Topics In Contemporary Mathematics

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Topics in Contemporary Mathematical Physics

Topics in Contemporary Mathematical Physics Pdf/ePub eBook Author: ,
Editor: World Scientific Publishing Company
ISBN: 981466782X
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Topics in Contemporary Mathematical Physics by , Summary

This new (second) edition contains a general treatment of quantum field theory (QFT) in a simple scalar field setting in addition to the modern material on the applications of differential geometry and topology, group theory, and the theory of linear operators to physics found in the first edition. All these are introduced without assuming more background on the part of the reader than a good foundation in undergraduate (junior) level mathematical physics. The new material entirely focuses on an introduction to quantum field theory, emphasizing the Feynman path (functional integral) approach to QFT and the renormalization group. With respect to the latter, the focus is on an introduction of its application to critical phenomena in statistical physics, following the outgrowth of the Callan–Symanzik equation originally developed in the context of high energy physics, and the seminal contributions of Kenneth Wilson. One of the overriding aims of the new material is also to draw students' attention to the deep connections between high energy physics and statistical mechanics. The unavoidable technical aspects are explained with a minimum of prerequisite material and jargon, and conceptual understanding is always given prominence before mastery of technical details, but the importance of the latter is never underestimated. Derivational details and motivational discussions are provided in abundance in order to ensure continuity of reading, and to avoid trying the readers' patience.

Topics in Contemporary Mathematical Analysis and Applications

Topics in Contemporary Mathematical Analysis and Applications Pdf/ePub eBook Author: Hemen Dutta
Editor: CRC Press
ISBN: 1000204219
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Topics in Contemporary Mathematical Analysis and Applications by Hemen Dutta Summary

Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems This book is written for individual researchers, educators, students, and department libraries.

Topics in Contemporary Mathematical Physics

Topics in Contemporary Mathematical Physics Pdf/ePub eBook Author: Kai S Lam
Editor: World Scientific Publishing Company
ISBN: 9813102306
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Topics in Contemporary Mathematical Physics by Kai S Lam Summary

This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry. The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

Advanced Topics in Mathematical Analysis

Advanced Topics in Mathematical Analysis Pdf/ePub eBook Author: Michael Ruzhansky,Hemen Dutta
Editor: CRC Press
ISBN: 1351142119
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Advanced Topics in Mathematical Analysis by Michael Ruzhansky,Hemen Dutta Summary

Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.

Trends in Contemporary Mathematics

Trends in Contemporary Mathematics Pdf/ePub eBook Author: Vincenzo Ancona,Elisabetta Strickland
Editor: Springer
ISBN: 3319052543
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Trends in Contemporary Mathematics by Vincenzo Ancona,Elisabetta Strickland Summary

The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.

Diverse Topics in Theoretical and Mathematical Physics

Diverse Topics in Theoretical and Mathematical Physics Pdf/ePub eBook Author: Roman Jackiw
Editor: World Scientific
ISBN: 9814502235
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Diverse Topics in Theoretical and Mathematical Physics by Roman Jackiw Summary

In this volume, topics are drawn from field theory, especially gauge field theory, as applied to particle, condensed matter and gravitational physics, and concern a variety of interesting subjects. These include geometricalDtopological effects in quantum theory, fractional charge, time travel, relativistic quantized fields in and out of thermal equilibrium and quantum modifications of symmetry in physical systems. Many readers will find this a useful volume, especially theoretical physicists and mathematicians. The material will be of interest to both the expert who will find well-presented novel and stimulating viewpoints of various subjects and the novice who will find complete, detailed and precise descriptions of important topics of current interest, in theoretical and mathematical physics. Contents:Anomalies and Fractional Charge:Non-Canonical Behavior in Canonical TheoriesQuantum Mechanical Symmetry BreakingDelta Function Potentials in Two- and Three-Dimensional Quantum MechanicsUpdate on Anomalous TheoriesFermion FractionizationThe Chiral AnomalyGauge Theories and Gravity: Yang-Mills Vacuum as a Bloch WaveBifurcation and Stability in Yang-Mills Theory with SourcesTopological Structures in the Standard Model at High TPlanar GravityTime Travel?Gauge Theories for Gravity on a LineSymmetry Behavior:Introducing Scale SymmetryHidden Symmetry of Magnetic Point Monopole and VortexInvariance, Symmetry and Periodicity in Gauge TheoriesSymmetry Restoration at Finite TemperatureMean Field Theory for Non-Equilibrium Quantum FieldsApproaches to Quantum Theories Following Dirac:Canonical Light-Cone Commutators and Their ApplicationsInvariant Quantization, Scale Symmetry and Euclidean Field Theory(Constrained) Quantization Without TearsAnalysis on Infinite-Dimensional Manifolds — Schrödinger Representation for Quantized FieldsSolitons, Instantons and Semi-Classical Quantum Field Theory:Non-Perturbative and Topological Methods in Quantum Field TheorySelf-Dual Chern-Simons Solitions Readership: Theoretical physicists and mathematicians. keywords:Anomalies;Fractional Charge;Yang–Mills Theory;Gauge Theory of Gravity;Symmetry;Light-Cone Commutatorsconstrained;Quantizationsolitons;Instantons;Chern–Simons Theoriy;Gravity-in the Plane;On a Line;Schrodinger Representation for Field Theory “Altogether this collection of articles provide in one place a valuable and very comprehensive source for understanding quantum field theory, and quantum mechanics, which I would recommend not just for libraries but also for penurious PhD students. It deserves to stand next to the well known collection of articles by Sidney Coleman which added greatly to the understanding of a generation of theoretical physicists.” Contemporary Physics

