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Book Synopsis Morse Theory. (AM-51), Volume 51 by : John Milnor
Download or read book Morse Theory. (AM-51), Volume 51 written by John Milnor and published by Princeton University Press. This book was released on 2016-03-02 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.? Milnor has published five books with Princeton University Press.
Book Synopsis Lecture Notes in Microeconomic Theory by : Ariel Rubinstein
Download or read book Lecture Notes in Microeconomic Theory written by Ariel Rubinstein and published by Princeton University Press. This book was released on 2012-03-04 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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/.
Book Synopsis Lectures on Morse Homology by : Augustin Banyaga
Download or read book Lectures on Morse Homology written by Augustin Banyaga and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed presentation of results needed to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. The text presents results that were formerly scattered in the mathematical literature, in a single reference with complete and detailed proofs. The core material includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory.
Book Synopsis Notes On The Theory Of Choice by : David Kreps
Download or read book Notes On The Theory Of Choice written by David Kreps and published by Routledge. This book was released on 2018-05-04 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Professor Kreps presents a first course on the basic models of choice theory that underlie much of economic theory. This course, taught for several years at the Graduate School of Business, Stanford University, gives the student an introduction to the axiomatic method of economic analysis, without placing too heavy a demand on mathematical sophistication.The course begins with the basics of choice and revealed preference theory and then discusses numerical representations of ordinal preference. Models with uncertainty come next: First is von Neumann?Morgenstern utility, and then choice under uncertainty with subjective uncertainty, using the formulation of Anscombe and Aumann, and then sketching the development of Savage's classic theory. Finally, the course delves into a number of special topics, including de Finetti's theorem, modeling choice on a part of a larger problem, dynamic choice, and the empirical evidence against the classic models.
Book Synopsis A Course in Model Theory by : Katrin Tent
Download or read book A Course in Model Theory written by Katrin Tent and published by Cambridge University Press. This book was released on 2012-03-08 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introduction to current topics in model theory, including simple and stable theories.
Book Synopsis Network Information Theory by : Abbas El Gamal
Download or read book Network Information Theory written by Abbas El Gamal and published by Cambridge University Press. This book was released on 2011-12-08 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.
Book Synopsis Lecture Notes on the General Theory of Relativity by : Øyvind Grøn
Download or read book Lecture Notes on the General Theory of Relativity written by Øyvind Grøn and published by Springer Science & Business Media. This book was released on 2009-04-20 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects lectures on the general theory of relativity given by Dr. Øyvind Grøn at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book.
Book Synopsis Lecture Notes on the General Theory of Relativity by : Øyvind Grøn
Download or read book Lecture Notes on the General Theory of Relativity written by Øyvind Grøn and published by Springer Science & Business Media. This book was released on 2010-03-23 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects lectures on the general theory of relativity given by Dr. Øyvind Grøn at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book.
Book Synopsis Basic Bundle Theory and K-Cohomology Invariants by : Dale Husemöller
Download or read book Basic Bundle Theory and K-Cohomology Invariants written by Dale Husemöller and published by Springer. This book was released on 2007-12-10 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. It aims to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, comes from quantum field theory, where topological invariants play an important role.
Book Synopsis A Primer in Density Functional Theory by : Carlos Fiolhais
Download or read book A Primer in Density Functional Theory written by Carlos Fiolhais and published by Springer. This book was released on 2008-01-11 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density functional theory (DFT) is by now a well-established method for tackling the quantum mechanics of many-body systems. Originally applied to compute properties of atoms and simple molecules, DFT has quickly become a work horse for more complex applications in the chemical and materials sciences. The present set of lectures, spanning the whole range from basic principles to relativistic and time-dependent extensions of the theory, is the ideal introduction for graduate students or nonspecialist researchers wishing to familiarize themselves with both the basic and most advanced techniques in this field.
Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Download or read book Continuum Theory written by Sam Nadler and published by CRC Press. This book was released on 2017-07-12 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for either a semester or year course for graduate students of mathematics who have had at least one course in topology. Introduces continuum theory through a combination of classical and modern techniques. Annotation copyright Book News, Inc. Portland, Or.
Book Synopsis Lecture Notes on Field Theory in Condensed Matter Physics by : Christopher Mudry
Download or read book Lecture Notes on Field Theory in Condensed Matter Physics written by Christopher Mudry and published by World Scientific Publishing Company. This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Number Theory and Its Applications by : Cem Y. Yildrim
Download or read book Number Theory and Its Applications written by Cem Y. Yildrim and published by CRC Press. This book was released on 2020-03-06 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey.
Book Synopsis Lecture Notes on Chern-Simons-Witten Theory by : Sen Hu
Download or read book Lecture Notes on Chern-Simons-Witten Theory written by Sen Hu and published by World Scientific. This book was released on 2001 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on lectures on topological quantum field theory given in 1989 at Princeton University by E. Witten, in which he unified several important mathematical works in terms of the Donaldson polynomial, Gromov/Floer homology, and Jones polynomials. Witten explained his three-dimensional construction of Jones polynomials, "an elegant construction of a new polynomial invariant in three-dimensional space" (per the author), via quantization of Chern-Simons gauge theory. Hu (Princeton U.) adds missing details and some new developments in the field. Annotation copyrighted by Book News Inc., Portland, OR.
Book Synopsis Recursion Theory by : Joseph R. Shoenfield
Download or read book Recursion Theory written by Joseph R. Shoenfield and published by CRC Press. This book was released on 2018-04-27 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.
Book Synopsis Statistical Structure of Quantum Theory by : Alexander S. Holevo
Download or read book Statistical Structure of Quantum Theory written by Alexander S. Holevo and published by Springer Science & Business Media. This book was released on 2001-06-20 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.
