Good Physics Books For a Math PhD Student? 418
An anonymous reader writes "As a third-year PhD math student, I am currently taking Partial Differential Equations. I'm working hard to understand all the math being thrown at us in that class, and that is okay. The problem is, I have never taken any physics anywhere. Most of the problems in PDEs model some sort of physical situation. It would be nice to be able to have in the back of my mind where this is all coming from. We constantly hear about the heat equation, wave equation, gravitational potential, etc. I'm told I should not worry about what the equations describe and just learn how to work with them, but I would rather not follow that advice. Can anyone recommend physics books for someone in my position? I don't want to just pick up a book for undergrads. Perhaps there are things out there geared towards mathematicians?"
Why not a book for undergrads... (Score:1, Interesting)
Re:Some recommendations from another Math Ph.D (Score:4, Interesting)
Re:Some recommendations from another Math Ph.D (Score:4, Interesting)
Jumping Jesus on a pogo stick, you're pointing him to The Black Death straight out of the gate? Why not give him underwear made of wolverine chow? Wheeler would have died ten years ago if not for the life-giving tears of those who opened that book unprepared. That is to say, everyone.
Seriously, dial it back a bit. First, hit the Feynman lectures (stop when you get to 'partons'.) Then, for someone coming from a mathematical bent, I'd suggest starting with Sokolnikoff's book "Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua", which covers a lot of ground besides GR. Due to the absence of a just and loving god it is out of print, but surely one of the profs in a math department with a PhD program has a copy (or at minimum the library.) And there's always copies on Alibris.
And, seconding suggestions from other posters, Kittel and Kroemer's "Thermal Physics" is a good starting point on thermo, As for quantum, in the absence of all knowledge in the field I'd start with Tipler's "Modern Physics", with the goal of ramping up to Cohen-Tannoudji, Diu, and Laloe's "Quantum Mechanics".
Re:PDEs now? (Score:3, Interesting)
No. ODE's are typical of Undergrad. But, PDE's are typical of Masters. That isn't to say that PDE's are taught in Undergrad, period. Rather that PDE's in Undergrad is atypical. At least in North America. Other parts of the world either have vastly superior high-school/Undergrad or skip a lot of the, necessary for actually understanding, stuff. Germany and China are respective examples.
Re:Books (Score:4, Interesting)
As a 4th-year Physics undergrad, I have to voice my opinion that I absolutely can't stand Feynman's texts.
They're nice to glance at, but approach the subject in a considerably different manner than any of the other renowned physics texts.
Similarly, his proofs were terse to the point of being difficult to follow. I'll admit that my mathematical intuition isn't the greatest, though I can't help but think that this was intentional on Feynman's part, as to weed out those with weak mathematical skills from his freshman lectures. This makes them rather frustrating to use as a general reference. Similarly, the texts are largely theoretical, and offer little advice with regard to problem-solving.
Personally, I've had good experiences with the Landau/Lifshitz series of texts, and it's hard to go wrong with Griffith's books on EM and QM. Goldstein's text on Classical Mechanics is also a well-known classic.
That's not to say that that Feynman's texts are all bad. Some sections are outright brilliant, and he actually takes the time to explain himself rather extensively in many sections, which many physics (and math) writers frequently neglect to do. I keep a copy of all 3 volumes on my bookshelf, as they are occasionally handy. However, I wouldn't dream of using them as my only reference.
V.I Arnold (Score:2, Interesting)
I don't know if it has been mentioned here, but V.I. Arnold (Lectures on Partial Differential Equations) might be a starting point. Arnold emphasizes physics in his writing. His introduction to classical mechanics is an absolute must for everyone interested in this kind of topics! He really blows away the fog.
Re:I'm gunna say this once.. (Score:4, Interesting)
> So what kind of university are you at?
An American one. They specialize *much* later than the English [who are down to 3 subjects, eg Maths, More Maths, and Physics] for A levels [at 16]. Once at university Americans still have to take a relatively broad range of classes for the first 2 years. So, even in good US universities the first year or two only gets them up to A level standard. Top performers make up for it later on because after being held back from focusing only on what interests them for so long its such a relief to be able to concentrate that they really get stuck into it.
