions
  187 (2)
  Chapter 6 Prisoner Puzzle
  189 (2)
  Last Man Sitting
  189 (1)
  Lucky 7?
  189 (1)
  Changing of the Guard
  190 (1)
  Chapter 7 Broken Calculators
  191 (2)
  Calculator 1
  191 (1)
  Calculator 2
  191 (1)
  Calculator 3
  191 (1)
  Calculator 4
  192 (1)
  Calculator 5
  192 (1)
  Chapter 8 Dominoes and Checkerboards
  193 (4)
  Constructing Tilings
  193 (2)
  Counting Tilings
  195 (2)
  Chapter 9 Fair Division
  197 (6)
  Rectangles, Triangles, Squares
  197 (1)
  Quadrilaterals and Squares
  198 (5)
  Chapter 10 Jumping Julia
  203 (1)
Mazes and Graph Theory   203 (4)
Make Your Own Maze   207