(Part 2) Reddit mentions: The best mathematical physics books

Under my Stuff I Actually Need Wish List, you'll find, well, stuff I actually need now that I've moved away for my first year at my new university (Today's my second day of classes! Super excited!)


I need (any pf these would be wonderful):

• This hanging hamper for my tiny dorm room- $11.99
  
  
• Periodic Table poster so I can not fail my chem class- $4.22
  
  
• Periodic Table study sheet- $4.45
  
  
• Physics study reference binder sheet- $5.65
  
  
  
• Toilet brush- $6.73
  
  
  
• Salt and Pepper Shakers- $8.14
  
  
  Thanks for the contest! This was a great way to spend a study break! Oy, where's the asprin?

Mostly commenting here in case someone else comes along with a more proper answer...

I'm assuming you're asking for literature, as in the studies he's citing as he goes along, etc. I don't have that, but you can probably get a lot of them from looking at the "textbooks" for the class. In the first lecture, he mentions these 2 books as essentially the "textbooks" for the course:

Why Zebras Don't Get Ulcers, Robert Sapolsky

Chaos: Making a New Science, James Gleick

​

Later on, he also brings up Stephen Wolfram's A New Kind of Science

And since that lecture series was done, in 2017, Sapolsky published a book, Behave: The Biology of Humans at Our Best and Worst, which has TONS of overlap with the lecture series. He doesn't go into the same exact stuff, especially in the later chapters versus the later lectures, but he follows the exact same pattern of explaining the biology of human behaviors. He even tells a lot of the same stories and personal insights.

It wouldn't surprise me if the vast majority of the literature he cites in the lectures are all referenced across those books, too, so it would be a totally valuable avenue to dig in on. I haven't personally read through the first two all the way yet (I'm about halfway through Zebras right now). Behave is worth reading in addition to the lectures, despite the huge overlap, imho, and probably lists most of the same studies he cites in its Notes section.

This is excellent! I've already installed ZeroNet. I have some resources I'd like to share once I get a better internet connection.
I can't find the book Essays on Mirror Manifolds by Shing-Tung Yau et al. anywhere.
It's quite expensive and Amazon doesn't really ship to where I live so I'd very much appreciate a copy.
Thank you for your work.

I really encourage you to try and study special relativity. Basic relativity does not involve math beyond algebra and your misunderstandings about relativity are very basic.

As for the black hole stuff, as far as I know there is not "infinite" gravitation. When the Einstein field equations are solved for you, black hole physics becomes pretty simple also. "Infinite" accumulation violates the second law of thermodynamics, and I'm pretty sure that's why Hawking radiation is emitted by black holes. It has also been theorized that black holes have corresponding white holes which expel matter at the same rate. That seems really far-fetched to me.

Edit: Check out this chapter of a book called Reflections on Relativity. It's a pretty good book, not extremely advanced either.

I read both your comment and the article and they are very interesting. I think that there's more to it than just current academic system, but I agree that it has resulted in something that's in a way opposite of what science should be.

I was taught differential geometry from this book:

https://www.amazon.com/Differential-Geometry-Lie-Groups-Physicists/dp/0521187966

It's pretty good for self-study since you need to derive almost everything. It's written by a physicist, for physicists, so again it's not 100% rigorous. Maybe you could give it a try.^^pdf

It entirely depends on what you want to do. Everyone here so far is suggesting QM techniques, I use molecular dynamics for free energy simulations and algorithm development. If you are looking to use classical mechanics, i would suggest this and this.

Also a good understanding of Statistical Mechanics is a must, so check out this (google it). If you are looking for a free MD engine GROMACS and NAMD are free and would suggest on NAMD over GROMACS because the code seems to cut a lot of corners, but I use neither.

If this is more along the lines of what you are looking to do, feel free to pm me.

If you look at pretty much any book written for particle physics and Lie Groups they cover examples first (usually spin and angular momentum), but I don't think you'll find exactly what you are looking for. Lie Groups for Pedestrians starts by generating representations of the SU(2) Lie Algebra using creation and annihilation operators, so it might be along the lines of what you are looking for.

Edit: Also, I believe Ryder's book on QFT explicitly uses co-sets and more formal aspects of group theory to talk about gauge-fixing. That might be a good place to look for how those more formal ideas are applied. Of course, Weinberg's book on QFT (vol 2.) also talks about some aspects of representation theory with examples that might be a good way to connect to the math you are cranking out (for example how the adjoint representation relates to gauge bosons).

For textbooks, like what /u/Axi_om mentioned, I believe University Physics should be sufficient for most purposes. Generally, the IPhO doesn't test content that is obscure, but more of application and manipulation of formulae and algebra.

Calculus is a definite must, it's literally impossible to find a year which doesn't require it. However, the level of calc required isn't too high, as long as you can differentiate and integrate functions using basic techniques like substitution you should be fine.

Good practice books include http://www.amazon.com/Guide-Physics-Problems-Part-Electrodynamics/dp/0306446790 and http://www.amazon.com/200-Puzzling-Physics-Problems-Solutions/dp/0521774802, although the first book (A Guide to Physics Problems) might sometimes include content too deep for the physics olympiads.

Do ask away if you have anymore questions, ex IPhO participant here :)

Not my sub-field, but I'll try.

