In two decades, the Colorado Springs Mathematics Olympiad has become an annual state-wide competition. This book tells the history of the competition as well as an outline of all the problems and solutions that have been a part of the contest over the years.
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 Washingtonp/ppiAfter 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. /ii/i/p—Peter D. Johnson, Jr., Auburn Universitysup/sup/ppiLike 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./ii/i/pp— Cecil Rousseau Chair, USA Mathematical Olympiad Committee/ppiA delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved./ii/i/pp—Paul Erdős/ppiThe 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./i/p —Martin Gardner
This book gathers the best presentations from the Topic Study Group 30: Mathematics Competitions at ICME-13 in Hamburg, and some from related groups, focusing on the field of working with gifted students. Each of the chapters includes not only original ideas, but also original mathematical problems and their solutions. The book is a valuable resource for researchers in mathematics education, secondary and college mathematics teachers around the globe as well as their gifted students.
Fascinating Mathematical People is a collection of informal interviews and memoirs of sixteen prominent members of the mathematical community of the twentieth century, many still active. The candid portraits collected here demonstrate that while these men and women vary widely in terms of their backgrounds, life stories, and worldviews, they all share a deep and abiding sense of wonder about mathematics. Featured here--in their own words--are major research mathematicians whose cutting-edge discoveries have advanced the frontiers of the field, such as Lars Ahlfors, Mary Cartwright, Dusa McDuff, and Atle Selberg. Others are leading mathematicians who have also been highly influential as teachers and mentors, like Tom Apostol and Jean Taylor. Fern Hunt describes what it was like to be among the first black women to earn a PhD in mathematics. Harold Bacon made trips to Alcatraz to help a prisoner learn calculus. Thomas Banchoff, who first became interested in the fourth dimension while reading a Captain Marvel comic, relates his fascinating friendship with Salvador Dalí and their shared passion for art, mathematics, and the profound connection between the two. Other mathematical people found here are Leon Bankoff, who was also a Beverly Hills dentist; Arthur Benjamin, a part-time professional magician; and Joseph Gallian, a legendary mentor of future mathematicians, but also a world-renowned expert on the Beatles. This beautifully illustrated collection includes many photographs never before published, concise introductions by the editors to each person, and a foreword by Philip J. Davis. Some images inside the book are unavailable due to digital copyright restrictions.
Bartel Leendert van der Waerden made major contributions to algebraic geometry, abstract algebra, quantum mechanics, and other fields. He liberally published on the history of mathematics. His 2-volume work Modern Algebra is one of the most influential and popular mathematical books ever written. It is therefore surprising that no monograph has been dedicated to his life and work. Van der Waerden’s record is complex. In attempting to understand his life, the author assembled thousands of documents from numerous archives in Germany, the Netherlands, Switzerland and the United States which revealed fascinating and often surprising new information about van der Waerden. Soifer traces Van der Waerden’s early years in a family of great Dutch public servants, his life as professor in Leipzig during the entire Nazi period, and his personal and professional friendship with one of the great physicists Werner Heisenberg. We encounter heroes and villains and a much more numerous group in between these two extremes. One of them is the subject of this book. Soifer’s journey through a long list of archives, combined with an intensive correspondence, had uncovered numerous details of Van der Waerden’s German intermezzo that raised serious questions and reproaches. Dirk van Dalen (Philosophy, Utrecht University) Professor Soifer’s book implicates the anthropologists’ and culture historians’ core interest in the evolution of culture and in the progress of human evolution itself on this small contested planet. James W. Fernandez (Anthropology, University of Chicago) The book is fascinating. Professor Soifer has done a great service to the discipline of history, as well as deepening our understanding of the 20th century. Peter D. Johnson, Jr. (Mathematics, Auburn University) This book is an important contribution to the history of the twentieth century, and reads like a novel with an ever-fascinating cast of characters. Harold W. Kuhn (Mathematics, Princeton University) This is a most impressive and important book. It is written in an engaging, very personal style and challenges the reader’s ability of moral and historical judgment. While it is not always written in the style of ‘objective’ professional historiography, it satisfies very high standards of scholarly documentation. Indeed the book contains a wealth of source material that allows the reader to form a highly detailed picture of the events and personalities discussed in the book. As an exemplar of historical writing in a broader sense it can compete with any other historical book. Moritz Epple (History of Mathematics, Frankfurt University)
Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.
This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
This book contains the problems and solutions of a famous Hungarian mathematics competition for high school students, from 1929 to 1943. The competition is the oldest in the world, and started in 1894. Two earlier volumes in this series contain the papers up to 1928, and further volumes are planned. The current edition adds a lot of background material which is helpful for solving the problems therein and beyond. Multiple solutions to each problem are exhibited, often with discussions of necessary background material or further remarks. This feature will increase the appeal of the book to experienced mathematicians as well as the beginners for whom it is primarily intended.
Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s problems—problems that previously seemed hopeless.The book provides supplementary reading materials to students at various levels interested in pursuing mathematics, especially in algebra, geometry, or combinatorial geometry.
This Thematic Study is a joint venture between ICOMOS, the advisory body to UNESCO on cultural sites, and the International Astronomical Union. It presents an overall vision on astronomical heritage, attempts to identify what constitutes "outstanding universal significance to humankind" in relation to astronomy, and identifies broad issues that could arise in the assessment of cultural properties relating to astronomy. This is the first Thematic Study in any field of science heritage. It is elaborated using examples of properties from around the world, including some already on the World Heritage List or national Tentative Lists. The subject matter ranges from early prehistory to modern astrophysics and space heritage, and also prominently includes dark sky issues and modern observatory sites. An e-version of the Thematic Study was published in June 2010 in time to be presented to the 2010 meeting of UNESCO's World Heritage Committee, where it was duly approved. It has been circulated officially by the WHC to all of UNESCO's National Commissions. This full-colour paperback edition with some updates, and reformatted to new ICOMOS standards, was published in 2011 and is now offered for public sale.
