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The Colorado Mathematical Olympiad and Further Explorations


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Table of Contents

Preface.- Olympiad History: What it is and How it Started.- Three Celebrated Ideas.- Year 1.- Year 2.- Year 3.- Year 4.- Year 5.- Year 6.- Year 7.- Year 8.- Year 9.- Year 10.- Further Explorations.- Rooks in Space.- Chromatic Number of the Plane.- Polygons in a Colored Circle, Polyhedra in a colored Sphere.- How Does one Cut a Triangle?.- Points in Convex Figures.- Triangles in a Colored Plane.- Rectangles in a Colored Plane.- Colored Polygons.- Infinite-Finite.- Schur Theorem.- Bibliography.- Year 11.- Year 12.- Year 13.- Year 14.- Year 15.- Year 16.- Year 17.- Year 18.- Year 19.- Year 20.- Further Explorations.- Chromatic Number of a Grid.- Stone Age Entertainment.- The Erdoes Problem.- Squares in a Square.- Washington Recangles.- Olde Victorian Map Colouring.- More Stone Age Entertainment.- The 1-10-100 Problem.- King Arthur and the Knights of the Round Table.- A Map Coloring "Game".- Bibliography.

About the Author

Alexander Soifer has published around 100 articles and four other books entitled, Mathematics as Problem-Solving, 2/e How Does one Cut a Triangle? 2/e Mathematical Coloring Book, and Geometric Etudes in Combinatorial Mathematics. The 2nd ed. of Mathematical Coloring Book (forthcoming with Spenser). We are publishing 2nd ed. of the other three books. Soifer is renowned for creating significant problems and conjectures, and this book could be helpful to others thinking about organizing an olympiad. Soifer is at Princeton and Colorado. Author confirms sales of 3000 copies of all three books listed above, (excluding Mathematical Coloring Book) all self-sold by author. These three books are out of stock.


"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 " ... this book is not so much mathematical literature as it is literature built around mathematics... with the Further Explorations sections, anyone so inclined could spend a lifetime on the mathematics sprouting from this volume." -Peter D. Johnson, Jr., Auburn University "I finished reading the book in one sitting - I just could not put it down. Professor Soifer has indebted us all by first making the effort to organize the Colorado Mathematical Olympiads, and then making the additional effort to tell us about it in such an engaging and useful way." -Branko Grunbaum, University of Washington "A delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved." -Paul Erdos "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

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