The Colorado Mathematical Olympiad: The Third Decade and Further Explorations

1. Front Matter

   Pages i-lii

   PDF

2. The Third Decade

   1. Front Matter

      Pages 1-1

      PDF

   2. Twenty-First Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 3-25

   3. Twenty-Second Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 27-42

   4. Twenty-Third Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 43-58

   5. Twenty-Fourth Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 59-69

   6. Twenty-Fifth Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 71-83

   7. Twenty-Sixth Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 85-95

   8. Twenty-Seventh Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 97-110

   9. Twenty-Eighth Colorado Mathematical Olympiad

      • Alexander Soifer

      Pages 111-121

   10. Twenty-Ninth Colorado Mathematical Olympiad

       • Alexander Soifer

       Pages 123-134

   11. Thirtieth Colorado Mathematical Olympiad

       • Alexander Soifer

       Pages 135-152

   12. A Round Table Discussion of the Olympiad, or Looking Back from a 30-Year Perspective

       • Alexander Soifer

       Pages 153-165

3. Further Explorations of the Third Decade

   1. Front Matter

      Pages 167-167

      PDF

   2. Introduction to Part II

      • Alexander Soifer

      Pages 169-169

   3. E21. Cover-Up with John Conway, Mitya Karabash, and Ron Graham

      • Alexander Soifer

      Pages 171-182

   4. E22. Deep Roots of Uniqueness

      • Alexander Soifer

      Pages 183-184

   5. E23: More about Love and Death

      • Alexander Soifer

      Pages 185-188

   6. E24: One Amazing Problem and Its Connections to Everything—A Conversation in Three Movements

      • Alexander Soifer

      Pages 189-198

   7. E25: The Story of One Old Erdős Problem

      • Alexander Soifer

      Pages 199-201

 

Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year. This book presents a year-by-year history of the CMO from 2004–2013 with all the problems from the competitions and their solutions. Additionally, the book includes 10 further explorations, bridges from solved Olympiad problems to ‘real’ mathematics, bringing young readers to the forefront of various fields of mathematics. This book contains more than just problems, solutions, and event statistics — it tells a compelling story involving the lives of those who have been part of the Olympiad, their reminiscences of the past and successes of the present.

I am almost speechless facing the ingenuity and inventiveness demonstrated in the problems proposed in the third decade of these Olympics. However, equally impressive is the drive and persistence of the originator and living soul of them. It is hard for me to imagine the enthusiasm and commitment needed to work singlehandedly on such an endeavor over several decades.

<—Branko Grünbaum, University of Washington

After decades of hunting for Olympiad problems, and struggling to create Olympiad problems, he has become an extraordinary connoisseur and creator of Olympiad problems.  The Olympiad problems were very good, from the beginning, but in the third decade the problems have become extraordinarily good.  Every brace of 5 problems is a work of art.  The harder individual problems range in quality from brilliant to work-of-genius… The same goes for the “Further Explorations” part of the book.  Great mathematics and mathematical questions are immersed in a sauce of fascinating anecdote and reminiscence.  If you could have only one book to enjoy while stranded on a desert island, this would be a good choice.  

Like Gauss, Alexander Soifer would not hesitate to inject Eureka! at the right moment. Like van der Waerden, he can transform a dispassionate exercise in logic into a compelling account of sudden insights and ultimate triumph.

— Cecil Rousseau Chair, USA Mathematical Olympiad Committee

A delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved.

—Paul Erdős

The book is a gold mine of brilliant reasoning with special emphasis on the power and beauty of coloring proofs. Strongly recommended to both serious and recreational mathematicians on all levels of expertise.

—Martin Gardner

• Advanced high school mathematics
• Colorado Olympiad
• Mathematical Olympiad
• Olympiad problems
• Erdös problem
• Schur theorem
• Algebra
• Colored Plane
• problem solving
• high school

“The book under review presents a year-by-year history of the Colorado Mathematical Olympiad from 2004 to 2013 with all the problems from the competitions and their solutions. … this book offers a great treasure of interesting problems, potential avenues of exploration and research for students, and new insights into solving elementary problems. No library will want to be without a copy, nor will anyone involved in mathematics competitions at this level.” (Teodora-Liliana Rădulescu, zbMATH 1371.97003, 2017)

• College of Letters, Arts, and Sciences, University of Colorado at Colorado Springs, Colorado Springs, USA

  Alexander Soifer

Alexander Soifer is Professor of Mathematics, art, and film history at the University of Colorado, Colorado Springs. Dr. Soifer has authored several books with Springer/Birkhäuser including The Colorado Mathematical Olympiad and Further Explorations; The Mathematical Coloring Book; The Scholar and the State: In Search of van der Waerden; Geometric Etudes and Combinatorial Mathematics, and more.

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