This second edition of Alexander Soifer’s How Does One Cut a Triangle? demonstrates how different areas of mathematics can be juxtaposed in the solution of a given problem. The author employs geometry, algebra, trigonometry, linear algebra, and rings to develop a miniature model of mathematical research.
This book is the outcome of the work of contributors who participated in the wo- shop “Mapping Different Geographies (MDG)” in February 2010, held in Puchberg am Schneeberg, Austria. This meeting brought together cartographers, artists and geoscientists who research and practice in applications that focus on enhancing o- to-one communication or develop and evaluate methodologies that provide inno- tive methods for sharing information. The main intention of the workshop was to investigate how ‘different’ geographies are being mapped and the possibilities for developing new theories and techniques for information design and transfer based on place or location. So as to communicate these concepts it was important to appreciate the many contrasting meanings of ‘mapping’ that were held by workshop participants. Also, the many (and varied) viewpoints of what different geographies are, were ela- rated upon and discussed. Therefore, as the focus on space and time was embedded within everyone’s felds of investigation, this was addressed during the workshop. This resulted in very engaging discourse, which, in some cases, exposed the restrictions that certain approaches need to consider. For participants, this proved to be most useful, as this allowed them to appreciate the limits and restrictions of their own approach to understanding and representing different geographies. As well, the workshop also was most helpful as a vehicle for demonstrating the common ground of interest held by the very diverse areas of endeavour that the workshop participants work within.
The last decade has seen a steady increase in the application of concepts from noncooperative game theory to such diverse fields as economics, political science, law, operations research, biology and social psychology. As a byproduct of this increased activity, there has been a growing awareness of the fact that the basic noncooperative solution concept, that of Nash equilibrium, suffers from severe drawbacks. The two main shortcomings of this concept are the following: (i) In extensive form games, a Nash strategy may prescribe off the equilibrium path behavior that is manifestly irrational. (Specifically, Nash equilibria may involve incredible threats), (ii) Nash equilibria need not be robust with respect to small perturbations in the data of the game. Confronted with the growing evidence to the detriment of the Nash concept, game theorists were prompted to search for more refined equilibrium notions with better properties and they have come up with a wide array of alternative solution concepts. This book surveys the most important refinements that have been introduced. Its objectives are fourfold (i) to illustrate desirable properties as well as drawbacks of the various equilibrium notions by means of simple specific examples, (ii) to study the relationships between the various refinements, (iii) to derive simplifying characterizations, and (iv) to discuss the plausibility of the assumptions underlying the concepts.
Whether it's childhood make-believe, the theater, sports, or even market speculation, play is one of humanity's seemingly purest activities: a form of entertainment and leisure and a chance to explore the world and its possibilities in an imagined environment or construct. But as Roberte Hamayon shows in this book, play has implications that go even further than that. Exploring play's many dimensions, she offers an insightful look at why play has become so ubiquitous across human cultures. Hamayon begins by zeroing in on Mongolia and Siberia, where communities host national holiday games similar to the Olympics. Within these events Hamayon explores the performance of ethical values and local identity, and then she draws her analysis into larger ideas examinations of the spectrum of play activities as they can exist in any culture. She explores facets of play such as learning, interaction, emotion, strategy, luck, and belief, and she emphasizes the crucial ambiguity between fiction and reality that is at the heart of play as a phenomenon. Revealing how consistent and coherent play is, she ultimately shows it as a unique modality of action that serves an invaluable role in the human experience.
For the past twenty-five years John Moore has taught biology instructors how to teach biology--by emphasizing the questions people have asked about life through the ages and the ways natural philosophers and scientists have sought the answers. This book makes Moore's uncommon wisdom available to students in a lively and richly illustrated account of the history and workings of life. Employing a breadth of rhetoric strategies--including vividly written case histories, hypotheses and deductions, and chronological narrative--Science as a Way of Knowing provides not only a cultural history of biology but also a splendid introduction to the procedures and values of science.
Just one hundred and ten miles south of the Texas-Louisiana border, beneath the waters of the Gulf of Mexico, lie two coral reefs, together called the Flower Garden Banks. This coral community, the northernmost reef system in the United States and a national marine sanctuary, is home to hundreds of kinds of fish and other tropical sea life. Manta rays and turtles visit regularly, as do whale sharks and schools of hammerhead sharks. Other wonders include the annual mass coral spawns and a briny depression called Gollum Lake. Nearby are two other reefs. Stetson Bank, its top spotted with hard corals, mollusks, and sponges, is known for its diversity--from black sea hares to golden smooth trunkfish. At Geyer Bank, thousands of butterfly fish dominate a huge population of tropical fish whose density rivals that of the coral reefs in the South Pacific. Protruding from the flat, muddy continental shelf, these and thirty other natural reefs support an exceptional amount and variety of sea life in Texas waters. They sit amid hundreds of oil and gas platforms, which create their own special reef ecosystems. These reefs, equal in their profusion of life and color to the storied reefs of Florida and Hawaii, have not been widely known to Texans outside of a small group of scientists and divers. With extraordinary photographs and a knowledgeable first-person narrative, author Jesse Cancelmo instills an appreciation for the beauty and fragility of one of the state's least-known natural environments. Texas Coral Reefs will inspire adventurers--both the underwater and armchair varieties--to enjoy these spectacular but little-known sites that lie so close to home.