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Mathematical Circle Diaries, Year 2: Complete Curriculum for Grades 6 to 8
 
Anna Burago Prime Factor Math Circle, Seattle, WA
A co-publication of the AMS and Mathematical Sciences Research Institute
Mathematical Circle Diaries, Year 2
Softcover ISBN:  978-1-4704-3718-3
Product Code:  MCL/20
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Sale Price: $33.00
eBook ISBN:  978-1-4704-4809-7
Product Code:  MCL/20.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
Sale Price: $30.00
Softcover ISBN:  978-1-4704-3718-3
eBook: ISBN:  978-1-4704-4809-7
Product Code:  MCL/20.B
List Price: $105.00 $80.00
MAA Member Price: $94.50 $72.00
AMS Member Price: $84.00 $64.00
Sale Price: $63.00 $48.00
Mathematical Circle Diaries, Year 2
Click above image for expanded view
Mathematical Circle Diaries, Year 2: Complete Curriculum for Grades 6 to 8
Anna Burago Prime Factor Math Circle, Seattle, WA
A co-publication of the AMS and Mathematical Sciences Research Institute
Softcover ISBN:  978-1-4704-3718-3
Product Code:  MCL/20
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Sale Price: $33.00
eBook ISBN:  978-1-4704-4809-7
Product Code:  MCL/20.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
Sale Price: $30.00
Softcover ISBN:  978-1-4704-3718-3
eBook ISBN:  978-1-4704-4809-7
Product Code:  MCL/20.B
List Price: $105.00 $80.00
MAA Member Price: $94.50 $72.00
AMS Member Price: $84.00 $64.00
Sale Price: $63.00 $48.00
  • Book Details
     
     
    MSRI Mathematical Circles Library
    Volume: 202018; 362 pp
    MSC: Primary 97; 00

    Mathematical circles, with their question-driven approach and emphasis on problem solving, expose students to the type of mathematics that stimulates the development of logical thinking, creativity, analytical abilities, and mathematical reasoning. These skills, while scarcely introduced at school, are in high demand in the modern world.

    This book, a sequel to Mathematical Circle Diaries, Year 1, teaches how to think and solve problems in mathematics. The material, distributed among twenty-nine weekly lessons, includes detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The book covers a broad range of problem-solving strategies and proofing techniques, as well as some more advanced topics that go beyond the limits of a school curriculum. The topics include invariants, proofs by contradiction, the Pigeonhole principle, proofs by coloring, double counting, combinatorics, binary numbers, graph theory, divisibility and remainders, logic, and many others. When students take science and computing classes in high school and college, they will be better prepared for both the foundations and advanced material. The book contains everything that is needed to run a successful mathematical circle for a full year.

    This book, written by an author actively involved in teaching mathematical circles for fifteen years, is intended for teachers, math coaches, parents, and math enthusiasts who are interested in teaching math that promotes critical thinking. Motivated students can work through this book on their own.

    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.

    Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

    Readership

    Teachers, parents, research mathematicians, and undergraduate and graduate students interested in teaching extracurricular math to middle and high school students.

