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Lectures on Polytopes
Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
"Gina Says": Adventures In The Blogosphere String War
In the summer of 2006 two books attacking string theory, a prominent theory in physics, appeared: Peter Woit's 'Not Even Wrong' and Lee Smolin's 'The Trouble with Physics'. A fierce public debate, much of it on weblogs, ensued.Gina is very curious about science blogs. Can they be useful for learning about or discussing science? What happens in these blogs and who participates in them? Gina is eager to learn the issues and to form her own opinion about the string theory controversy. She is equipped with some academic background, including in mathematics, and has some familiarity with academic life. Her knowledge of physics is derived mainly from popular accounts. Gina likes to debate and to a...
The Trouble with Physics
The Trouble with Physics is a groundbreaking account of the state of modern physics: of how we got from Einstein and Relativity through quantum mechanics to the strange and bizarre predictions of string theory, full of unseen dimensions and multiple universes. Lee Smolin not only provides a brilliant layman’s overview of current research as we attempt to build a ‘theory of everything’, but also questions many of the assumptions that lie behind string theory. In doing so, he describes some of the daring, outlandish ideas that will propel research in years to come.
Analysis of Boolean Functions
This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.
Building Bridges II
This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of László Lovász. The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization. László Lovász is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, “building bridges” between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to László Lovász's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.
Selected Works of Oded Schramm
This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.
Convex Geometric Analysis
Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.
Mathematics without Apologies
An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma a...
Normal Rationality
Normal Rationality is a selection of the most important work of Edna Ullmann-Margalit, presenting some influential and widely admired essays alongside some that are not well known. She was an unorthodox and deeply original philosopher whose work illuminated the largest mysteries of human life. Much of her writing focuses on two fundamental questions. (1) How do people proceed when they cannot act on the basis of reasons, or project likely consequences? (2) How is social order possible? Ullmann-Margalit's answers, emphasizing what might be called biased rationality, are important not only for philosophy, but also for political science, psychology, sociology, cognitive science, economics (incl...
Proofs from THE BOOK
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
