Mathematics

[DavidW]

Actually, it was Michigan. Things may be different now though, that was mid-1970s. And you're right: we didn't see Hamilton at all in that course. However, where I teach now, our upper division classical mechanics course does at least show the students Hamilton's equations.

That is good to hear.  Since my experience is based upon when I went to college it is dated.  As a big example, what I did in college were all pencil and paper calculations.  My former students that went into Physics became so well versed in computational methods that they ended up in careers in data science instead of physics!

[Biffo]

That is good to hear.  Since my experience is based upon when I went to college it is dated.  As a big example, what I did in college were all pencil and paper calculations.  My former students that went into Physics became so well versed in computational methods that they ended up in careers in data science instead of physics!

I am beginning to feel a bit less decrepit - but not much. Here in the UK they were starting to introduce 'Modern Maths' and I was in the last year at my school that did the old syllabus. Modern Maths seem to date from the 18th century or later, the stuff I did from the 5th century BCE. Actually we did a lot of calculus (late 17th century). Pocket caculators were still in the future and we used log tables.

[krummholz]

That is good to hear.  Since my experience is based upon when I went to college it is dated.  As a big example, what I did in college were all pencil and paper calculations.  My former students that went into Physics became so well versed in computational methods that they ended up in careers in data science instead of physics!

Similar experience here: I didn't learn much about computational methods in class and had to teach myself how to code when doing my dissertation. In our courses, we learned analytical methods exclusively... and despite the importance of computers today in research, even today, where I work now, the same is true in the core courses, including classical, quantum, and E&M. Junior/senior lab is a different story, and colleagues who've taught it have taken the opportunity to introduce the students to Python and to computational techniques (I've yet to be assigned to teach that course though).

[Mapman]

That is good to hear.  Since my experience is based upon when I went to college it is dated.  As a big example, what I did in college were all pencil and paper calculations.  My former students that went into Physics became so well versed in computational methods that they ended up in careers in data science instead of physics!

At my college, they introduced Lagrangian mechanics to some freshmen, but only ones who had taken AP Physics. I didn't, so I don't know the full contents of that course. The advanced classical mechanics course covered most of the book by Taylor, which includes a brief introduction to Hamiltonian mechanics; however I didn't understand the connection to Quantum until graduate Classical Mechanics.

We had two undergraduate courses in Quantum mechanics, the first mostly wave mechanics and the second heavily using linear algebra. I much preferred the second semester. (Instead of Griffiths, we used the two books by Townsend. The second semester used Quantum Mechanics.)

I, like you, also took the Putnam exam (twice), and was able to solve one problem each time. (Although, to be fair, one of the years had a particularly "easy" first problem.)

[Archaic Torso of Apollo]

At my college, they introduced Lagrangian mechanics to some freshmen, but only ones who had taken AP Physics. I didn't, so I don't know the full contents of that course. The advanced classical mechanics course covered most of the book by Taylor, which includes a brief introduction to Hamiltonian mechanics; however I didn't understand the connection to Quantum until graduate Classical Mechanics.

I have no idea what you guys are talking about; however, it reminds me of possibly the most off-putting intro to a textbook ever written. This is from States of Matter by David L. Goodstein:

"Ludwig Boltzmann, who spent much of his life studying Statistical Mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study Statistical Mechanics."

[Biffo]

I have no idea what you guys are talking about; however, it reminds me of possibly the most off-putting intro to a textbook ever written. This is from States of Matter by David L. Goodstein:

"Ludwig Boltzmann, who spent much of his life studying Statistical Mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study Statistical Mechanics."

Strange (?) coincidence, the lecturer who taught us Statistical Mechanics also committed suicide.

[DavidW]

I, like you, also took the Putnam exam (twice), and was able to solve one problem each time. (Although, to be fair, one of the years had a particularly "easy" first problem.)

Nice!

[Scion7]

[Florestan]

I have no idea what you guys are talking about; however, it reminds me of possibly the most off-putting intro to a textbook ever written. This is from States of Matter by David L. Goodstein:

"Ludwig Boltzmann, who spent much of his life studying Statistical Mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study Statistical Mechanics."

Strange (?) coincidence, the lecturer who taught us Statistical Mechanics also committed suicide.

As a Romanian poet put it:

Do not inquire into these laws,
For you go crazy if you understand them.

Original, rhyming:

Nu cerceta aceste legi,
Că eşti nebun când le-nţelegi!

[steve ridgway]

Certainly you've mastered turning it off and then on again!

The usual answer to that was "I can't find the power button with all the lights in here having gone off"!

[Szykneij]

The usual answer to that was "I can't find the power button with all the lights in here having gone off"!

   

[steve ridgway]

Or "Well it all worked last Friday when we were in the old warehouse".

[Florestan]

Thank you all for your replies. I'm not surprised that most of you/us are at least mathematically literate.

Btw, in the last two evenings I tried hard to remember how to prove Pythagora's Theorem. I managed it for an isosceles triangle but not for the general triangle. Any suggestions? Just a hint, please, not the whole thing, thank you. 

[DavidW]

Thank you all for your replies. I'm not surprised that most of you/us are at least mathematically literate.

Btw, in the last two evenings I tried hard to remember how to prove Pythagora's Theorem. I managed it for an isosceles triangle but not for the general triangle. Any suggestions? Just a hint, please, not the whole thing, thank you. 

Try square packing.  That is consider the squares that have edge length a, b and c respectively.  Consider the original triangle.  See what you can do.  You can even draw them, cut them out and then move the pieces around.

[Florestan]

Try square packing.  That is consider the squares that have edge length a, b and c respectively.  Consider the original triangle.  See what you can do.  You can even draw them, cut them out and then move the pieces around.

Thanks a lot, will work it out tomorrow.

[coffee]

For the OP, I was a bit of a math star in high school, winning some local competitions, but I was never at a national level.

I still enjoy math a bit, but I've forgotten so much that I can barely do anything....

That Pythagoras, man. Someone should've told him he was an irrational number.

[DavidW]

Coffee, he said just a hint!

[coffee]

Coffee, he said just a hint!

My bad! I'll delete it!

[Florestan]

My bad! I'll delete it!

Oh yes, please do! 

Btw, hearty congrats for starting to contribute in various threads. I was right in telling you that you do have interesting things to say. Keep them coming, buddy!

[coffee]

Oh yes, please do! 

Btw, hearty congrats for starting to contribute in various threads. I was right in telling you that you do have interesting things to say. Keep them coming, buddy!

My purpose is to persuade you to let me do my thing here. I haven't surrendered.