  • Table of Contents
     
     
    • Cover
    • Title page
    • Contents
    • Acknowledgments
    • Preliminaries
    • Mathematical Circles
    • A Few Words about This Book
    • Potential Students
    • Curriculum
    • Part 1 . Session Plans
    • Introduction
    • Lessons and Problem Sets
    • Chapter 1. Session 1: Checkerboard Problems
    • 1.1. Introduction
    • 1.2. Math Warm-up
    • 1.3. Discussion of the Day: Checkerboard Problems
    • 1.4. In-Class Problem Set
    • 1.5. A Few Words about Problem Sets
    • 1.6. Take-Home Problem Set
    • 1.7. Additional “Checkerboard” Problems
    • Chapter 2. Session 2: Review: Math Logic and Other Problem-Solving Strategies
    • 2.1. Math Warm-up
    • 2.2. Discussion of the Day: Problem-Solving Strategies
    • 2.3. Take-Home Problem Set
    • Chapter 3. Session 3: Invariants
    • 3.1. Warm-up Discussion. Are Proofs Really Necessary?
    • 3.2. Discussion of the Day: Invariants
    • 3.3. Take-Home Problem Set
    • Chapter 4. Session 4: Proof by Contradiction
    • 4.1. Math Warm-up
    • 4.2. Discussion of the Day: Proof by Contradiction
    • 4.3. Take-Home Problem Set
    • Chapter 5. Session 5: Decimal Number System and Problems on Digits
    • 5.1. Warm-up Discussion. Egyptian Number System
    • 5.2. Discussion of the Day: Problems on Digits
    • 5.3. In-Class Problem Set
    • 5.4. Take-Home Problem Set
    • 5.5. Additional Problems
    • Chapter 6. Session 6: Binary Numbers I
    • 6.1. Math Warm-up
    • 6.2. Discussion of the Day: Binary Land—an Informal Introduction to Binaries
    • 6.3. Binary Number System
    • 6.4. Binary Notation
    • 6.5. Computers and Binary Numbers
    • 6.6. Take-Home Problem Set
    • Chapter 7. Session 7: Binary Numbers II
    • 7.1. Math Warm-up
    • 7.2. Discussion of the Day: Binary Arithmetic
    • 7.3. How to Convert Decimals to Binary
    • 7.4. Take-Home Problem Set
    • Chapter 8. Session 8: Mathematical Dominoes Tournament
    • 8.1. Math Warm-up
    • 8.2. Rules of Mathematical Dominoes
    • 8.3. Mathematical Dominoes Problems
    • 8.4. Take-Home Problem Set
    • Chapter 9. Session 9: Pigeonhole Principle
    • 9.1. Math Warm-up
    • 9.2. Discussion of the Day: Pigeonhole Principle
    • 9.3. Take-Home Problem Set
    • 9.4. Additional Problems
    • Chapter 10. Session 10: Geometric Pigeonhole Principle
    • 10.1. Math Warm-up
    • 10.2. Discussion of the Day: Geometric Pigeonhole
    • 10.3. Take-Home Problem Set
    • 10.4. Additional Problems
    • Chapter 11. Session 11: Mathematical Olympiad I
    • 11.1. Event of the Day: Mathematical Olympiad
    • 11.2. Mathematical Olympiad I. First Set of Problems
    • 11.3. Mathematical Olympiad I. Second Set of Problems
    • 11.4. Mathematical Olympiad I. Additional Problems
    • Chapter 12. Session 12: Combinatorics I. Review
    • 12.1. Math Warm-up
    • 12.2. Discussion of the Day: Review of Combinatorics Techniques
    • 12.3. In-Class Problem Set
    • 12.4. Take-Home Problem Set
    • 12.5. Additional Problems
    • Chapter 13. Session 13: Combinatorics II. Combinations
    • 13.1. Math Warm-up
    • 13.2. Discussion of the Day: Combinations
    • 13.3. Take-Home Problem Set
    • Chapter 14. Session 14: Mathematical Auction
    • 14.1. Math Warm-up
    • 14.2. Event of the Day: Mathematical Auction Game
