hello
what is advance mathematics?
what is advance mathematics?
I recall just one time in my calculus course when our problem could actually be answered with an actual number, and I did so. The professor marked it down, even though he admitted my answer was correct AND I had shown all my work in getting to the answer. He explained that I should have stopped a step earlier, that mathematicians find numerical answers repugnant and devoid of meaning."Advanced" is in the eye of the beholder, but in terms of a university curriculum, a reasonable criterion is that advanced math courses are based on proofs rather than calculation. Your homeworks and tests in an advanced math class will very likely include more words than numbers. Some examples: linear algebra, abstract algebra, analysis (real/complex/functional), topology, geometry (algebraic/differential), number theory.
Sounds like you actually had a mathematician teaching the class; did you do proofs? My calculus courses were purely mechanical; we were told the theorems, shown the techniques, and plugged-and-chugged our way to the answer. (To be fair, my Calc I teacher usually included an extra credit question asking us to prove, or at least justify with words, some theorem or procedure.)I recall just one time in my calculus course when our problem could actually be answered with an actual number, and I did so. The professor marked it down, even though he admitted my answer was correct AND I had shown all my work in getting to the answer. He explained that I should have stopped a step earlier, that mathematicians find numerical answers repugnant and devoid of meaning.
He was definitely a true mathematician. I don't really recall doing proofs although I'm sure we were shown them. Working to get the answers is all I can remember. There were some doozies.Sounds like you actually had a mathematician teaching the class; did you do proofs? My calculus courses were purely mechanical; we were told the theorems, shown the techniques, and plugged-and-chugged our way to the answer. (To be fair, my Calc I teacher usually included an extra credit question asking us to prove, or at least justify with words, some theorem or procedure.)
This reminds me way back when. Did you do them with a slide rule like I did?Working to get the answers is all I can remember. There were some doozies.
Certainly not in math class - no numbers allowed. But we did plenty of calculations in Chem Engineering. I was amongst the first classes to use calculators instead of slide rules. I had both and knew how to use both, but of course quickly dropped the slide rule.This reminds me way back when. Did you do them with a slide rule like I did?
I never did stochastic calculus explicitly. I took a course on stochastic processes and stochastic signal processing. I think that is related, but probably as a subtopic.I have two candidates for Advanced Mathematics and I'd be surprised if anyone had studied either one:
I learned the former and was completely humbled by the latter.
- Stochastic Caclulus, including Ito's Lemma and the Feynman-Kac theorem
- Calculus of Variations
I can relate. I got placed into P-chem the first semester of my freshman year but was only is second semester calculus. So I had never really dealt with differential equations (and was a year out of taking Diffy-Q) when all of a sudden we were having to deal with partial differential equations in P-chem. I definitely struggled in that course. Most of the other folks did as well, but I was way out on a limb in comparison to the majority. Fortunately one of the chem majors took some pity on this floundering freshman and we studied together. I ended up with a B in the course and was happy to take it.The most advanced math I recall, and I call it that only because I never really ‘got it’, was differential equations. Oh wait, that stuff in P Chem was even worse. I got an A in both those classes but only because everyone else was more lost than I was.
Can you explain why Nature cannot ? I can see that Advanced Math is dealing with Ratio's but how? is "All math just ratios"Advanced math is advanced ratios. All math is just ratios. Just a tool.
Advanced math can ratio apples and oranges. Nature can not.
If it was going to be anybody, you would be at the top of the list.I never did stochastic calculus explicitly. I took a course on stochastic processes and stochastic signal processing. I think that is related, but probably as a subtopic.
I did calculus of variations in a couple of my senior physics courses, one dealing with mechancis and the other with electromagnetics. It was pretty interesting, but I would have to agree it was initially quite humbling.
So... surprise!!
There's not much time spent on probability or statistics of any kind. I got a big dose of it once I went to graduate school, and made good use of it on the job. That experience convinced me that it would have been nice to learn it much earlier. Maybe less time studying poetry or French history or whatever the hell else they tried to shove in our heads.Other fun topics we covered that are rarely seen in the US were combinatorics and tesselations. Combinatorics like there are 15 people at a party, 3 named Smith and 2 named Jones. If everyone shakes hands except people with the same name, how many hanshakes occur?
The Stochastic Calculus deals with functions that are everywhere continuous but nowhere differentiable. In common terms they are made up of corners like the one at the origin for the absolute value function. A Wiener process is an example.I never did stochastic calculus explicitly. I took a course on stochastic processes and stochastic signal processing. I think that is related, but probably as a subtopic.
I did calculus of variations in a couple of my senior physics courses, one dealing with mechancis and the other with electromagnetics. It was pretty interesting, but I would have to agree it was initially quite humbling.
So... surprise!!
I must have seen some proofs somewhere, but I can't remember where. At one point, my Calculus teacher asked me where I got a certain number and I replied in one word, "Identity". I think he didn't expect me to know that. In fact, I didn't expect me to know that because it had been at least 10 years since I learned it! All I'm sure of is that some proofs wandered through the class room somewhere in the 1960's.I don't really recall doing proofs although I'm sure we were shown them.
by Gary Elinoff
by Robert Keim