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eBook
Mumford , David; Oda, Tadao
Hindustan Book Agency
, 2015
; English
; 517 Pages
Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.
eBook
Mumford , David; Oda, Tadao
Hindustan Book Agency
, 2015
; English
; 517 Pages
Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.
eBook
Sunder, V. S.
Hindustan Book Agency
, 2015
; English
; 111 Pages
This book's principal goals are:
(i) to present the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus,
(ii) to present a proof without digressing into a course on the Gelfand theory of commutative Banach algebras,
(iii) to introduce the reader to the basic facts concerning the various von Neumann-Schatten ideals, the compact operators, the trace-class operators and all bounded operators, and finally,
(iv) to serve as a primer on the theory of bounded linear operators on separable Hilbert space.
Sunder, V. S.
Hindustan Book Agency
, 2015
; English
; 111 Pages
This book's principal goals are:
(i) to present the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus,
(ii) to present a proof without digressing into a course on the Gelfand theory of commutative Banach algebras,
(iii) to introduce the reader to the basic facts concerning the various von Neumann-Schatten ideals, the compact operators, the trace-class operators and all bounded operators, and finally,
(iv) to serve as a primer on the theory of bounded linear operators on separable Hilbert space.
eBook
Problems in the theory of modular forms
Murty, M. Ram; Dewar, Michael; Graves, Hester
Hindustan Book Agency
, 2015
; English
; 309 Pages
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, it can be used by the undergraduate and graduate student for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ -function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
Murty, M. Ram; Dewar, Michael; Graves, Hester
Hindustan Book Agency
, 2015
; English
; 309 Pages
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, it can be used by the undergraduate and graduate student for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ -function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
eBook
Surveys in theoretical high energy physics 2: lecture notes from SERC schools
Rangarajan, R.; Sivakumar, M.
Hindustan Book Agency
, 2014
; English
; 312 Pages
Every student of particle physics needs to be well-equipped with a basic understanding of the many concepts underlying the Standard Models of Particle Physics and of Cosmology. This is particularly true today when experimental results from colliders such as LHC (Large Hadron Collider) and RHIC (Relativistic Heavy Ion Collider) as well as inferences from cosmological observations are expected to further expand our understanding of particle physics at high energies.
This volume is the second in the Surveys in Theoretical High Energy Physics Series (SThEP), the aim of which is to bring pedagogical reviews of important topics in high energy physics to the particle physics community.
Topics covered in this collection, based on lectures that were delivered at the SERC Schools in Theoretical High Energy Physics at the Physical Research Laboratory, Ahmedabad and the University of Hyderabad, include Quark-Gluon Plasma, Thermal Field Theory, Perturbative Quantum Chromodynamics, Anomalies and Cosmology.
Rangarajan, R.; Sivakumar, M.
Hindustan Book Agency
, 2014
; English
; 312 Pages
Every student of particle physics needs to be well-equipped with a basic understanding of the many concepts underlying the Standard Models of Particle Physics and of Cosmology. This is particularly true today when experimental results from colliders such as LHC (Large Hadron Collider) and RHIC (Relativistic Heavy Ion Collider) as well as inferences from cosmological observations are expected to further expand our understanding of particle physics at high energies.
This volume is the second in the Surveys in Theoretical High Energy Physics Series (SThEP), the aim of which is to bring pedagogical reviews of important topics in high energy physics to the particle physics community.
Topics covered in this collection, based on lectures that were delivered at the SERC Schools in Theoretical High Energy Physics at the Physical Research Laboratory, Ahmedabad and the University of Hyderabad, include Quark-Gluon Plasma, Thermal Field Theory, Perturbative Quantum Chromodynamics, Anomalies and Cosmology.
eBook
Tao, Terence
Hindustan Book Agency
, 2014
; English
; 369 Pages
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
eBook
Tao, Terence
Hindustan Book Agency
, 2014
; English
; 369 Pages
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
eBook
Tao, Terence
Hindustan Book Agency
, 2014
; English
; 237 Pages
This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.
The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
In the third edition, several typos and other errors have been corrected and few new exercises have been added.
Tao, Terence
Hindustan Book Agency
, 2014
; English
; 237 Pages
This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.