    • 14.3. Mathematical Auction Problems
    • 14.4. Take-Home Problem Set
    • Chapter 15. Session 15: Combinatorics III. Complements. Snake Pit Game
    • 15.1. Math Warm-up
    • 15.2. Discussion of the Day: Complements
    • 15.3. Activity of the Day: Snake Pit on Combinatorics
    • 15.4. Take-Home Problem Set
    • Chapter 16. Session 16: Combinatorics IV. Combinatorial Conundrum
    • 16.1. Math Warm-up
    • 16.2. Discussion of the Day: Combinatorial Craftiness
    • 16.3. Take-Home Problem Set
    • 16.4. Additional Problems
    • Chapter 17. Session 17: Magic Squares and Related Problems
    • 17.1. Math Warm-up
    • 17.2. Discussion of the Day: Magic Squares from 1 to 9
    • 17.3. More on 3×3 Magic Squares
    • 17.4. Magic Squares Extended
    • 17.5. Take-Home Problem Set
    • Chapter 18. Session 18: Double Counting, or There Is More than One Way to Cut a Cake
    • 18.1. Math Warm-up
    • 18.2. Discussion of the Day: Double Counting
    • 18.3. Take-Home Problem Set
    • 18.4. Additional Problems
    • Chapter 19. Session 19: Mathematical Olympiad II
    • 19.1. Event of the Day: Mathematical Olympiad
    • 19.2. Mathematical Olympiad II. First Set of Problems
    • 19.3. Mathematical Olympiad II. Second Set of Problems
    • 19.4. Mathematical Olympiad II. Additional Problems
    • Chapter 20. Session 20: Divisibility I. Review
    • 20.1. Math Warm-up
    • 20.2. Discussion of the Day: Divisibility
    • 20.3. Prime Factorization Practice. Set 1
    • 20.4. Prime Factorization Practice. Set 2
    • 20.5. Take-Home Problem Set
    • 20.6. Additional Problems
    • Chapter 21. Session 21: Divisibility II. Relatively Prime Numbers; GCF and LCM
    • 21.1. Math Warm-up: Mysteries of Prime Numbers
    • 21.2. Discussion of the Day: Relatively Prime Numbers
    • 21.3. Greatest Common Factor (GCF)
    • 21.4. Least Common Multiple (LCM)
    • 21.5. How GCF and LCM Are Related
    • 21.6. GCF and LCM. In-Class Practice Problems
    • 21.7. Take-Home Problem Set
    • 21.8. Additional Problems
    • Chapter 22. Session 22: Divisibility III. Mathematical Race Game
    • 22.1. Math Warm-up
    • 22.2. Event of the Day: Mathematical Race
    • 22.3. Take-Home Problem Set
    • Chapter 23. Session 23: Mathematical Auction
    • 23.1. Event of the Day: Mathematical Auction Game
    • 23.2. Mathematical Auction Problems
    • 23.3. Take-Home Problem Set
    • Chapter 24. Session 24: Divisibility IV. Divisibility by 3 and Remainders
    • 24.1. Math Warm-up
    • 24.2. Discussion of the Day: Remainders When Divided by 3
    • 24.3. Arithmetic of Remainders
    • 24.4. Take-Home Problem Set
    • 24.5. Additional Problems
    • Chapter 25. Session 25: Divisibility V. Divisibility and Remainders
    • 25.1. Math Warm-up
    • 25.2. Discussion of the Day: Divisibility and Remainders
    • 25.3. Divisibility and Remainders Practice
    • 25.4. Take-Home Problem Set
    • 25.5. Additional Problems
    • Chapter 26. Session 26: Graph Theory I. Graphs and Their Applications
    • 26.1. Math Warm-up
    • 26.2. Discussion of the Day: Why Graphs Are Important
    • 26.3. How to Calculate the Number of Edges in a Graph
    • 26.4. Take-Home Problem Set
    • Chapter 27. Session 27: Graph Theory II. Handshaking Theorem
    • 27.1. Math Warm-up
    • 27.2. Discussion of the Day: Odd Vertices Theorem
    • 27.3. In-Class Problem Set
