Alexander Soifer - Böcker

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this new second edition, "Mathematics as Problem Solving". Each new chapter builds off the previous one, enhancing the reader to reach new levels of using logic to solve problems. Every topic is presented in self-contained chapters, offering classical solutions as well as Soifer's own discoveries that he found through his problem-solving experiences. With roughly 200 different problems and multiple proofs for each, the reader is challenged to approach problems from different angles, and in this way can experience the beauty of mathematics. Review from the first edition: "Retelling the best solutions and sharing the secrets of discovery are part of the process of teaching problem solving. Ideally, this process is characterized by mathematical skill, good taste, and wit. It is a characteristically personal process and the best such teachers have surely left their personal marks on students and readers.Alexander Soifer is a teacher of problem solving and his book, "Mathematics as Problem Solving", is designed to introduce problem solving to the next generation".The American Mathematical Monthly Originally self-published by Alexander Soifer, 1987 at the Center for Excellence in Mathematical Education, Colorado Springs, CO.

This second edition, "How Does One Cut a Triangle?", shows how different areas of mathematics can be intertwined to solve a given problem. Soifer brings together geometry, algebra, trigonometry, linear algebra, and rings in a juxtaposition of different mathematical areas that enables mathematics to come alive. In the process the reader is given a taste of what mathematics can do and how mathematicians go about their research. "How Does One Cut a Triangle?" contains many analytical proofs and counterexamples such as a pool table problem, fifty-dollar problem, five-point problem, and joint problem. By proving these additional examples, Soifer proves that research is a collection of mathematical ideas that have been developed throughout the course of history. Review of the first edition: "It is impossible to convey the spirit of the book by merely listing the problems considered or even a number of solutions. The manner of presentation and the gentle guidance toward a solution and hence to generalizations and new problems takes this elementary treatise out of the prosaic and into the stimulating realm of mathematical creativity.Not only young talented people but dedicated secondary teachers and even a few mathematical sophisticates will find this reading both pleasant and profitable." The Mathematical Reviews Originally self-published by Alexander Soifer, 1990 at the Center for Excellence in Mathematical Education, Colorado Springs, CO.

A mathematician, like a painter or a poet, is a maker of patterns. A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.

Over the past two decades, the once small local Colorado Springs Mathematics Olympiad, founded by the author himself, has now become an annual state-wide competition, hosting over one-thousand high school contenders each year. This updated printing of the first edition of Colorado Mathematical Olympiad: the First Twenty Years and Further Explorations offers an interesting 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. Many of the essay problems were inspired by Russian mathematical folklore and written to suit the young audience; for example, the 1989 Sugar problem was written as a pleasant Lewis Carroll-like story. Some other entertaining problems involve old Victorian map colorings, King Arthur and the knights of the round table, rooks in space, Santa Claus and his elves painting planes, football for 23, and even the Colorado Springs subway system.The book is more than just problems, their solutions, and event statistics; it tells a compelling story involving the lives of those who have been part of the Olympiad from every perspective.

Ramsey theory is a relatively “new,” approximately 100 year-old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics, number theory, geometry, ergodic theory, topology, combinatorial geometry, set theory, and measure theory. Ramsey theory possesses its own unifying ideas, and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory can be formulated as: any finite coloring of a large enough system contains a monochromatic subsystem of higher degree of organization than the system itself, or as T.S. Motzkin famously put it, absolute disorder is impossible.Ramsey Theory: Yesterday, Today, and Tomorrow explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.