Mathematics++

Mathematics++ Pdf/ePub eBook Author: Ida Kantor, Jiří Matoušek,Robert Šámal
Editor: American Mathematical Soc.
ISBN: 1470422611
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Mathematics++ by Ida Kantor, Jiří Matoušek,Robert Šámal Summary

Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.

Topics in Harmonic Analysis and Ergodic Theory

Topics in Harmonic Analysis and Ergodic Theory Pdf/ePub eBook Author: Joseph Rosenblatt,Alexander M. Stokolos
Editor: American Mathematical Soc.
ISBN: 0821842358
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Topics in Harmonic Analysis and Ergodic Theory by Joseph Rosenblatt,Alexander M. Stokolos Summary

There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory. Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2-4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multi-dimensional trigonometric series, and Bellman and $s$-functions. In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multi-dimensional trigonometric series.

Convex Functions and Their Applications

Convex Functions and Their Applications Pdf/ePub eBook Author: Constantin P. Niculescu,Lars-Erik Persson
Editor: Springer
ISBN: 3319783378
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Convex Functions and Their Applications by Constantin P. Niculescu,Lars-Erik Persson Summary

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Basic Concepts in Modern Mathematics

Basic Concepts in Modern Mathematics Pdf/ePub eBook Author: John Edward Hafstrom
Editor: Courier Corporation
ISBN: 0486316270
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Basic Concepts in Modern Mathematics by John Edward Hafstrom Summary

In-depth overview, geared toward undergraduates of all backgrounds, covers natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. 1961 edition.

Topics In Contemporary Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of The 8th International Workshop On Complex Structures And Vector Fields

Topics In Contemporary Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of The 8th International Workshop On Complex Structures And Vector Fields Pdf/ePub eBook Author: Kouei Sekigawa,Stancho Dimiev
Editor: World Scientific
ISBN: 9814475025
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Topics In Contemporary Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of The 8th International Workshop On Complex Structures And Vector Fields by Kouei Sekigawa,Stancho Dimiev Summary

This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.

Combinatorial and Geometric Group Theory

Combinatorial and Geometric Group Theory Pdf/ePub eBook Author: Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain
Editor: American Mathematical Soc.
ISBN: 0821828223
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Combinatorial and Geometric Group Theory by Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain Summary

This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.

Algebraic and Geometric Methods in Discrete Mathematics

Algebraic and Geometric Methods in Discrete Mathematics Pdf/ePub eBook Author: Heather A. Harrington,Mohamed Omar,Matthew Wright
Editor: American Mathematical Soc.
ISBN: 1470423219
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Algebraic and Geometric Methods in Discrete Mathematics by Heather A. Harrington,Mohamed Omar,Matthew Wright Summary

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.

Topics in Complex Analysis

Topics in Complex Analysis Pdf/ePub eBook Author: Dorothy Brown Shaffer
Editor: American Mathematical Soc.
ISBN: 0821850377
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Topics in Complex Analysis by Dorothy Brown Shaffer Summary

