Mathematics for Physics (2009) [pdf] | Hacker News Reader

Mathematics for Physics (2009) [pdf]

goldbart.gatech.edu

233 pointslainon34 comments

On the other side of the spectrum, I would recommend Spivak's Physics for Mathematicians [1] strongly. I don't think anything else could come close for a mathematician who wants to learn physics.

[] https://www.amazon.com/Physics-Mathematicians-Mechanics-Mich...

For QFT, I liked this one a lot: Folland, QFT - A Tourist Guide for Mathematicians[1].

[1] https://www.amazon.com/Quantum-Theory-Mathematical-Surveys-M...

For relativity, there is the venerable General Relativity for Mathematicians.

https://www.amazon.com/General-Relativity-Mathematicians-Gra...

As someone with a mathematical background, I was wondering what were some motivations for wanting to "learn physics"? Not being argumentative, just genuinely curious on what drives people to self study textbooks on physics after college/grad school.

I will defer to others to write a general apology for mathematics. Here I will simply mention the reason Michael Spivak has given for writing books: namely, to learn the subject himself. Because of this, I would suggest that anything written by Spivak is worth reading.

So, why study physics? Answer: because Michael Spivak has written a book on the subject. Consequently, you now have available to you a map for understanding a subject with no less clarity than the mathematician who wrote it.

What? Spivak is alive!? That's great. I honestly never even considered looking him up on YouTube. I just assumed he was dead.

This is like finding out that Feynman is still alive and giving lectures that I haven't seen.

* I wanted to major in physics, but went into computer engineering instead.

* Physics always seemed glamorous. I know the reality is different, but studying physics makes me feel like a wizard (EDIT: in training).

* I want to be able to read pop-physics and actually be able to dissect it.

* I want to be able to simulate GR.

* I want to understand QFT

* I want to be able to simulate atoms and molecules from first-principles.

* I want to UNDERSTAND

If you haven't already, I highly recommend Feynman's Lectures on Physics: http://feynmanlectures.caltech.edu

While much more advanced than typical introductory texts, it does provide deeper insights than typical introductory texts, which makes it worth the investment.

I'm more at the level of Goldstein for Mechanics, and learning about the Lagrangian. Of course, there's still much to learn from Feynman.

I'm a beginner, thinking about returning to school for physics, but I'm dipping in with this tome I purchased recently. He's a great explainer for someone at my level.

And I have to brush up on all of the math (and learn calculus...) in order to fully understand. It's exciting that reading him isn't just a cold hard wall. It's proving to be a great guide into what to sort of triage my studies.

I strongly second this one! (Though I have to admit that I purchased a not-cheap edition of the first volume to get started -- though I prefer reading from paper, and don't yet own an eReader and have a bit of a burgeoning library anyway. But thanks for the link! it's nice to have the rest on hand).

   > * I want to be able to simulate GR.
   > * I want to understand QFT
   > * I want to be able to simulate atoms and molecules from first-principles.

With the current technology, assuming standard model of particle physics (which is QFT) is the first-principle, simulating atoms would take trillions of the age of the universe, let alone molecules, or any effect of GR.

A lot of contemporary mathematics have physical roots. Some things I like: Donaldson theory and Seiberg-Witten theory in differential topology, Gromov-Witten theory in sympletic/algebraic geometry. Knowing physics is not necessary to learn these things, but some rough idea of what QFT is doesn't hurt.

For me it was that physics was about reality. In high school the key moment occurred when in a physics lab, after calculating and measuring and calculating more, we placed a cup on the floor, rolled a marble down the ramp and off the desk - and it landed in the cup! At that moment I realized that all the math I had been studying actually meant something in the real world, and was useful for explaining questions I had about the world.

And if the price is a bit much for you, check out http://alpha.math.uga.edu/~shifrin/Spivak_physics.pdf Elementary Mechanics from a Mathematician's Viewpoint which is based on eight lectures Spivak gave in 2004, and which he says "As explained in Lecture 1, these lectures cover material that I had just finished writing, and which I hope will constitute the ˇrst part of a book on Mechanics for Mathematicians."

Holy Shit the price!! No wonder students steal books.