The New Mathematical Coloring Book (TNMCB) includes striking results of the past 15-year renaissance that produced new approaches, advances, and solutions to problems from the first edition. A large part of the new edition “Ask what your computer can do for you,” presents the recent breakthrough by Aubrey de Grey and works by Marijn Heule, Jaan Parts, Geoffrey Exoo, and Dan Ismailescu. TNMCB introduces new open problems and conjectures that will pave the way to the future keeping the book in the center of the field. TNMCB presents mathematics of coloring as an evolution of ideas, with biographies of their creators and historical setting of the world around them, and the world around us.A new thing in the world at the time, TMCB I is now joined by a colossal sibling containing more than twice as much of what only Alexander Soifer can deliver: an interweaving of mathematics with history and biography, well-seasoned with controversy and opinion. –Peter D. Johnson, Jr.Auburn UniversityLike TMCB I, TMCB II is a unique combination of Mathematics, History, and Biography written by a skilled journalist who has been intimately involved with the story for the last half-century.  …The nature of the subject makes much of the material accessible to students, but also of interest to working Mathematicians. … In addition to learning some wonderful Mathematics, students will learn to appreciate the influences of Paul Erdős, Ron Graham, and others.–Geoffrey ExooIndiana State UniversityThe beautiful and unique Mathematical coloring book of Alexander Soifer is another case of “good mathematics”, containing a lot of similar examples (it is not by chance that Szemerédi’s Theorem story is included as well) and presenting mathematics as both a science and an art…–Peter MihókMathematical Reviews, MathSciNetA postman came to the door with a copy of the masterpiece of the century.  I thank you and the mathematics community should thank you for years to come.  You have set a standard for writing about mathematics and mathematicians that will be hard to match.– Harold W. KuhnPrinceton UniversityI have never encountered a book of this kind.  The best description of it I can give is that it is a mystery novel… I found it hard to stop reading before I finished (in two days) the whole text. Soifer engages the reader's attention not only mathematically, but emotionally and esthetically.  May you enjoy the book as much as I did!– Branko GrünbaumUniversity of WashingtonI am in absolute awe of your 2008 book.–Aubrey D.N.J. de GreyLEV Foundation

The New Mathematical Coloring Book (TNMCB) includes striking results of the past 15-year renaissance that produced new approaches, advances, and solutions to problems from the first edition. A large part of the new edition “Ask what your computer can do for you,” presents the recent breakthrough by Aubrey de Grey and works by Marijn Heule, Jaan Parts, Geoffrey Exoo, and Dan Ismailescu. TNMCB introduces new open problems and conjectures that will pave the way to the future keeping the book in the center of the field. TNMCB presents mathematics of coloring as an evolution of ideas, with biographies of their creators and historical setting of the world around them, and the world around us.A new thing in the world at the time, TMCB I is now joined by a colossal sibling containing more than twice as much of what only Alexander Soifer can deliver: an interweaving of mathematics with history and biography, well-seasoned with controversy and opinion. –Peter D. Johnson, Jr.Auburn UniversityLike TMCB I, TMCB II is a unique combination of Mathematics, History, and Biography written by a skilled journalist who has been intimately involved with the story for the last half-century.  …The nature of the subject makes much of the material accessible to students, but also of interest to working Mathematicians. … In addition to learning some wonderful Mathematics, students will learn to appreciate the influences of Paul Erdős, Ron Graham, and others.–Geoffrey ExooIndiana State UniversityThe beautiful and unique Mathematical coloring book of Alexander Soifer is another case of “good mathematics”, containing a lot of similar examples (it is not by chance that Szemerédi’s Theorem story is included as well) and presenting mathematics as both a science and an art…–Peter MihókMathematical Reviews, MathSciNetA postman came to the door with a copy of the masterpiece of the century.  I thank you and the mathematics community should thank you for years to come.  You have set a standard for writing about mathematics and mathematicians that will be hard to match.– Harold W. KuhnPrinceton UniversityI have never encountered a book of this kind.  The best description of it I can give is that it is a mystery novel… I found it hard to stop reading before I finished (in two days) the whole text. Soifer engages the reader's attention not only mathematically, but emotionally and esthetically.  May you enjoy the book as much as I did!– Branko GrünbaumUniversity of WashingtonI am in absolute awe of your 2008 book.–Aubrey D.N.J. de GreyLEV Foundation

In fact, the prototype of such problems is the following: If each point of the plane is to be given a color, how many colors do we need if every two points at unit distance are to receive distinct colors?

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.

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.

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.