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This book presents, in his own words, the life of Hugo Steinhaus (1887–1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who “discovered” the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus’s personal story of the turbulent times he survived – including two world wars and life postwar under the Soviet heel – cannot but be of consumi...
Numerous photographs and diagrams explain mathematical phenomena in series of thought-provoking expositions. From simple puzzles to more advanced problems, topics include psychology of lottery players, new and larger prime numbers, and more. 391 illustrations.
Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.
Both a challenge to mathematically inclined readers and a useful supplementary text for high school and college courses, One Hundred Problems in Elementary Mathematics presents an instructive, stimulating collection of problems. Many problems address such matters as numbers, equations, inequalities, points, polygons, circles, ellipses, space, polyhedra, and spheres. An equal number deal with more amusing or more practical subjects, such as a picnic ham, blood groups, rooks on a chessboard, and the doings of the ingenious Dr. Abracadabrus. Are the problems in this book really elementary? Perhaps not in the lay reader’s sense, for anyone who desires to solve these problems must know a fair amount of mathematics, up to calculus. Nevertheless, Professor Steinhaus has given complete, detailed solutions to every one of his 100 problems, and anyone who works through the solutions will painlessly learn an astonishing amount of mathematics. A final chapter provides a true test for the most proficient readers: 13 additional unsolved problems, including some for which the author himself does not know the solutions.
100 problems—with instructive solutions—on numbers, equations, polygons, polyhedra, and many other topics. Very challenging. Additional 13 problems without solutions.
This book covers 250 milestones in mathematical history, beginning millions of years ago with ancient "ant odometers" and moving through time to our modern-day quest for new dimensions.
Within the last ten years, the interest of historians and philosophers of science in the epistemological writings of the Polish medical microbiologist Ludwik Fleck (1896-1961), who had up to then been almost completely unknown, has advanced with great strides. His main writings on epistemological questions were published in the mid-1930's, but they remained almost unnoticed. Today, however, one may rightly call Fleck a 'classical' figure both of episte mology and of the historical sociology of science, one whose works are comparable with Popper's Logic of Scientific Discovery or Merton's pioneer ing study of the relations among economics, Puritanism, and natural science, both also originally published in the mid-1930's. The story of this book of 'materials on Ludwik Fleck' is also the story of the reception of Ludwik Fleck. In this volume, some essential materials which have been produced by that reception have been gathered together. We will sketch both the reception and the materials.
Courage and Fear is a study of a multicultural city in times when all norms collapse. Ola Hnatiuk presents a meticulously documented portrait of Lviv’s ethnically diverse intelligentsia during World War Two. As the Soviet, Nazi, and once again Soviet occupations tear the city’s social fabric apart, groups of Polish, Ukrainian, and Jewish doctors, academics, and artists try to survive, struggling to manage complex relationships and to uphold their ethos. As their pre-war lives are violently upended, courage and fear shape their actions. Ola Hnatiuk employs diverse sources in several languages to tell the story of Lviv from a multi-ethnic perspective and to challenge the national narratives dominant in Central and Eastern Europe.
Join math detective in solving nearly 40 puzzles inspired by methods in computer science and mathematics. The Tower of Lego, Odd Doors Problem, Spies and Double Agents, many more. Solutions.