Probably because it's out of print, and sold used from private sellers. My copy of On Lisp cost like $300.

I thought _On Lisp_ was available as a free pdf, which should have caused the price to drop. (I think he joked about the people who were planning to retire on the proceeds at the time).

I just checked Amazon, and it turns out the lowest price one is $ 52.00, and the one I thought was a reprint turned out to be upon closer examination a translation into Japanese. (Which is about thirty dollars or so, from 2007).

I already had the PDF, but wanted a nice small book with the same form factor as ANSI Common Lisp. I guess I was making a lot of money at the time, and this is before I had completely come around to e-books.

This book is fantastic! It's Spivak so it doesn't sacrifice prose for precision, and it does more than teach physics from a mathematical point of view. It also illustrates the massive gap between theoretical physics and experimental physics-- why physics is so hard. An early example in the book is trying to calculate the way a chain hanging off an edge falls: Several pages of investigation reveal how devilishly hard it is to apply the theory to a particular problem-- even demonstrating that a popular physics book gets the problem wrong and the best guide for how to analyze it correctly is experiment.

I hope there's a sequel!

Also on this side of the spectrum, other near-encyclopedic volumes on physics written for mathematicians that I love:

The Clay Institute Monograph on D-Branes (http://www.claymath.org/library/monographs/cmim04.pdf)

The 1996 IAS semester on QFT (https://www.math.ias.edu/qft)

This feels like newer version of "Elements Of Applied Mathematics" by YA. B. Zeldovich, A. D. Myskis [1]. That book title is somewhat misleading as it is not about Applied Mathematics in modern sense, but is rather about how to apply math to solve various problems in physics.

And this is exactly what Michael Stone and Paul Goldbart did in their book as well, albeit their book is more dense/stricter and cover more advanced topics like differential geometry.

[1] - https://archive.org/details/ZeldovichMyskisElementsOfApplied...

So, if, let's say, one knows all the relevant mathematics, how much is left as the (theoretical) physics proper? I mean, sure, we have all these fundamental constants and elementary particles to learn about, but is there anything else that is essentially physics and not math?

There is the entire half of physics that is the empirical verification of the hypotheses left, for example. Theoretical physics cannot be separated from that, in my view.

> Theoretical physics cannot be separated from that

Sure, but books on theoretical physics seem to rarely mention empirical verification. It's mostly math, and I am not sure what is left if you remove it (as known).

as physics student you quickly come to figure out that physical intuition is not the same as mathematical intuition. there are many hacks (for lack of a better term) in physics that a mathematician would've never been able to come up with because they're physically intuitive but not mathematically (a famous example is the Feynman path integral)

Right, we know that much of mathematics grew from physics, but the question remains: what is there in the known theoretical physics that is not (applied) math? (Well, I think I may already know the answer: nothing; but it does not matter, because science is not about what is known...)

I've used this textbook, and frankly, it's good only for people who already know the material and want a fresh look at it. The chapters on group theory and complex analysis are good. Most of the rest are not.

Is there anything covered in the text besides Linear Algebra that may be relevant for Software Engineering and Computer Science?

The chapter on groups is a good introduction. It is tailored for physical applications but the basic is really nicely presented and can be useful before reading, say, books on cryptography.

Hahahaha, funny seeing this here. I took this course at UIUC about 6 years ago taught by Stone.

this is another in the long line of math methods books that plague/bewilder/frustrate physics undergrads

standard: https://www.amazon.com/Mathematical-Methods-Physicists-Seven...

gentler: https://www.amazon.com/Mathematical-Methods-Physical-Science...

another recent addition: https://www.amazon.com/Mathematical-Tools-Physics-Dover-Book...

"purer" than the rest: https://www.amazon.com/Mathematical-Physics-Chicago-Lectures...

"more fun" than the rest: https://www.amazon.com/Geometry-Physics-Introduction-Theodor...

this pair is probably the most rigorous and difficult of the bunch (at least from what i remember):

https://www.amazon.com/Classical-Mathematical-Physics-Dynami...

https://www.amazon.com/Quantum-Mathematical-Physics-Walter-T...

and the grand-daddy of them all

https://www.amazon.com/Methods-Theoretical-Physics-Internati...