    • 27.4. Take-Home Problem Set
    • 27.5. Additional Problems
    • Chapter 28. Session 28: Graph Theory II. Solving Problems with Graphs
    • 28.1. Math Warm-up
    • 28.2. Discussion of the Day: Graphs Potpourri
    • 28.3. Take-Home Problem Set
    • Chapter 29. Session 29: Mathematical Olympiad III
    • 29.1. Event of the Day: Mathematical Olympiad
    • 29.2. Mathematical Olympiad III. First Set of Problems
    • 29.3. Mathematical Olympiad III. Second Set of Problems
    • Part 2 . Mathematical Contests and Competitions
    • Mathematical Contests
    • Mathematical Auction
    • What Is Special about Mathematical Auctions?
    • Rules of Mathematical Auction
    • A Sample Round
    • Team Work
    • Advice for a Teacher
    • Examples of Mathematical Auction Problems
    • Mathematical Dominoes
    • Rules of Mathematical Dominoes
    • Why Students Like Mathematical Dominoes
    • Why Teachers Like Mathematical Dominoes
    • Useful Details
    • Scorecards
    • Dominoes Cards: How to Make Them
    • Odds and Ends
    • Mathematical Snake Pit
    • Rules of Snake Pit Game
    • Useful Details
    • Score Table
    • Mathematical Race
    • Rules of Mathematical Race
    • Useful Details
    • Score Table
    • Mathematical Olympiad
    • Planning for an Oral Olympiad
    • Running an Olympiad
    • Olympiads in This Book
    • Awards and Prizes
    • Short Entertaining Math Games
    • Giotto and Math Giotto
    • Nim
    • Black Box
    • Part 3 . More Teaching Advice
    • How to Be a Great Math Circle Teacher
    • Teaching Style
    • Your Target Group
    • What Comes Next?
    • The Farewell
    • Part 4 . Solutions
    • Session 1. Checkerboard Problems
    • Session 2. Review: Math Logic and Other Problem-Solving Strategies
    • Session 3. Invariants
    • Session 4. Proof by Contradiction
    • Session 5. Decimal Number System and Problems on Digits
    • Session 6. Binary Numbers I
    • Session 7. Binary Numbers II
    • Session 8. Mathematical Dominoes Tournament
    • Session 9. Pigeonhole Principle
    • Session 10. Geometric Pigeonhole Principle
    • Session 11. Mathematical Olympiad I
    • Session 12. Combinatorics I. Review
    • Session 13. Combinatorics II. Combinations
    • Session 14. Mathematical Auction
    • Session 15. Combinatorics III. Complements. Snake Pit Game
    • Session 16. Combinatorics IV. Combinatorial Conundrum
    • Session 17. Magic Squares and Related Problems
    • Session 18. Double Counting, or There Is More than One Way to Cut a Cake
    • Session 19. Mathematical Olympiad II
    • Session 20. Divisibility I. Review
    • Session 21. Divisibility II. Relatively Prime Numbers; GCF and LCM
    • Session 22. Divisibility III. Mathematical Race Game
    • Session 23. Mathematical Auction
    • Session 24. Divisibility IV. Divisibility by 3 and Remainders
    • Session 25. Divisibility V. Divisibility and Remainders
    • Session 26. Graph Theory I. Graphs and Their Applications
    • Session 27. Graph Theory II. Handshaking Theorem
    • Session 28. Graph Theory III. Solving Problems with Graphs
    • Session 29. Mathematical Olympiad III
    • Appendix to Session 6
    • “Convert Decimal to Binary” Blank Table
    • Bibliography
    • Back Cover
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 202018; 362 pp
MSC: Primary 97; 00