Cellular automaton can be used to model extremely complex systems which have simple interaction rules. Fluid dynamics is one thing that comes to mind. Particles have extremely simple rules for interacting: bounce around.

However, I can't find much post-80s. Probably because methods for numerically solving equations, massive parallelization, and CPU speed in general took off in the 90s.

You might have a look at:

http://www.amazon.com/Cellular-Automata-Modeling-Collection-Alea-Saclay/dp/0521673453

For some ideas. But please, check libraries before you buy a book like this.

There's actually a bunch of stories I could tell about him because he was so controversial of a professor within the department. I knew this because I was on pretty good terms with the other professors, and I got the impression that they weren't fans of him.

His way of thinking was just erratic. The class started with a general guide to QM, then moved to Georg Cantor's Diagonal argument for transfinites, then moved to super symmetry and string theory, and just kept going off in a ton of different directions.

Also, it was super hard. You could tell he had no clue what students he had in his class because the textbook he referred to was something like this:

We're talking about undergrad phil students that likely haven't even had a college-level physics course. Also, from the beginning of the entire course I called bullshit on him knowing string theory. There's no way he understood the material in that textbook.

Then again, this is a professor who claimed to be more well read on structural engineering than the vast majority of all engineers, so the delusion was strong in this one.

Condensed matter folks have had supersymmetry for decades: http://www.amazon.com/Supersymmetry-Disorder-Chaos-Konstantin-Efetov/dp/0521663822

Also, CMT has the most fun. THERE I SAID IT.

ETA: Tarun Grover is an extraordinary young physicist, and pretty much everything he's done in the past several years is really neat.

I'll list books that I've encountered along with some brief comments about them.

• I think that Jost's book is exactly what you're looking for. The last chapters in particular are excellent.
  
• If you're interested in avoiding the (necessary) difficulties associated with jumping directly into higher dimensional problems, you should also check out Buttazzo, Giaquinta, and Hildebrandt's book about 1-dimensional variational problems. I read mostly the early chapters, and I found it to be down-to-earth without sacrificing rigor at all.
  
• If you're interested in direct methods, you can't go wrong with Dacorogna's book on the subject.
  
• Although I've never personally used it in my work, I have had occasion to browse Fonseca and Leoni's book; it's without a doubt self-contained, although I wouldn't say it starts out explaining things like you're five.
  
• If none of these grab you, Courant and Hilbert have some helpful worked examples and discussions (of course, this book is older than the 1960s).
  
  Hope this gets the ball rolling!

The best I’ve seen is ‘A Modern Approach to Critical Phenomena’. I really appreciate the clarity and style of the author, it’s not overly long has exercises with solutions and is relatively modern.

Mathematicians and physicists use linear algebra for pretty different things, and with different mental models.

If it isn't a requirement at your school I would assume that your program will teach you what you need in classes. However, it certainly won't hurt to learn it formally. I recommend taking the class if you can but if you can't then this video series is amazing, and if you want to learn it in the rigorous way physicists use it (with crazy ass notation included) then chapter 1 of Shankar has a pretty good overview (it gets a bit abstractly mathy toward the end of chapter 1 though and can be hard to follow since he doesn't tie it to the applications immediately).

I think what you want is propagation of uncertainties. Yours is the third case, f=AB, with sigma_A and sigma_B being your errors. You don't say whether the measurements are correlated: if not, the third term is zero.

This is a drastic simplification though. The best resource I know of is this book, at least if you are happy just doing practical/pragmatic statistics.

Feedback would be greatly appreciated on this one. It's a prototype analysis for a book idea I had.

I'm toying with the idea of writing a book about statistical analyses of classic games. The target audience would be mathematically interested laypeople, much like Jeffrey Rosenthal's book Struck by Lightning ( https://www.amazon.ca/Struck-Lightning-Jeffrey-S-Rosenthal/dp/0006394957 ).

The twist would be that chapter would contain step-by-step R code or Python code so that the reader could do the same analysis and make changes based on their own questions.

Hmmm, I would suggest The amazing story of Quantum Mechanics for more concepts rather than equations. If you're looking for equations and some of their back stories I suggest (as long as this is the same book I read) Physics for Poets. If you'd like to watch something to take a break from reading, try The fabric of the Cosmos.

https://www.amazon.com/Mathematics-Physicists-Introductory-Concepts-Methods/dp/1108471226

This will give you all the maths you will need for your bachelors degree and then some starting points for the mathematics needed for graduate level physics. It’s very well structured so you will easily recognize what’s important to you.

To get a real grasp of all this is quite hard. This is very subtle group theory that relies on already having a solid grasp of QFT.

This book tries to cover these topics but he didn't go into too much depth. I don't actually know of another book that goes deep into the topic besides Weinberg. Luckily, Weinberg covers this topic within the first ~15 pages of actual content in his book, so if you sit down and hammer it out after learning some QFT you could pick it up.

Seconded, excellent book.

Also, I LOVE this book personally, but ymmv.

https://www.amazon.com/Principles-Quantum-Mechanics-R-Shankar/dp/146157675X

Physics for Poets
http://www.amazon.com/Physics-Poets-Robert-H-March/dp/0070402485

http://www.amazon.com/Physics-Poets-Robert-H-March/dp/0070402485

It's close!