The Universe Is Not Locally Real

[Fireball]

A linear algebra class offered by the math department seems to be one of those classes few physics majors take. Not sure why. It's a great intro to proofs. My alma mater also offered a class that used Dennis Sentilles' book for a class that focused primarily on how to "do" proofs. I got a tiny bit of series solutions and Fourier Transforms at the very end of my DE class. I went to work in electromagnetic propagation topics right out of uni. I didn't get enough of what I needed at uni. Antenna radiation propagation and scattering is full of it. I got out of the antenna business 22 years ago, and don't remember much. I remember even less about quantum mechanics, which I never used.

That's odd, as linear algebra figures prominently in Quantum Mechanics, and also in tensor calculus.  One good book is, "Mathematical Methods in the Physical Sciences" by the late Professor Mary L. Boas.   Her son, an academic mathematician, keeps an errata of his mother's book.

We used Boas' book in our junior-level Mathematical Physics class. There was indeed a lot of linear algebra in it. That part was easier for me, as I had already studied LA before taking that class. Like I said, I had no dealings with QM after I graduated. Maybe your memory is better than mine from 40 years ago?

[Jehanne]

That's odd, as linear algebra figures prominently in Quantum Mechanics, and also in tensor calculus.  One good book is, "Mathematical Methods in the Physical Sciences" by the late Professor Mary L. Boas.   Her son, an academic mathematician, keeps an errata of his mother's book.

We used Boas' book in our junior-level Mathematical Physics class. There was indeed a lot of linear algebra in it. That part was easier for me, as I had already studied LA before taking that class. Like I said, I had no dealings with QM after I graduated. Maybe your memory is better than mine from 40 years ago?

The only QM book that I have studied is David Griffiths', but ladder operators figure prominently in QM.

[polymath257]

We used Boas' book in our junior-level Mathematical Physics class. There was indeed a lot of linear algebra in it. That part was easier for me, as I had already studied LA before taking that class. Like I said, I had no dealings with QM after I graduated. Maybe your memory is better than mine from 40 years ago?

The only QM book that I have studied is David Griffiths', but ladder operators figure prominently in QM.

Mostly when discussing angular momentum/spin. There are also many approximation methods that relay on finding eigenvalues to matrices.

[polymath257]

A linear algebra class offered by the math department seems to be one of those classes few physics majors take. Not sure why. It's a great intro to proofs. My alma mater also offered a class that used Dennis Sentilles' book for a class that focused primarily on how to "do" proofs. I got a tiny bit of series solutions and Fourier Transforms at the very end of my DE class. I went to work in electromagnetic propagation topics right out of uni. I didn't get enough of what I needed at uni. Antenna radiation propagation and scattering is full of it. I got out of the antenna business 22 years ago, and don't remember much. I remember even less about quantum mechanics, which I never used.

Math classes don't emphasize Fourier series and transforms nearly enough. The difficulty is that the main results are not so easy to prove and there are a LOT of subtleties quite close to even undergraduate courses.

For example, take a continuous periodic function and look at its Fourier series. Does that series actually converge to the original function?

The answer is complicated. In general, the series does NOT have to converge everywhere, let alone converge to the function. But it *does* converge 'almost everywhere' to the function. But this is very difficult to prove and is usually not even done in graduate classes unless it is specifically for those going into harmonic analysis.

Even the partial results mentioned in undergraduate classes are usually not proved in those classes. The proofs are MUCH deeper than can be done effectively at the undergraduate level.

Even a good treatment of the dirac delta 'function' usually waits until graduate level measure theory.

[polymath257]

We used Boas' book in our junior-level Mathematical Physics class. There was indeed a lot of linear algebra in it. That part was easier for me, as I had already studied LA before taking that class. Like I said, I had no dealings with QM after I graduated. Maybe your memory is better than mine from 40 years ago?

The only QM book that I have studied is David Griffiths', but ladder operators figure prominently in QM.

Eisberg and Resnik is a very good book for the undergraduate level.

[Jehanne]

The only QM book that I have studied is David Griffiths', but ladder operators figure prominently in QM.

Eisberg and Resnik is a very good book for the undergraduate level.

While we're at it, have to mention Fundamentals of Physics by Halliday, Resnick and Walker, voted the greatest introductory physics textbook by the American Physical Society.

[Mister Agenda]

My C in Calculus does not bode well for taking on QM at a deeper level. I'm 60 though, will qualify for free classes soon and I'm planning to retire in a couple of years. I've got a good layman's grasp of evolutionary biology, I might go deeper into that. Or take stuff relevant to financial planning so my retirement goes smoother (better late than never).

[Jehanne]

My C in Calculus does not bode well for taking on QM at a deeper level. I'm 60 though, will qualify for free classes soon and I'm planning to retire in a couple of years. I've got a good layman's grasp of evolutionary biology, I might go deeper into that. Or take stuff relevant to financial planning so my retirement goes smoother (better late than never).

As far as graduate school goes, crappy grades are not necessarily a showstopper; you can always take the GRE, both general and subject tests in physics and mathematics, and prove yourself there. If an admissions committee would inquire further, you can make-up whatever excuse suits the moment to explain away your undergraduate record. Really good graduate schools will also test their potential candidates with written and oral exams, yet another opportunity to prove one's self.

[Anomalocaris]

I just realized I don’t understand anything about quantum mechanics because I think quantum mechanics is something i can understand.

[Mister Agenda]

My C in Calculus does not bode well for taking on QM at a deeper level. I'm 60 though, will qualify for free classes soon and I'm planning to retire in a couple of years. I've got a good layman's grasp of evolutionary biology, I might go deeper into that. Or take stuff relevant to financial planning so my retirement goes smoother (better late than never).

As far as graduate school goes, crappy grades are not necessarily a showstopper; you can always take the GRE, both general and subject tests in physics and mathematics, and prove yourself there.  If an admissions committee would inquire further, you can make-up whatever excuse suits the moment to explain away your undergraduate record.  Really good graduate schools will also test their potential candidates with written and oral exams, yet another opportunity to prove one's self.

Yah, the professor was in his eighties and hard of hearing. I think I could have done better with an instructor who answered the questions I asked instead of the ones he heard. Maybe I'll re-take Calculus and see if I can do better...hopefully my 60-year old brain is still capable.