Re:3rd year PhD student taking PDE? (Score:3, Interesting)
There are applications, too. The operators in quantum mechanics form a C*-algebra acting on a Hilbert space. Learning the properties of a C*-algebra is easier than trying to deduce what the properties of the momentum and position operators might be and then attempting to generalize from there to other operators.
If you ever hear someone talk about symmetries in physics (immensely important and useful, BTW), they are talking about groups. A symmetry in physics shows up when you can take any solution, transform it in a well defined way, and get another solution. Ok, so now you have another solution. You can transform that in another way, and get another solution. So we see that these transformations compose to form another transformation. Take a glance at the other group axioms, and you find that your symmetry operations form a group. So, the results of group theory are useful to deduce properties of systems that have certain symmetries.
Outside of theoretical physics: True and False, together with AND and OR as plus and times (I can't remember which is which) form a field. You can make a vector space over any field you like, and once you can make a vector space, you can make matrices. Once you can make matrices, you can use them to solve coupled linear equations: for instance, take a set of Boolean equations. You can either work out what the solution is tediously by hand, or you can just pack them into a matrix and invert it.
Re:PDEs now? (Score:3, Interesting)
The other answer is based on my experience. I went to a medium-tier school where math existed to teach people Calc I-III. Beyond that I was lucky to have a great Algebra teacher and did some independent studies, REUs and semesters abroad on dynamical systems, finite fields, generating functions, and other assorted topics. But my differential equations was woefully inadequate to the point where I couldn't tell you anything beyond rabbits and foxes. Thankfully everything in the undergrad curriculum, even at the school I'm at now which is pretty demanding of undergrads, I learned on the fly as I taught it in recitations well enough to get high recommendations. The thing is once you get into a graduate degree, undergrad math seems like a series of trivial facts you can pick up when you need 'em. It's not so much about breadth of knowledge as being sharp and willing to do some work, so there are a good amount of us at decent grad schools that went to not-so-decent undergrad schools in terms of math. The masters portion of the general math degree at my school is more about acquiring the basic algebra and analysis knowledge that is so fundamental to mathematics (and conveniently the subject matter of the quals).
I actually sympathize with the original poster, I'm a third year grad and I need to learn more PDEs and physics both. The one thing I really regret is not taking advanced physics as an undergrad along the way, although I don't regret the philosophy and lit courses I took instead of them.
Re:He said "Mathematician" (Score:4, Interesting)
You've got to remember that there was an awful lot that was obvious to Feynman - hell he won the Putnam without breaking a sweat. He ran into a classmate who wondered why he wasn't taking the Putnam exam and Feynman told him he'd finished the exam. The interchange took place when there were a couple of hours left on the exam clock and none of the other contenders completed the test in the allotted time.
He felt that Mathematicians spent an awful lot of energy developing stuff that was obvious, and hence a waste of his time. He used to harangue math graduate students that if they could clearly state what they were working on, he could reproduce and finish what they were doing within the evening. The thing was, he could do it. He was far more interested in why things worked the way they did rather than proving that the math he was using was correctly applied - the results mattered to him far more than the technique.
He used to say that the renormalization techniques he used developing QED which won him the Nobel Prize probably weren't kosher math but they produced the right answer to the tenth decimal place.
In the end, that's what doomed the Feynman Physics Undergraduate books - they were simply too advanced for the vast majority of their intended audience. While he was giving the lectures, the undergraduate attendance declined while the graduate attendance increased thereby keeping the room full which misled him as to how clearly he was teaching his intended audience. It wasn't until the mid terms came in that he realized something was amiss. If the average Caltech student couldn't suss what he was saying, it's a fair bet few other physics undergrads would be able to. The graduate students, and other faculty, on the other hand, loved the class because it gave them insights into topics they thought they completely understood.