Mathematical circles, with their question-driven approach and emphasis on problem solving, expose students to the type of mathematics that stimulates the development of logical thinking, creativity, analytical abilities, and mathematical reasoning. These skills, while scarcely introduced at school, are in high demand in the modern world.

This book, a sequel to Mathematical Circle Diaries, Year 1, teaches how to think and solve problems in mathematics. The material, distributed among twenty-nine weekly lessons, includes detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The book covers a broad range of problem-solving strategies and proofing techniques, as well as some more advanced topics that go beyond the limits of a school curriculum. The topics include invariants, proofs by contradiction, the Pigeonhole principle, proofs by coloring, double counting, combinatorics, binary numbers, graph theory, divisibility and remainders, logic, and many others. When students take science and computing classes in high school and college, they will be better prepared for both the foundations and advanced material. The book contains everything that is needed to run a successful mathematical circle for a full year.

This book, written by an author actively involved in teaching mathematical circles for fifteen years, is intended for teachers, math coaches, parents, and math enthusiasts who are interested in teaching math that promotes critical thinking. Motivated students can work through this book on their own.

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.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Readership

Teachers, parents, research mathematicians, and undergraduate and graduate students interested in teaching extracurricular math to middle and high school students.

  • Cover
  • Title page
  • Contents
  • Acknowledgments
  • Preliminaries
  • Mathematical Circles
  • A Few Words about This Book
  • Potential Students
  • Curriculum
  • Part 1 . Session Plans
  • Introduction
  • Lessons and Problem Sets
  • Chapter 1. Session 1: Checkerboard Problems
  • 1.1. Introduction
  • 1.2. Math Warm-up
  • 1.3. Discussion of the Day: Checkerboard Problems
  • 1.4. In-Class Problem Set
  • 1.5. A Few Words about Problem Sets
  • 1.6. Take-Home Problem Set
  • 1.7. Additional “Checkerboard” Problems
  • Chapter 2. Session 2: Review: Math Logic and Other Problem-Solving Strategies
  • 2.1. Math Warm-up
  • 2.2. Discussion of the Day: Problem-Solving Strategies
  • 2.3. Take-Home Problem Set
  • Chapter 3. Session 3: Invariants
  • 3.1. Warm-up Discussion. Are Proofs Really Necessary?
  • 3.2. Discussion of the Day: Invariants
  • 3.3. Take-Home Problem Set
  • Chapter 4. Session 4: Proof by Contradiction
  • 4.1. Math Warm-up
  • 4.2. Discussion of the Day: Proof by Contradiction
  • 4.3. Take-Home Problem Set
  • Chapter 5. Session 5: Decimal Number System and Problems on Digits
  • 5.1. Warm-up Discussion. Egyptian Number System
  • 5.2. Discussion of the Day: Problems on Digits
  • 5.3. In-Class Problem Set
  • 5.4. Take-Home Problem Set
  • 5.5. Additional Problems
  • Chapter 6. Session 6: Binary Numbers I
  • 6.1. Math Warm-up
  • 6.2. Discussion of the Day: Binary Land—an Informal Introduction to Binaries
  • 6.3. Binary Number System
  • 6.4. Binary Notation
  • 6.5. Computers and Binary Numbers
  • 6.6. Take-Home Problem Set
  • Chapter 7. Session 7: Binary Numbers II
  • 7.1. Math Warm-up
  • 7.2. Discussion of the Day: Binary Arithmetic
  • 7.3. How to Convert Decimals to Binary
  • 7.4. Take-Home Problem Set
  • Chapter 8. Session 8: Mathematical Dominoes Tournament
  • 8.1. Math Warm-up
  • 8.2. Rules of Mathematical Dominoes
  • 8.3. Mathematical Dominoes Problems
  • 8.4. Take-Home Problem Set