The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
In the third edition, several typos and other errors have been corrected and few new exercises have been added.
eBook
Fragility of glass-forming liquids
Greer, A. Lindsay; Kelton, Kenneth F.; Sastry, Srikanth
Hindustan Book Agency
, 2014
; English
; 531 Pages
Fragility is a key property of liquids---in particular glass-forming liquids---characterizing the rapidity of change of their dynamical properties when cooled near the glass transition. Given the diversity of glass-forming substances and their properties, fragility serves as an important organizing principle. Since the time the concept was introduced and extensively studied by C. Austen Angell, a leading authority on many aspects of liquid-state science in the mid 1980's, thousands of papers have been published analyzing fragility in a variety of liquids, extending and probing the basic concept. The current volume contains reviews by leading experts, and reprints of key articles on fragility. It thus contains material that is essential reading for anybody with a serious interest in liquids and glasses.
Greer, A. Lindsay; Kelton, Kenneth F.; Sastry, Srikanth
Hindustan Book Agency
, 2014
; English
; 531 Pages
Fragility is a key property of liquids---in particular glass-forming liquids---characterizing the rapidity of change of their dynamical properties when cooled near the glass transition. Given the diversity of glass-forming substances and their properties, fragility serves as an important organizing principle. Since the time the concept was introduced and extensively studied by C. Austen Angell, a leading authority on many aspects of liquid-state science in the mid 1980's, thousands of papers have been published analyzing fragility in a variety of liquids, extending and probing the basic concept. The current volume contains reviews by leading experts, and reprints of key articles on fragility. It thus contains material that is essential reading for anybody with a serious interest in liquids and glasses.
eBook
Introduction to the theory of standard monomials, second edition
Seshadri, C. S.
Hindustan Book Agency
, 2014
; English
; 238 Pages
The aim of this book is to give an introduction to what has come to be known as Standard Monomial Theory (SMT). SMT deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated to these groups. Besides its intrinsic interest, SMT has applications to the study of the geometry of Schubert varieties. SMT has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by "standard monomials". In its modern form, SMT was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili.
This book is a reproduction of a course of lectures given by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in SMT due to the work of Peter Littelmann. Seshadri's course of lectures (reproduced in this book) remains an excellent introduction to SMT.
In the second edition, Conjectures of a Standard Monomial Theory (SMT) for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as Appendix C. Many typographical errors have been corrected, and the bibliography has been revised.
Seshadri, C. S.
Hindustan Book Agency
, 2014
; English
; 238 Pages
The aim of this book is to give an introduction to what has come to be known as Standard Monomial Theory (SMT). SMT deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated to these groups. Besides its intrinsic interest, SMT has applications to the study of the geometry of Schubert varieties. SMT has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by "standard monomials". In its modern form, SMT was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili.
This book is a reproduction of a course of lectures given by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in SMT due to the work of Peter Littelmann. Seshadri's course of lectures (reproduced in this book) remains an excellent introduction to SMT.
In the second edition, Conjectures of a Standard Monomial Theory (SMT) for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as Appendix C. Many typographical errors have been corrected, and the bibliography has been revised.
eBook
Connected at infinity II: a selection of mathematics by Indians
Bhatia, Rajendra; Rajan, C. S.; Singh, Ajit Iqbal
Hindustan Book Agency
, 2013
; English
; 194 Pages
Like its predecessor volume, this is a special collection of articles describing the work of some of the best known mathematicians from India. It contains eight articles written by experts, each of whom has chosen one major research contribution by an Indian mathematician, and explained its context, significance and impact. This is done in a way that makes the main ideas accessible to someone whose own research interests might be in a different area.
Bhatia, Rajendra; Rajan, C. S.; Singh, Ajit Iqbal
Hindustan Book Agency
, 2013
; English
; 194 Pages
Like its predecessor volume, this is a special collection of articles describing the work of some of the best known mathematicians from India. It contains eight articles written by experts, each of whom has chosen one major research contribution by an Indian mathematician, and explained its context, significance and impact. This is done in a way that makes the main ideas accessible to someone whose own research interests might be in a different area.
eBook
Sane, Sharad S.
Hindustan Book Agency
, 2013
; English
; 484 Pages
This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them.
The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups.
All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
eBook
Sane, Sharad S.
Hindustan Book Agency
, 2013
; English
; 484 Pages
This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them.
The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups.
All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
