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Lectures On Algebraic Topology
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
How the World Changed Social Media
How the World Changed Social Media is the first book in Why We Post, a book series that investigates the findings of anthropologists who each spent 15 months living in communities across the world. This book offers a comparative analysis summarising the results of the research and explores the impact of social media on politics and gender, education and commerce. What is the result of the increased emphasis on visual communication? Are we becoming more individual or more social? Why is public social media so conservative? Why does equality online fail to shift inequality offline? How did memes become the moral police of the internet? Supported by an introduction to the project’s academic framework and theoretical terms that help to account for the findings, the book argues that the only way to appreciate and understand something as intimate and ubiquitous as social media is to be immersed in the lives of the people who post. Only then can we discover how people all around the world have already transformed social media in such unexpected ways and assess the consequences
Handbook of Homotopy Theory
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
Algebraic Topology
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Algebraic Topology
During the Winter and spring of 1985 a Workshop in Algebraic Topology was held at the University of Washington. The course notes by Emmanuel Dror Farjoun and by Frederick R. Cohen contained in this volume are carefully written graduate level expositions of certain aspects of equivariant homotopy theory and classical homotopy theory, respectively. M.E. Mahowald has included some of the material from his further papers, represent a wide range of contemporary homotopy theory: the Kervaire invariant, stable splitting theorems, computer calculation of unstable homotopy groups, and studies of L(n), Im J, and the symmetric groups.
Function Estimates
This volume collects together papers presented at the 1985 Conference in Function Estimation held at Humboldt State University. The papers focus especially on various types of spline estimations and convolution problems. The use of estimation and approximation methods as applied to geophysics, numerical analysis, and nonparametric statistics was a special feature of this conference.
Topological Modular Forms
The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on ellip...
Fundamentals of Linear Control
The must-have textbook introducing the analysis and design of feedback control systems in less than 400 pages.
On Thom Spectra, Orientability, and Cobordism
Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.
The Ancient Guide to Modern Life
It's time for us to re-examine the past. Our lives are infinitely richer if we take the time to look at what the Greeks and Romans have given us in politics and law, religion and philosophy and education, and to learn how people really lived in Athens, Rome, Sparta and Alexandria. This is a book with a serious point to make but the author isn't simply a classicist but a comedian and broadcaster who has made television and radio documentaries about humour, education and Dorothy Parker. This is a book for us all. Whether political, cultural or social, there are endless parallels between the ancient and modern worlds. Whether it's the murder of Caesar or the political assassination of Thatcher; the narrative arc of the hit HBO series The Wire or that of Oedipus; the popular enthusiasm for the Emperor Titus or President Obama - over and over again we can be seen to be living very much like people did 2,000 or more years ago.
