Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book also includes exercises and proofed examples to test the students' understanding of the various concepts, as well as to extend the text's themes.
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'This is a beautifully crafted book. ... Peter Szekeres presents in the most elegant and compelling manner a magnificent overview of how classic areas such as algebra, topology, vector spaces and differential geometry form a consistent and unified language that has enabled us to develop a description of the physical world reaching a truly profound level of comprehension. ... Szekeres's style is clear, thorough and immensely readable. His selection of topics concentrates on areas where a fully developed rigorous mathematical exposition is possible. ... One cannot help but be slightly awed by the beauty and the capability with which seemingly abstract concepts, often developed in the realms of pure mathematics, turn out to be applicable ... I recommend that you get hold of this book for yourself or for your library.' Times Higher Education Supplement
'The superb layout and an index contribute to the excellent overall impression of this book ...'. Zentralblatt MATH
' ... the book may serve as an easily accessible introductory text on a wide range of the standard and more basic topics in mathematics and mathematical physics for the beginner, with an emphasis on differential geometry. a nice feature is that a considerable number of examples and exercises is provided, together with numerous suggestions for further reading: there is also an extensive index which will be particularly helpful for beginners in the subject.' General Relativity and Gravitation Journal
'The superb layout and an index contribute to the excellent overall impression of this book ...'. Zentralblatt MATH
' ... the book may serve as an easily accessible introductory text on a wide range of the standard and more basic topics in mathematics and mathematical physics for the beginner, with an emphasis on differential geometry. a nice feature is that a considerable number of examples and exercises is provided, together with numerous suggestions for further reading: there is also an extensive index which will be particularly helpful for beginners in the subject.' General Relativity and Gravitation Journal
Book Description
This book provides an introduction to the mathematics of modern physics, presenting concepts and techniques in mathematical physics at a level suitable for advanced undergraduates and beginning graduate students. It aims to introduce the reader to modern mathematical thinking within a physics setting. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book includes exercises and worked examples, to test the students' understanding of the various concepts, as well as extending the themes covered in the main text.
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Most Helpful Customer Reviews
38 of 39 people found the following review helpful:
3.0 out of 5 stars
A fast introduction to mathematics in physics,
By Juhani (Finland) - See all my reviews
This review is from: A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry (Hardcover)
The book does not assume prior knowledge of the topics covered. However, the reader will find use of prior knowledge in algebra, in particular group theory, and topology. Compared to texts, such as Arfken Weber, Mathematical Methods for Physics, A Course in Modern Mathematical Physics is different, and emphasis is on proof and theory. The text is reasonably rigorous and build around stating theorems, giving the proofs and lemmas with occasional examples. The style is not the strictest, although making the text more reader friendly, it is easy to get confused with which assumptions have been made, and the direction of the proof. Sometimes only the "if" part is proven.
Students familiar with algebra will notice that the emphasis is on group theory, interestingly the concept of ideals is left mostly untouched. For more on representation theory a good reference is Groups Representations and Physics by H.F. Jones where solutions to some of the exercises can be found, and examples of the use of the fundamental orthogonality theorem applied to characters of represenations. The first 6 chapters are relatively straight forward, but in chapter 7 Tensors the text becomes much more advanced and difficult. Chapter 10 on topology offers some lighter material but the reader should be careful, these consepts are to re-appear in the discussion of differential geometry, differentiable forms, integration on manifolds and curvature. These are not the most simple subjects and it is clear that they deserve entire courses of their own. The book has insight and makes many good remarks. However, chapter 15 on Differential Geometry is perhaps too brief considering the importance of understanding this material, which is applied in the chapters thereinafter. The book is suitable for second to third year student in theoretical physics.
12 of 12 people found the following review helpful:
5.0 out of 5 stars
A serious, wide spectrum introduction to modern mathematical physics,
By
This review is from: A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry (Hardcover)
This book covers almost every subject one needs to begin a serious graduate study in mathematical and/or theoretical physics. The language is clear, objective and the concepts are presented in a well organized and logical order. This book can be regarded as a solid preparation for further reading such as the works of Reed/Simon, Bratteli/Robinson or Nakahara.
3 of 3 people found the following review helpful:
5.0 out of 5 stars
Provides an excellent foundation for advanced studies,
By Gu'an (India) - See all my reviews
This review is from: A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry (Hardcover)
I started this book with very little mathematical background (just an electrical engineer's or applied physicist's exposure to mathematics). By the end of this book, I had an advanced exposure to foundational modern mathematics. Now, I am planning to start on "Differential Topology and Quantum Field Theory" by Charles Nash (with other mathematics reference books to complete the proofs in it).
This book also provides a good amount of material showing the application of mathematical structures in physics - Tensors and Exterior algebra in Special relativity and Electromagnetics, Functional Analysis in Quantum mechanics, Differentiable Forms in Thermodynamics (Caratheodory's) and Classical mechanics (Lagrangian, Hamiltonian, Symplectic structures etc), General Relativity etc.
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Inside This Book
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First Sentence:
The object of mathematical physics is to describe the physical world in purely mathematical terms. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
minimal annihilating polynomial, adiabatic enclosure, free vector space, free associative algebra, relative topology induced, real inner product space, coordinate chart, bracket product, map det, finite dimensional inner product space, embedded submanifold, integral submanifold, connected neighbourhood, closure with respect, geodesic deviation, parametrized curve, empirical temperature, standard topology, factor algebra, exterior product, basis lei, vector space isomorphism, multilinear maps, differentiable structure, tangent map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Problems Problem, New York, Cambridge University Press, Academic Press, The University of Chicago Press, Princeton University Press, Advanced Calculus, Englewood Cliffs, Van Nostrand Company, Problem Problem, San Diego, Oxford University Press, Van Nostrand Reinhold Company, World Scientific, Adam Hilger, Dover Publications, John Wiley, The Geometry of Physics, Lecture Notes, Mathematical Foundations of Quantum Mechanics, Physical Problems, References Problem, Scott Foresman New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The object of mathematical physics is to describe the physical world in purely mathematical terms. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
minimal annihilating polynomial, adiabatic enclosure, free vector space, free associative algebra, relative topology induced, real inner product space, coordinate chart, bracket product, map det, finite dimensional inner product space, embedded submanifold, integral submanifold, connected neighbourhood, closure with respect, geodesic deviation, parametrized curve, empirical temperature, standard topology, factor algebra, exterior product, basis lei, vector space isomorphism, multilinear maps, differentiable structure, tangent map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Problems Problem, New York, Cambridge University Press, Academic Press, The University of Chicago Press, Princeton University Press, Advanced Calculus, Englewood Cliffs, Van Nostrand Company, Problem Problem, San Diego, Oxford University Press, Van Nostrand Reinhold Company, World Scientific, Adam Hilger, Dover Publications, John Wiley, The Geometry of Physics, Lecture Notes, Mathematical Foundations of Quantum Mechanics, Physical Problems, References Problem, Scott Foresman New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 60
books:
See all 60 books this book cites
- Mathematical Physics (Chicago Lectures in Physics) by Robert Geroch on 11 pages
- Advanced Calculus, Revised Edition by Loomis on 8 pages
- Lectures on Differential Geometry (Series on University Mathematics) by Shiing-Shen Chern on 6 pages
- Differential Geometry (Proceedings of Symposia in Pure Mathematics, vol. 27, pt. 2) by Shiing-Shen Chern on 6 pages
- Foundations of Mathematical Physics by Sadri Hassani on 5 pages
See all 60 books this book cites
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