Most of the mathematical ideas presented in this volume are based on papers given at an AMS meeting held at Fairfield University in October 1983. The unifying theme of the talks was Geometric Function Theory. Papers in this volume generally represent extended versions of the talks presented by the authors. In addition, the proceedings contain several papers that could not be given in person. A few of the papers have been expanded to include further research results obtained in the time between the conference and submission of manuscripts. In most cases, an expository section or history of recent research has been added. The authors' new research results are incorporated into this more general framework. The collection represents a survey of research carried out in recent years in a variety of topics. The paper by Y. J. Leung deals with the Loewner equation, classical results on coefficient bodies and modern optimal control theory.Glenn Schober writes about the class $\Sigma$, its support points and extremal configurations. Peter Duren deals with support points for the class $S$, Loewner chains and the process of truncation. A very complete survey about the role of polynomials and their limits in class $S$ is contributed by T. J. Suffridge. A generalization of the univalence criterion due to Nehari and its relation to the hyperbolic metric is contained in the paper by David Minda. The omitted area problem for functions in class $S$ is solved in the paper by Roger Barnard. New results on angular derivatives and domains are represented in the paper by Burton Rodin and Stefan E. Warschawski, while estimates on the radial growth of the derivative of univalent functions are given by Thom MacGregor. In the paper by B. Bshouty and W. Hengartner a conjecture of Bombieri is proved for some cases.Other interesting problems for special subclasses are solved by B. A. Case and J. R. Quine; M. O. Reade, H. Silverman and P. G. Todorov; and, H. Silverman and E. M. Silvia. New univalence criteria for integral transforms are given by Edward Merkes. Potential theoretic results are represented in the paper by Jack Quine with new results on the Star Function and by David Tepper with free boundary problems in the flow around an obstacle. Approximation by functions which are the solutions of more general elliptic equations are treated by A. Dufresnoy, P. M. Gauthier and W. H. Ow. At the time of preparation of these manuscripts, nothing was known about the proof of the Bieberbach conjecture. Many of the authors of this volume and other experts in the field were recently interviewed by the editor regarding the effect of the proof of the conjecture. Their ideas regarding future trends in research in complex analysis are presented in the epilogue by Dorothy Shaffer.A graduate level course in complex analysis provides adequate background for the enjoyment of this book.

Non-commutative Geometry in Mathematics and Physics

Non-commutative Geometry in Mathematics and Physics Pdf/ePub eBook Author: Giuseppe Dito
Editor: American Mathematical Soc.
ISBN: 0821841475
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Non-commutative Geometry in Mathematics and Physics by Giuseppe Dito Summary

This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics. It also contains an article based on the XI Memorial Lectures given by M. Kontsevich, which were delivered as part of the conference. This is an excellent introductory volume for readers interested in learning about quantization as deformation, Hopf algebras, and Hodge structures in the framework of non-commutative algebraic geometry.

Handbook of Research on Field-Based Teacher Education

Handbook of Research on Field-Based Teacher Education Pdf/ePub eBook Author: Hodges, Thomas E.,Baum, Angela C.
Editor: IGI Global
ISBN: 1522562508
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Handbook of Research on Field-Based Teacher Education by Hodges, Thomas E.,Baum, Angela C. Summary

Teacher education is an evolving field with multiple pathways towards teacher certification. Due to an increasing emphasis on the benefits of field-based learning, teachers can now take alternative certification pathways to become teachers. The Handbook of Research on Field-Based Teacher Education is a pivotal reference source that combines field-based components with traditional programs, creating clinical experiences and “on-the-job” learning opportunities to further enrich teacher education. While highlighting topics such as certification design, preparation programs, and residency models, this publication explores theories of teaching and learning through collaborative efforts in pre-Kindergarten through grade 12 settings. This book is ideally designed for teacher education practitioners and researchers invested in the policies and practices of educational design.

Topics in Industrial Mathematics

Topics in Industrial Mathematics Pdf/ePub eBook Author: H Neunzert,Abul Hasan Siddiqi
Editor: Springer Science & Business Media
ISBN: 1475732228
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Topics in Industrial Mathematics by H Neunzert,Abul Hasan Siddiqi Summary

Industrial Mathematics is a relatively recent discipline. It is concerned primarily with transforming technical, organizational and economic problems posed by indus try into mathematical problems; "solving" these problems byapproximative methods of analytical and/or numerical nature; and finally reinterpreting the results in terms of the original problems. In short, industrial mathematics is modelling and scientific computing of industrial problems. Industrial mathematicians are bridge-builders: they build bridges from the field of mathematics to the practical world; to do that they need to know about both sides, the problems from the companies and ideas and methods from mathematics. As mathematicians, they have to be generalists. If you enter the world of indus try, you never know which kind of problems you will encounter, and which kind of mathematical concepts and methods you will need to solve them. Hence, to be a good "industrial mathematician" you need to know a good deal of mathematics as well as ideas already common in engineering and modern mathematics with tremen dous potential for application. Mathematical concepts like wavelets, pseudorandom numbers, inverse problems, multigrid etc., introduced during the last 20 years have recently started entering the world of real applications. Industrial mathematics consists of modelling, discretization, analysis and visu alization. To make a good model, to transform the industrial problem into a math ematical one such that you can trust the prediction of the model is no easy task.

Topics In Mathematical Analysis

Topics In Mathematical Analysis Pdf/ePub eBook Author: Paolo Ciatti,Eduardo Gonzalez,Massimo Lanza De Cristoforis,Gian Paolo Leonardi
Editor: World Scientific
ISBN: 9814471356
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Topics In Mathematical Analysis by Paolo Ciatti,Eduardo Gonzalez,Massimo Lanza De Cristoforis,Gian Paolo Leonardi Summary

This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide the reader with material otherwise difficult to find and written in a manner which is also accessible to nonexperts.