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Complete this override request if you are requesting to take/re-take ONE physics lecture or physics lab on its own. The courses specifically are PHYS 203, PHYS 203L, PHYS 204, PHYS 204L, PHYS 205, PHYS 205L, PHYS 206, PHYS 206L. Your advisor's signature is NOT required. Capacity overrides are NOT granted.

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 :)

Just before entering in the modern world of physics I would suggest few basic lectures for the winter evenings, near the fireplace (I'm sorry I write them down in french because I read them in french).

" I want to explore the working of elementary physics ... which I have always found so hard to fathom.[...]I have written this work in order to learn the subject myself, in a form that I find comprehensible.[...]By physics I mean ... well, physics, what physicists mean by physics, i.e., the actual study of physical objects ... (rather than the study of symplectic structures on cotangent bundles, for example)."

It tries to touch almost all areas in physics, including the hot ones. Penrose emphasizes the mathematical part (especially the geometric interpretations), and avoids to be superficial (many scientific writers, when trying to make the things easier, use misleading metaphors). One warning is to be careful that sometimes he expresses his personal viewpoint, which is not always mainstream. But it is clear when he does this, and he is very careful to make justice to the mainstream viewpoint, by presenting it very well.

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.

The Quantum Theory of Fields, volume 1 by Steven Weinberg. I found this book to be much less impenetrable (from the point of view of a mathematician who foolishly stopped taking physics courses when he was an undergraduate) than the typical QFT textbook.

The Feynman lectures are good, but one of the main things which separates physics from mathematics is the role of experiment and observation. Physics is not just a matter of getting the formulae and models right, but also of testing mathematical models against observations to see whether they stand up or break down in "the real world". Part of the role of mathematical models is to give physicists some guidance on potentially fruitful places to look.

So it rather depends whether you are looking at mathematical/theoretical physics as a mathematician/theoretician would understand it, or whether you are looking to understand the role of mathematics in physics as a discipline.

Edit: The list below fits not that good to the requirements you describe, but the texts there are what I found helpfull. If you can read German books, I would recommend W. Greiner's "Theoretische Physik", which explains basically all the needed mathematics. Usefull too may be J. Baez' "Gauge Fields, Knots and Gravity", which contains a "rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations".

And then, I found F. C.'s recommendation to Nahm's very fascinating "Conformal Field Theory and Torsion Elements of the Bloch Group" very good, e.g. Nahm writes "readable for mathematicians", "much of this article is aimed at mathematicians who want to see quantum field theory in an understandable language .... all computations should be easily reproducible by the reader". Nahm's issue is a strange connection between some quantum field theories and algebraic K-theory and he hopes, his article could stimulate mathematicians to become interested in these exciting topic. A forthcoming article by Zagier on "quantum modular forms" may relate to that too.

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.

Jeffrey Rabin has written a lightning-fast introduction to physics designed for exactly the audience you describe: people with "the mathematical background of a first-year graduate student," but "[no] prior knowledge of physics beyond F = ma."

Hmmm, the first thing that occurs to me is that mathematicians need to learn about "time", because something as fundamental as "conservation of energy" is not directly to be found in mathematics in its physics form. The two are connected by what is usually known as "Noether's theorem" and so this provides a more manageable question: where can mathematicians genuinely learn about the role of symmetry principles in physics? This starts getting us somewhere, but observe what goes on: the traditional route goes through calculus of variations in some form, and that is a theory not in Bourbaki.

So the deal looks like this to me: do we want to "bridge the gap" between contemporary mathematics and contemporary physics on the way that hits the Zeno paradox? Or do we want to invoke a bisection method and claim that it works? In the first, the question "are we doing real physics yet?" has the status of the kids in the back of the car asking "are we nearly there yet?": you only get anywhere close to the destination long after you stop asking. And probably if you have to be told what is "real" physics you aren't even close. The second idea seems more promising. If I just said "find a readable introduction to moment maps and find out how they work, and you will have grasped a Bourbaki-type intermediate between mathematics for its own sake and mainstream Newtonian dynamics, avoiding calculus of variations, with use of symmetry", it seems to me that I have communicated something. I don't know the second thing about physics (which might be how you would know that you had quantised a system) but what I have said might be a first thing,

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.

A unified account of the principles of theoretical physics, A Unified Grand Tour of Theoretical Physics, Second Edition stresses the inter-relationships between areas that are usually treated as independent. The profound unifying influence of geometrical ideas, the powerful formal similarities between statistical mechanics and quantum field theory, and the ubiquitous role of symmetries in determining the essential structure of physical theories are emphasized throughout. This second edition conducts a grand tour of the fundamental theories that shape our modern understanding of the physical world. The book covers the central themes of space-time geometry and the general relativistic account of gravity, quantum mechanics and quantum field theory, gauge theories and the fundamental forces of nature, statistical mechanics, and the theory of phase transitions. The basic structure of each theory is explained in explicit mathematical detail with emphasis on conceptual understanding rather than on the technical details of specialized applications. The book gives straightforward accounts of the standard models of particle physics and cosmology. 2351a5e196

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