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Those diagrams sure do look like a nice formalization of the stuff we were talking about, so I'll bet you're right. Susskind looks awesome! I'll let you know if I run into anything I want to know more on.
Actually, there is one thing: do we have any more motivation for Einstein's special relativity postulates other than "it makes sense and, seriously, what other way would you try to formalize reality?"
The course is called "Modern Physics"--I think it covers relativity and maybe some QM. I'm planning to sit in on some QM classes in the future, but I haven't taken a proper physics class since...2010? so I figured I'd start here.
The example is the moving light clock one that demonstrates special relativity since the light must travel further as compared to the light in a stationary clock.
Semester started yesterday, so the past couple of days have been a lot of last-minute rushing about getting everything ready to go.
I'm TAing a senior/grad level class and I am excited to be able to have expectations of my students. Teaching intro classes is fun, but it's nice to expect people to know the basics & thus be able to spend time talking about the more interesting stuff. Some of my students this semester have been my students in the past, so I know I've got some sharp cookies. It's going to be fun & also too much C.
I'm sitting in on a modern physics class this semester since I have approximate knowledge of how that stuff works but little formal/mathematical understanding. I'm used to graduate classes: the professor was discussing an example, and said, "we'll do the math for this on Friday" and I thought to myself, "but I want the math NOW!"
Cool, sounds like a good all-around useful class. (Well, useful as far as general mathematical knowledge goes...)
I'd love to! Probably over the summer, since this semester I'm TAing a different class.
"Category theory is the result of taking concrete, easy to understand ideas and abstracting them until they're incomprehensible." --Philip Wadler
I'm sure it can--phonics is a good example: once you know it, you can almost always pronounce words that you haven't seen before. Same thing with algebra and equations/derivations/proofs you haven't seen: if the axioms are part of how your mind works, the math comes naturally to you.
Interestingly, I think computer science has some things to learn from linguistics about how to teach programming. I'd like to take the time to properly develop a curriculum for teaching a programming language as a written language one of these days.
I think sequences and series are quite cool, and they tend to pop up all over the place in other fields, including probability, combinatorics, computer science, and communications.
I'm interested: what all does your proofs class cover? Is it something like a foundations class, where you start off with a few definitions and axioms and prove a bunch of stuff, or does it focus on logic and different proof techniques, or a mix?
Perhaps the best thing I can recommend for this whole "why are things true" business is to find someone else in the class to compare and critique proofs with.
Oooh, alignat looks nice! I'll keep that post in mind next time I write a proof (which will hopefully be soon--I've got a little side tangent that I've been working on here and there that I'd like to get online sometime soon). Thanks!
- Like a medical school that ends with a pie eating contest to determine who gets to become a doctor.
This is a disturbingly apt comparison.
- Hell, now I feel like I should rewrite most of the complex numbers primer that I made since I have assumed that the reader is prepared to do some heavy lifting instead of (at least that's how it seemed to me) being 'spoon-fed'.
I say leave it as-is. At least part of the problem I see is that bad math education tends to hand people properties that seem to have appeared from thin air. On the other hand, if you say, "why is X true?", then that gives an explicit clue to people that they should (if interested) sit down and try to work that out.
Proofs are tricky things to write, but I do prefer a proof written to explain, rather than simply to derive the conclusion. A little exposition here and there can go a long way towards showing others the relationships you see. I am hardly innocent here, though!
I do need to work out a good way of writing proofs in LaTeX. It feels like mine always get compressed into a paragraph of math symbols. Maybe I just need to focus on writing a sentence or two of exposition per step and make one paragraph per conceptual step.
Here, it's a little different:
- Derivatives, antiderivatives for single-variable functions
- Riemann sums
- Basic integration, up to u-substitution
- Trigonometric substitutions
- Partial fraction decomposition; applications to integration
- Natural logarithm/Euler's constant
- Logarithmic differentiation
- L'hopital's rule
- Indefinite integrals
- Sequences & series
- Taylor series
- First-order ODEs
The most infuriating part of Calc II is that students are expected to be able to do basic convergence/divergence proofs for the series & sequences part without ever having learned how to write a proper proof in their lives. Grading those exams is painful because the class uses online math homework, so for many, the first time they have to write a proof for another human is on that exam. Each answer you have to read closely to see if they understand the ideas but can't explain them well or if they just wrote random words on the page.
So many students give up on that section since it's not well connected to any other material in the class and some of the concepts (especially the various remainder theorems) cannot easily be rotely applied to a problem.
And, yeah, "I can do this on a computer" does you no favors when you're trying to understand why some technique (even in another field of study) works, rather than just "oh I have this technique, let me apply it to some problems".
Anyway, you and I should be thankful that we've had something of a nonstandard education in math, and do our best to help others see what we see.