These answers are the mathematical versions of physics classical constructions, but it would be very difficult to appreciate them if you have no pedestrian introduction of physics. You may enjoy also Aristotles' book "Physics", as a first dish, just for tasting the flavor of physics :)

Second, if you have the time I would encourage you to read physics books that are written for physicists, not for mathematicians. There are numerous differences in terminology and worldview between the physics and mathematics community, even when the underlying subject matter is in some sense the same. It's very valuable for a mathematician to be able to read and understand recent physics arxiv postings, and the only way to do this is to go through some (perhaps accelerated) version of physics grad school.


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Here is a list of books I find useful that present some physical topics from a mathematical viewpoint. Sadly I don't know a good reference for electromagnetism, quantum field theory or statistical physics.

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

Open a book on partial differential equations that doesn't cover theory (Only the methods of solutions) . About 90& of classical physics and much of quantum physics is about solving differential equations . After you finish differential equations , read Jackson electrodynamics book to understand classical field theory .

As an introduction to quantum mechanics, try Mathematical Structure of Quantum Mechanics, by F. Strocchi. I also like this because it starts out describing (classical) physics in terms of observables and experiments, which is a crucial prerequisite to understanding how physicists think.

2- Dynamics. You have to know the basics of things like calculus of variations , Hamiltonians , Lagrangians , legendre transformations , The principle of least action etc . The best resource of this in my opinion is -Classical-Mechanics-Graduate-Mathematics/dp/0387968903/ref=sr_1_1?s=books&ie=UTF8&qid=1426831652&sr=1-1&keywords=mathematical+methods+of+classical+mechanics after you learn this , You can exercise using these tools by solving problems in any classical mechanics textbook .

4 - For classical electrodynamics , Landau's Classical field theory is most important. If you know the lagrangian and the hamiltonian ,you should read it. The idea is that you start from the principle that physics is invariant under lorentz transformations. This means , Spacetime is a four-dimensional semi-riemannian flat manifold with a metric $g_{\mu \nu}$. Expressions like $d^4x$ and $A_{\mu}A^{\mu}$ are invariant under lorentz transformation. So you can put these quantities in the action. At the end you can derive maxwell's equations. Most of classical electrdynamics is how to solve these maxwell's equations in various situations.

When reading physics textbooks , I found that I spend a lot of time doing stupid calculations like multiplying matrices , solving systems of linear equations etc so software like mathematica and matlab can be big time-savers .

For advanced students, "Modern Physics" by Kenneth S. Krane and "Modern Physics: An Introductory Text" by Shlomo Nir are highly recommended. These textbooks provide a more in-depth and rigorous treatment of modern physics concepts.

Online resources such as OpenStax, Khan Academy, and MIT OpenCourseWare offer free access to modern physics textbooks and course materials. Some textbooks also have companion websites with additional resources and practice problems.

Reading and homework may be assigned from these books for many of the Paradigms and Capstone courses. Your initial outlay for textbooks may be large at the beginning of your paradigms classes, but we try to keep this list unchanged for your later courses. Some students prefer to use alternate books (particularly for math methods--see suggestions below). You might like to look through several options before purchasing.

In the past, most professional physicists have found it useful to have one of the following handbooks available for reference. Many students now find that online resources are sufficient for their undergraduate needs.

We are committed to the preservation of physics for future generations, the success of physics students both in the classroom and professionally, and the promotion of a more scientifically literate society.

While the authors retain the copyright to the book, we have made this book available free of charge as our contribution toward a future with free textbooks! We firmly believe in the free market system, and in the case of upper division physics textbooks, traditional publishing methods usually make little economic sense for the author or reader. The small royalty from traditional publishing comes with a giant overhead that make the book nearly cost prohibitive to many students (especially those in developing countries), and the author gives up control of his work to the publishing company. Electronic tools make it easy to produce and distribute a professional product (see our section on creating a textbook), and it can be revised, corrected, and enhanced on the authors' timetable. If you are thinking about publishing a book this way, we highly recommend it.

The Physics Interactives includes a large collection of HTML5 interactive physics simulations. Designed with tablets such as the iPad and with Chromebooks in mind, this user-friendly section is filled with skill-building exercises, physics simulations, and game-like challenges.

Have you tried a Concept Builder lately? You should. This growing collection of cognitively-rich exercises will focus student attention on discrete learning goals. Filled with interactive elements, this section is the perfect tool for getting students thinking about the meaning of concepts. Perfect for students and 1:1 classrooms using iPads, Chromebooks, and the like. And for Chemistry types, we've added a large collection of Chemistry Concept Builders.

Writing good tests and quizzes for your physics class just got a whole lot easier! With The Physics Classroom's Question Bank, physics teachers can quickly put together multiple choice and free-response quizzes and tests that target concepts discussed at The Physics Classroom website. The Question Bank is available for purchase as a both a CD resource and as a Digital Download. Use of the Question Bank requires the Microsoft Word application. (Answers are NOT included on the Question Bank.)

This document is for those who want to contribute to the extensionof the functionality to the Geant4 toolkit - for example, to add anew physics process, to add a new particle, etc. It starts with theexplanation of the object-oriented analysis and design performed bythe original toolkit developers. Understanding this design ismandatory for a new toolkit developer. Then guidance on how toextend the functionality of each class category is given.

You bet! There are dozens of superb, up-to-date books on various aspectsof relativity theory. Most of these are currently in print and widely availablethrough university libraries and organizations such as Amazon.com and Barnes & Noble. In addition, severalclassic books have recently come back into print. It is not an exaggeration to saythat there has probably never been a better time to shop around for books onrelativity!

For the convenience of the rank beginner who wants to purchase one or more of thesetextbooks, here is a very rough guide to the coverage: all of these books introducetensors, including the matter and Riemann and Ricci tensors. All discuss geodesics,connections and covariant derivatives. All discuss the Equivalence Principle, weakfield theory, and at least one interpretation of the field equations. All discussthe classic predictions such as light bending, perihelion advance, gravitationalredshift. Among the exact solutions, all discuss in some detail the "usual suspects"(Schwarzschild vacuum and Friedmann dust). All discuss the linearized theory ofgravitational waves and Cartan's method of curvature forms.

Five of the six textbooks also discuss at length various of the following importanttopics: spinors, algebraic symmetries of tensors, the variational principle formulation ofGR, the initial value formulation of GR, the Petrov classification of curvature types,EXACT gravitational wave solutions, the singularity theorems, Penrose diagrams (conformalcompactification), Hawking radiation, and thermodynamics of black holes. e24fc04721

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