3 ms·

Galamian's book -- loved it! > convex optimization I assume you are minimizing -- maximizing is easily NP-hard. So, get some supporting hyperplanes of the co

by graycat 12y ago

Galamian's book -- loved it! > convex optimization I assume you are minimizing -- maximizing is easily NP-hard. So, get some supporting hyperplanes of the convex epigraph and use linear programming to minimize subject to those hyperplanes as constraints. Then add a constraint and try again. There is also a cute way to do central cutting planes that can be better numerically. So, for many non-linear problems, if are maximizing, then the dual is a convex minimization, and that can help. This can be called Lagrangian relaxation. I never thought that how to do violin practice was so tricky -- just work to get the fingers on the notes, in time and in tune, and then do it a lot until get a lot of facility (hear the note(s) just before playing them), sometimes return and play very slowly and deliberately, and then work on expression -- the fun part. But then I never made much progress. The best I did was the D major section of the Bach "Chaconne", and that was fantastic fun -- I played the repeated notes that made them sound insistent! I regard the end of the D major section as the climax of the piece and find it fantastic.

TTPrograms 12y ago
I find it interesting that you're response to studying a field that has entire conferences dedicated to it is "So, just do this!"
- graycat 12y ago
  > interesting It worked for me, in violin, As we know, things should be as simple as possible but not simpler. My approach to learning mathematics is quite different from learning to play violin but also is based mostly in independent study. In violin, I got started when I was a math grad student at Indiana University. Of course there is a terrific music school there, and at the time my dorm was next door with a lot of music students. One day one of the violin students, darned good, a Stern protege, put his violin under my left chin, and I was off and running, took a violin course in the music school. After some years of work from Galamian's book and just self-teaching, I went for some lessons. Sure, I started with the "Preludio" of the Bach E major partita. Of course early on there is a fast shift from 1st position to 5th; I happened to get the note after the shift right; and the teacher exclaimed "You could play in an orchestra!". Gee, that shift is the main issue for playing in an orchestra? I doubt that! Maybe he thought I was sight reading that music! Not a chance! I'd worked hours on each note, note by note, checking intonation over and over, etc. That shift I'd likely done 1000 times. I hadn't really been learning just the piece but had been using the piece as an exercise to learn to play violin, starting from very little! So, that shift to 5th position, at two places in that music, was the first I'd learned. Sure, I could have used that skill with that shift elsewhere. I learned the whole piece; the learning was a lot of fun. But, I learned it, self-teaching. I had a good ugrad math major but didn't like what the IU math department had me doing: Of the three courses they started me with, two of them had just what I'd already learned in ugrad school, and the third started with what I'd learned in an NSF summer program the previous summer. But there was other material I wanted to learn. So, IU and I didn't get along, and I went, got a job, and studied on evenings and weekends, independently. That study worked out well and was, really, except two graduate courses all I needed for my Ph.D. I did the research for that independently in my first summer after the two courses. So, my approach to learning has worked. Computer science and programming? I've taught college and grad courses in it, but I never really took one. What I'm saying did work for me. Of course if you want then you can try more complicated ways. For the OP, she was concerned that her playing sounded mechanical. Well, once she has the notes on time and in tune and practices until they are "in her fingers" well enough that she can concentrate on the expression, then she should, just think about how she wants it to sound. For convex minimization, once a guy had a 0-1 integer linear program with 40,000 constraints and 600,000 variables. He'd tried simulated annealing without much luck. I looked at his constraints, and 16 of them were special, and I put them in the objective function with Lagrange multipliers. Then the dual problem was to maximize a concave function, and I did the linear programming and supporting hyperplane approach I outlined. After about 500 primal-dual iterations in 900 seconds on a 90 MHz PC, linear programming via the IBM OSL, I found a feasible solution, guaranteed from the duality, to be within 0.025% of optimality. It was fun! But I do recommend the central cutting plane idea.
gtani 12y ago
That reminds me, somebody borrowed my Galamian and never returned it... I want to read that bit about vowels and consonants again. I think all of this is about you need to figure out how to practice or learn CUDA or Mandarin or whatever for yourself. My dad's advice on learning math was simple "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right". For some students, that's all they need to be told What this guy talks about at the bottom of page is similar, i.e. there are people who know the materials and teaching methods that have worked int he past, but the only person who can teach yourself is yourself: http://www.allaboutjazz.com/janek-gwizdala-cooking-up-a-little-bass-magic-janek-gwizdala-by-ian-patterson.php http://www.allaboutjazz.com/janek-gwizdala-cooking-up-a-litt...
- wallflower 12y ago
  > "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right" In Rafe Esquith's classroom, he talks about how they take that a step further. They knock the ball out of the park on standardized testing because they specifically try to come up with wrong answers for a math question. They learn the psychology of making test answers by doing - and don't fall into the traps. http://www.amazon.com/dp/B000OZ0NRG/ http://www.amazon.com/dp/B000OZ0NRG/

