Lecture Notes on Graph Theory

Lecture Notes on Graph Theory

Author: Sudev Naduvath

Publisher: Centre for Studies in Discrete Mathematics, Thrissur, India.

Published: 2017-12-08

Total Pages: 177

ISBN-13: 9352911474

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The book is based on the syllabus of Computer Science and Engineering Programme under APJ Abdul Kalam Technological University, Kerala.


Lecture Notes On Field Theory In Condensed Matter Physics

Lecture Notes On Field Theory In Condensed Matter Physics

Author: Christopher Mudry

Publisher: World Scientific Publishing Company

Published: 2014-02-28

Total Pages: 745

ISBN-13: 9814449121

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The aim of this book is to introduce a graduate student to selected concepts in condensed matter physics for which the language of field theory is ideally suited. The examples considered in this book are those of superfluidity for weakly interacting bosons, collinear magnetism, and superconductivity. Quantum phase transitions are also treated in the context of quantum dissipative junctions and interacting fermions constrained to one-dimensional position space. The style of presentation is sufficiently detailed and comprehensive that it only presumes familiarity with undergraduate physics.


Lecture Notes on Motivic Cohomology

Lecture Notes on Motivic Cohomology

Author: Carlo Mazza

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 240

ISBN-13: 9780821838471

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The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).


Noncommutative Geometry

Noncommutative Geometry

Author: Alain Connes

Publisher: Springer

Published: 2003-12-15

Total Pages: 364

ISBN-13: 3540397027

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Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.


Lecture Notes in Microeconomic Theory

Lecture Notes in Microeconomic Theory

Author: Ariel Rubinstein

Publisher: Princeton University Press

Published: 2012-03-04

Total Pages: 167

ISBN-13: 1400842468

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Ariel Rubinstein's well-known lecture notes on microeconomics—now fully revised and expanded This book presents Ariel Rubinstein's lecture notes for the first part of his well-known graduate course in microeconomics. Developed during the fifteen years that Rubinstein taught the course at Tel Aviv University, Princeton University, and New York University, these notes provide a critical assessment of models of rational economic agents, and are an invaluable supplement to any primary textbook in microeconomic theory. In this fully revised and expanded second edition, Rubinstein retains the striking originality and deep simplicity that characterize his famously engaging style of teaching. He presents these lecture notes with a precision that gets to the core of the material, and he places special emphasis on the interpretation of key concepts. Rubinstein brings this concise book thoroughly up to date, covering topics like modern choice theory and including dozens of original new problems. Written by one of the world's most respected and provocative economic theorists, this second edition of Lecture Notes in Microeconomic Theory is essential reading for students, teachers, and research economists. Fully revised, expanded, and updated Retains the engaging style and method of Rubinstein's well-known lectures Covers topics like modern choice theory Features numerous original new problems—including 21 new review problems Solutions manual (available only to teachers) can be found at: http://gametheory.tau.ac.il/microTheory/.


Theoretical Foundations of Programming Methodology

Theoretical Foundations of Programming Methodology

Author: M. Broy

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 655

ISBN-13: 9400978936

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Papers presented at the Marktoberdorf Summer School on Theoretical Foundations of Programming Methodology, organized under the auspices of the Technical University Münich and sponsored by the NATO Scientific Affairs Division, Germany, 1981


The Limits of Inference without Theory

The Limits of Inference without Theory

Author: Kenneth I. Wolpin

Publisher: MIT Press

Published: 2013-04-26

Total Pages: 197

ISBN-13: 0262019086

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The role of theory in ex ante policy evaluations and the limits that eschewing theory places on inference In this rigorous and well-crafted work, Kenneth Wolpin examines the role of theory in inferential empirical work in economics and the social sciences in general—that is, any research that uses raw data to go beyond the mere statement of fact or the tabulation of statistics. He considers in particular the limits that eschewing the use of theory places on inference. Wolpin finds that the absence of theory in inferential work that addresses microeconomic issues is pervasive. That theory is unnecessary for inference is exemplified by the expression “let the data speak for themselves.” This approach is often called “reduced form.” A more nuanced view is based on the use of experiments or quasi-experiments to draw inferences. Atheoretical approaches stand in contrast to what is known as the structuralist approach, which requires that a researcher specify an explicit model of economic behavior—that is, a theory. Wolpin offers a rigorous examination of both structuralist and nonstructuralist approaches. He first considers ex ante policy evaluation, highlighting the role of theory in the implementation of parametric and nonparametric estimation strategies. He illustrates these strategies with two examples, a wage tax and a school attendance subsidy, and summarizes the results from applications. He then presents a number of examples that illustrate the limits of inference without theory: the effect of unemployment benefits on unemployment duration; the effect of public welfare on women's labor market and demographic outcomes; the effect of school attainment on earnings; and a famous field experiment in education dealing with class size. Placing each example within the context of the broader literature, he contrasts them to recent work that relies on theory for inference.