  • Chapter 9. Session 9: Pigeonhole Principle
  • 9.1. Math Warm-up
  • 9.2. Discussion of the Day: Pigeonhole Principle
  • 9.3. Take-Home Problem Set
  • 9.4. Additional Problems
  • Chapter 10. Session 10: Geometric Pigeonhole Principle
  • 10.1. Math Warm-up
  • 10.2. Discussion of the Day: Geometric Pigeonhole
  • 10.3. Take-Home Problem Set
  • 10.4. Additional Problems
  • Chapter 11. Session 11: Mathematical Olympiad I
  • 11.1. Event of the Day: Mathematical Olympiad
  • 11.2. Mathematical Olympiad I. First Set of Problems
  • 11.3. Mathematical Olympiad I. Second Set of Problems
  • 11.4. Mathematical Olympiad I. Additional Problems
  • Chapter 12. Session 12: Combinatorics I. Review
  • 12.1. Math Warm-up
  • 12.2. Discussion of the Day: Review of Combinatorics Techniques
  • 12.3. In-Class Problem Set
  • 12.4. Take-Home Problem Set
  • 12.5. Additional Problems
  • Chapter 13. Session 13: Combinatorics II. Combinations
  • 13.1. Math Warm-up
  • 13.2. Discussion of the Day: Combinations
  • 13.3. Take-Home Problem Set
  • Chapter 14. Session 14: Mathematical Auction
  • 14.1. Math Warm-up
  • 14.2. Event of the Day: Mathematical Auction Game
  • 14.3. Mathematical Auction Problems
  • 14.4. Take-Home Problem Set
  • Chapter 15. Session 15: Combinatorics III. Complements. Snake Pit Game
  • 15.1. Math Warm-up
  • 15.2. Discussion of the Day: Complements
  • 15.3. Activity of the Day: Snake Pit on Combinatorics
  • 15.4. Take-Home Problem Set
  • Chapter 16. Session 16: Combinatorics IV. Combinatorial Conundrum
  • 16.1. Math Warm-up
  • 16.2. Discussion of the Day: Combinatorial Craftiness
  • 16.3. Take-Home Problem Set
  • 16.4. Additional Problems
  • Chapter 17. Session 17: Magic Squares and Related Problems
  • 17.1. Math Warm-up
  • 17.2. Discussion of the Day: Magic Squares from 1 to 9
  • 17.3. More on 3×3 Magic Squares
  • 17.4. Magic Squares Extended
  • 17.5. Take-Home Problem Set
  • Chapter 18. Session 18: Double Counting, or There Is More than One Way to Cut a Cake
  • 18.1. Math Warm-up
  • 18.2. Discussion of the Day: Double Counting
  • 18.3. Take-Home Problem Set
  • 18.4. Additional Problems
  • Chapter 19. Session 19: Mathematical Olympiad II
  • 19.1. Event of the Day: Mathematical Olympiad
  • 19.2. Mathematical Olympiad II. First Set of Problems
  • 19.3. Mathematical Olympiad II. Second Set of Problems
  • 19.4. Mathematical Olympiad II. Additional Problems
  • Chapter 20. Session 20: Divisibility I. Review
  • 20.1. Math Warm-up
  • 20.2. Discussion of the Day: Divisibility
  • 20.3. Prime Factorization Practice. Set 1
  • 20.4. Prime Factorization Practice. Set 2
  • 20.5. Take-Home Problem Set
  • 20.6. Additional Problems
  • Chapter 21. Session 21: Divisibility II. Relatively Prime Numbers; GCF and LCM
  • 21.1. Math Warm-up: Mysteries of Prime Numbers
  • 21.2. Discussion of the Day: Relatively Prime Numbers
  • 21.3. Greatest Common Factor (GCF)
  • 21.4. Least Common Multiple (LCM)
  • 21.5. How GCF and LCM Are Related
  • 21.6. GCF and LCM. In-Class Practice Problems
  • 21.7. Take-Home Problem Set
  • 21.8. Additional Problems
  • Chapter 22. Session 22: Divisibility III. Mathematical Race Game
  • 22.1. Math Warm-up
  • 22.2. Event of the Day: Mathematical Race
  • 22.3. Take-Home Problem Set
  • Chapter 23. Session 23: Mathematical Auction
  • 23.1. Event of the Day: Mathematical Auction Game
  • 23.2. Mathematical Auction Problems
  • 23.3. Take-Home Problem Set
  • Chapter 24. Session 24: Divisibility IV. Divisibility by 3 and Remainders
  • 24.1. Math Warm-up
  • 24.2. Discussion of the Day: Remainders When Divided by 3
  • 24.3. Arithmetic of Remainders
  • 24.4. Take-Home Problem Set
  • 24.5. Additional Problems
  • Chapter 25. Session 25: Divisibility V. Divisibility and Remainders
  • 25.1. Math Warm-up