by graycat 12y ago

TTPrograms 12y ago

I find it interesting that you're response to studying a field that has entire conferences dedicated to it is "So, just do this!"

graycat 12y ago
> interesting It worked for me, in violin, As we know, things should be as simple as possible but not simpler. My approach to learning mathematics is quite different from learning to play violin but also is based mostly in independent study. In violin, I got started when I was a math grad student at Indiana University. Of course there is a terrific music school there, and at the time my dorm was next door with a lot of music students. One day one of the violin students, darned good, a Stern protege, put his violin under my left chin, and I was off and running, took a violin course in the music school. After some years of work from Galamian's book and just self-teaching, I went for some lessons. Sure, I started with the "Preludio" of the Bach E major partita. Of course early on there is a fast shift from 1st position to 5th; I happened to get the note after the shift right; and the teacher exclaimed "You could play in an orchestra!". Gee, that shift is the main issue for playing in an orchestra? I doubt that! Maybe he thought I was sight reading that music! Not a chance! I'd worked hours on each note, note by note, checking intonation over and over, etc. That shift I'd likely done 1000 times. I hadn't really been learning just the piece but had been using the piece as an exercise to learn to play violin, starting from very little! So, that shift to 5th position, at two places in that music, was the first I'd learned. Sure, I could have used that skill with that shift elsewhere. I learned the whole piece; the learning was a lot of fun. But, I learned it, self-teaching. I had a good ugrad math major but didn't like what the IU math department had me doing: Of the three courses they started me with, two of them had just what I'd already learned in ugrad school, and the third started with what I'd learned in an NSF summer program the previous summer. But there was other material I wanted to learn. So, IU and I didn't get along, and I went, got a job, and studied on evenings and weekends, independently. That study worked out well and was, really, except two graduate courses all I needed for my Ph.D. I did the research for that independently in my first summer after the two courses. So, my approach to learning has worked. Computer science and programming? I've taught college and grad courses in it, but I never really took one. What I'm saying did work for me. Of course if you want then you can try more complicated ways. For the OP, she was concerned that her playing sounded mechanical. Well, once she has the notes on time and in tune and practices until they are "in her fingers" well enough that she can concentrate on the expression, then she should, just think about how she wants it to sound. For convex minimization, once a guy had a 0-1 integer linear program with 40,000 constraints and 600,000 variables. He'd tried simulated annealing without much luck. I looked at his constraints, and 16 of them were special, and I put them in the objective function with Lagrange multipliers. Then the dual problem was to maximize a concave function, and I did the linear programming and supporting hyperplane approach I outlined. After about 500 primal-dual iterations in 900 seconds on a 90 MHz PC, linear programming via the IBM OSL, I found a feasible solution, guaranteed from the duality, to be within 0.025% of optimality. It was fun! But I do recommend the central cutting plane idea.

gtani 12y ago

That reminds me, somebody borrowed my Galamian and never returned it... I want to read that bit about vowels and consonants again. I think all of this is about you need to figure out how to practice or learn CUDA or Mandarin or whatever for yourself. My dad's advice on learning math was simple "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right". For some students, that's all they need to be told What this guy talks about at the bottom of page is similar, i.e. there are people who know the materials and teaching methods that have worked int he past, but the only person who can teach yourself is yourself: http://www.allaboutjazz.com/janek-gwizdala-cooking-up-a-little-bass-magic-janek-gwizdala-by-ian-patterson.php http://www.allaboutjazz.com/janek-gwizdala-cooking-up-a-litt...

wallflower 12y ago
> "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right" In Rafe Esquith's classroom, he talks about how they take that a step further. They knock the ball out of the park on standardized testing because they specifically try to come up with wrong answers for a math question. They learn the psychology of making test answers by doing - and don't fall into the traps. http://www.amazon.com/dp/B000OZ0NRG/ http://www.amazon.com/dp/B000OZ0NRG/