Part I provides a simple introduction to basic topology, followed by a survey of homotopy. Calculus of differentiable manifolds is then developed, and a Riemannian metric is introduced along with the key concepts of connections and curvature. The final chapters lay out the basic notions of simplicial homology and de Rham cohomology as well as fibre bundles, particularly tangent and cotangent bundles. --

This book presents a survey of Topology and Differential Geometry and also, Lie Groups and Algebras, and their Representations. The first topic is indispensable to students of gravitation and related areas of modern physics (including string theory), while the second has applications in gauge theory and particle physics, integrable systems and nuclear physics.Part I provides a simple introduction to basic topology, followed by a survey of homotopy. Calculus of differentiable manifolds is then developed, and a Riemannian metric is introduced along with the key concepts of connections and curvature. The final chapters lay out the basic notions of simplicial homology and de Rham cohomology as well as fibre bundles, particularly tangent and cotangent bundles.Part II starts with a review of group theory, followed by the basics of representation theory. A thorough description of Lie groups and algebras is presented with their structure constants and linear representations. Root systems and their classifications are detailed, and this section of the book concludes with the description of representations of simple Lie algebras, emphasizing spinor representations of orthogonal and pseudo-orthogonal groups.The style of presentation is succinct and precise. Involved mathematical proofs that are not of primary importance to physics student are omitted. The book aims to provide the reader access to a wide variety of sources in the current literature, in addition to being a textbook of advanced mathematical methods for physicists.

This book presents a survey of Topology and Differential Geometry and also, Lie Groups and Algebras, and their Representations. The first topic is indispensable to students of gravitation and related areas of modern physics, (including string theory) while the second has applications in gauge theory and particle physics, integrable systems and nuclear physics. Part I provides a simple introduction to basic topology, followed by a survey of homotopy. Calculus of differentiable manifolds is then developed, and a Riemannian metric is introduced along with the key concepts of connections and curvature. The final chapters lay out the basic notions of simplicial homology and De Rham cohomology as well as fibre bundles, particularly tangent and cotangent bundles. Part II starts with a review of group theory, followed by the basics of representation theory. A thorough description of Lie groups and algebras is presented with their structure constants and linear representations. Root systems and their classifications are detailed, and this section of the book concludes with the description of representations of simple Lie algebras, emphasizing spinor representations of orthogonal and pseudo-orthogonal groups. The style of presentation is succinct and precise. Involved mathematical proofs that are not of primary importance to physics student are omitted. The book aims to provide the reader access to a wide variety of sources in the current literature, in addition to being a textbook of advanced mathematical methods for physicists.

This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

Practical, readable text focuses on fundamental applied math needed by advanced undergraduates and beginning graduate students to deal with physics and engineering problems. Covers elementary vector calculus, special functions of mathematical physics, calculus of variations, and much more. Excellent self-contained study resource. 1968 edition.

A user-friendly student guide to computer-assisted algebra with mathematical software packages such as Maple.

The book is designed for graduate students and researchers working in the field of theoretical physics and related fields.

The present book is an outcome of the SERC school on Computational Statistical Physics held at the Indian Institute of Technology, Guwahati, in December 2008. Numerical experimentation has played an extremely important role in statistical physics in recent years. Lectures given at the School covered a large number of topics of current and continuing interest. Based on lectures by active researchers in the field- Bikas Chakrabarti, S Chaplot, Deepak Dhar, Sanjay Kumar, Prabal Maiti, Sanjay Puri, Purusattam Ray, Sitangshu Santra and Subir Sarkar- the nine chapters comprising the book deal with topics that range from the fundamentals of the field, to problems and questions that are at the very forefront of current research. This book aims to expose the graduate student to the basic as well as advanced techniques in computational statistical physics. Following a general introduction to statistical mechanics and critical phenomena, the various chapters cover Monte Carlo and molecular dynamics simulation methodology, along with a variety of applications. These include the study of coarsening phenomena and diffusion in zeolites. /p In addition, graphical enumeration techniques are covered in detail with applications to percolation and polymer physics, and methods for optimisation are also discussed. Beginning graduate students and young researchers in the area of statistical physics will find the book useful. In addition, this will also be a valuable general reference for students and researchers in other areas of science and engineering.

The recent discovery at the Large Hadron Collider, of what is very likely the Higgs particle, has given a fillip to research in High Energy physics. These experiments hold the promise of a glimpse of physics beyond the Standard Model, which while having been verified to great accuracy, cannot be the final theory. Uncomfortable gaps -both theoretical and experimental- remain in our understanding. Lecture notes from the SERC School in Theoretical High Energy Physics held at IIT Bombay in February 2008 are contained in this volume. Topics that were covered then are of continuing importance, more so in the light of the ongoing LHC experiment. The various chapters in the book include an extensive survey of LHC physics that together with formal aspects and models of supersymmetry, review the state of the art in our understanding of the Standard Model and beyond. The article on B Physics and CP violations add to this, while the chapter on thermal field theory reviews the formalism necessary to understand the early universe and to embark on an analysis of quark-gluon plasma in heavy ion collisions. Written in a clear pedagogic style by active researchers, this text will prepare a beginner to work in the field and at the same time will also provide useful reference material for active researchers.