  • 25.2. Discussion of the Day: Divisibility and Remainders
  • 25.3. Divisibility and Remainders Practice
  • 25.4. Take-Home Problem Set
  • 25.5. Additional Problems
  • Chapter 26. Session 26: Graph Theory I. Graphs and Their Applications
  • 26.1. Math Warm-up
  • 26.2. Discussion of the Day: Why Graphs Are Important
  • 26.3. How to Calculate the Number of Edges in a Graph
  • 26.4. Take-Home Problem Set
  • Chapter 27. Session 27: Graph Theory II. Handshaking Theorem
  • 27.1. Math Warm-up
  • 27.2. Discussion of the Day: Odd Vertices Theorem
  • 27.3. In-Class Problem Set
  • 27.4. Take-Home Problem Set
  • 27.5. Additional Problems
  • Chapter 28. Session 28: Graph Theory II. Solving Problems with Graphs
  • 28.1. Math Warm-up
  • 28.2. Discussion of the Day: Graphs Potpourri
  • 28.3. Take-Home Problem Set
  • Chapter 29. Session 29: Mathematical Olympiad III
  • 29.1. Event of the Day: Mathematical Olympiad
  • 29.2. Mathematical Olympiad III. First Set of Problems
  • 29.3. Mathematical Olympiad III. Second Set of Problems
  • Part 2 . Mathematical Contests and Competitions
  • Mathematical Contests
  • Mathematical Auction
  • What Is Special about Mathematical Auctions?
  • Rules of Mathematical Auction
  • A Sample Round
  • Team Work
  • Advice for a Teacher
  • Examples of Mathematical Auction Problems
  • Mathematical Dominoes
  • Rules of Mathematical Dominoes
  • Why Students Like Mathematical Dominoes
  • Why Teachers Like Mathematical Dominoes
  • Useful Details
  • Scorecards
  • Dominoes Cards: How to Make Them
  • Odds and Ends
  • Mathematical Snake Pit
  • Rules of Snake Pit Game
  • Useful Details
  • Score Table
  • Mathematical Race
  • Rules of Mathematical Race
  • Useful Details
  • Score Table
  • Mathematical Olympiad
  • Planning for an Oral Olympiad
  • Running an Olympiad
  • Olympiads in This Book
  • Awards and Prizes
  • Short Entertaining Math Games
  • Giotto and Math Giotto
  • Nim
  • Black Box
  • Part 3 . More Teaching Advice
  • How to Be a Great Math Circle Teacher
  • Teaching Style
  • Your Target Group
  • What Comes Next?
  • The Farewell
  • Part 4 . Solutions
  • Session 1. Checkerboard Problems
  • Session 2. Review: Math Logic and Other Problem-Solving Strategies
  • Session 3. Invariants
  • Session 4. Proof by Contradiction
  • Session 5. Decimal Number System and Problems on Digits
  • Session 6. Binary Numbers I
  • Session 7. Binary Numbers II
  • Session 8. Mathematical Dominoes Tournament
  • Session 9. Pigeonhole Principle
  • Session 10. Geometric Pigeonhole Principle
  • Session 11. Mathematical Olympiad I
  • Session 12. Combinatorics I. Review
  • Session 13. Combinatorics II. Combinations
  • Session 14. Mathematical Auction
  • Session 15. Combinatorics III. Complements. Snake Pit Game
  • Session 16. Combinatorics IV. Combinatorial Conundrum
  • Session 17. Magic Squares and Related Problems
  • Session 18. Double Counting, or There Is More than One Way to Cut a Cake
  • Session 19. Mathematical Olympiad II
  • Session 20. Divisibility I. Review
  • Session 21. Divisibility II. Relatively Prime Numbers; GCF and LCM
  • Session 22. Divisibility III. Mathematical Race Game
  • Session 23. Mathematical Auction
  • Session 24. Divisibility IV. Divisibility by 3 and Remainders
  • Session 25. Divisibility V. Divisibility and Remainders
  • Session 26. Graph Theory I. Graphs and Their Applications
  • Session 27. Graph Theory II. Handshaking Theorem
  • Session 28. Graph Theory III. Solving Problems with Graphs
  • Session 29. Mathematical Olympiad III
  • Appendix to Session 6
  • “Convert Decimal to Binary” Blank Table
  • Bibliography
  • Back Cover
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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