December 11, 2013 7:05 AM Subscribe

I'm taking a numerical methods class and there are all these discretization schemes of partial differential equations named after pairs of dudes and they all are kinda the same, maybe a bit different in indexes....
I'm trying to organize it all in my head, like a frat house, with the dudes that worked on the same scheme being roommates, but it seems to be taking a long time to actually "find" a place for each scheme in their "rooms" and keeping it there in a sort of visual arrangement.
Test is no books no notes, and everything kinda of just jumbles inside my head right now.

posted by spacefire to Education (10 answers total) 2 users marked this as a favorite

posted by spacefire to Education (10 answers total) 2 users marked this as a favorite

It seems crazy to me that such straight memorization would be part of what was being "tested" on an exam. Is it possible there are big-picture conceptual ideas that you could organize these equations under? This would help you *both* with remembering the equation and with understanding the ideas that help you to know when to apply which equation.

posted by Betelgeuse at 7:35 AM on December 11, 2013

posted by Betelgeuse at 7:35 AM on December 11, 2013

Write them down.

Don't just look at it. Just keep writing it over and over and over and say it aloud to yourself every time you do. Do #1 until you have it memorized then add in #2. Memorize #2, go back and repeat 1&2. Now add #3, memorize #3, go back and repeat 1,2,&3. Continue.

Being 100% right on half the formulas is better than being 50% right on all the formulas.

Depending on how many there are when you get into the test, do not open the test book, do not look at any questions, do not look at any answers, especially don't look at anything with a number in it. On your scrap paper write them all down. Now take your test.

posted by magnetsphere at 7:35 AM on December 11, 2013 [5 favorites]

Don't just look at it. Just keep writing it over and over and over and say it aloud to yourself every time you do. Do #1 until you have it memorized then add in #2. Memorize #2, go back and repeat 1&2. Now add #3, memorize #3, go back and repeat 1,2,&3. Continue.

Being 100% right on half the formulas is better than being 50% right on all the formulas.

Depending on how many there are when you get into the test, do not open the test book, do not look at any questions, do not look at any answers, especially don't look at anything with a number in it. On your scrap paper write them all down. Now take your test.

posted by magnetsphere at 7:35 AM on December 11, 2013 [5 favorites]

Big +1 to magnetsphere -- always write your memorized formulas first at the beginning of the test.

Do you always use this "room" scheme for memorizing, or did you read it somewhere as a memorization trick and decide to use it now? Because frankly I don't think it's well suited to the task. Spatial tricks like this are really good for memorizing the ways that different things relate to one another, but it sounds like you just need to know each individual formula on its own.

Index cards and writing formulas over and over worked for me in my math classes. If you need to associate names with formulas, there is usually an overwrought mnemonic you can employ if you think hard enough... like "Thompson's formula's first operation is a + because + looks like T for Thompson." Silly but it gets the job done (eventually).

It's going to take time, unfortunately. If you have practice problems that you can work on that use the equations, that will be a good use of your time and help reinforce the memorization, but a good amount of time is going to have to be rote learning.

posted by telegraph at 7:41 AM on December 11, 2013

Do you always use this "room" scheme for memorizing, or did you read it somewhere as a memorization trick and decide to use it now? Because frankly I don't think it's well suited to the task. Spatial tricks like this are really good for memorizing the ways that different things relate to one another, but it sounds like you just need to know each individual formula on its own.

Index cards and writing formulas over and over worked for me in my math classes. If you need to associate names with formulas, there is usually an overwrought mnemonic you can employ if you think hard enough... like "Thompson's formula's first operation is a + because + looks like T for Thompson." Silly but it gets the job done (eventually).

It's going to take time, unfortunately. If you have practice problems that you can work on that use the equations, that will be a good use of your time and help reinforce the memorization, but a good amount of time is going to have to be rote learning.

posted by telegraph at 7:41 AM on December 11, 2013

How about a mnemonic device? "David is different from Davidson by inDex 2" or something.

Otherwise, I would picture the guys themselves rather than their frat rooms. Make David like the statue of David and make Davidson like a Harley gangster. The harley guy is more tough so he's +2 higher (or whatever).

posted by St. Peepsburg at 7:44 AM on December 11, 2013

Otherwise, I would picture the guys themselves rather than their frat rooms. Make David like the statue of David and make Davidson like a Harley gangster. The harley guy is more tough so he's +2 higher (or whatever).

posted by St. Peepsburg at 7:44 AM on December 11, 2013

I'm assuming by pairs of dudes you're referring to methods like Lax-Fredrichs, Lax-Wendroff, and Crank-Nicolson?

Instead of trying to memorize the equations, it may be better to visualize the different schemes by the shape of their respective stencils and think about the finite differences that approximate both the u_t term and the u_x term.

Picture a rectangular grid of points where the left-right axis represents space and the up-down axis represents time. When approximating the value of an arbitrary point in some row, what is the contribution of the points surrounding it?

Here's an example for the Crank-Nicolson method.

posted by RonButNotStupid at 7:45 AM on December 11, 2013 [2 favorites]

Instead of trying to memorize the equations, it may be better to visualize the different schemes by the shape of their respective stencils and think about the finite differences that approximate both the u_t term and the u_x term.

Picture a rectangular grid of points where the left-right axis represents space and the up-down axis represents time. When approximating the value of an arbitrary point in some row, what is the contribution of the points surrounding it?

Here's an example for the Crank-Nicolson method.

posted by RonButNotStupid at 7:45 AM on December 11, 2013 [2 favorites]

Peter Lax once rushed into a computing center that had been occupied by violent protesters and helped diffuse a bomb that would have seriously injured over a thousand people.

posted by RonButNotStupid at 8:06 AM on December 11, 2013 [2 favorites]

Whatever your method of memorization, once you actually get to the test, one tip is to do a "brain dump" right at the beginning. Basically spend the first few minutes writing down the formulas (or sketches of them) on a piece of scratch paper. Then when you do the questions, you can just refer to the scratch sheet.

I think**RonButNotStupid** is on the right track regarding keeping track of the different methods - a lot of them follow a general form, so you just need to memorize the differences - whether the grid points, basis functions, whatever.

posted by bluefly at 1:04 PM on December 11, 2013

I think

posted by bluefly at 1:04 PM on December 11, 2013

Don't do the room trick. That's best for sequences.

Self-test is the best way to learn anything. Repeated study-test. That's essentially what flash cards do. Focus on the differences if they're very similar.

posted by supercres at 1:36 PM on December 11, 2013

Self-test is the best way to learn anything. Repeated study-test. That's essentially what flash cards do. Focus on the differences if they're very similar.

posted by supercres at 1:36 PM on December 11, 2013

I've taken graduate-level numerical methods classes. The discretization and estimate-updating rules should be given to you on the exam. Check with your instructor, but tedious memorization should not be a major part of what the exam is testing.

posted by Nomyte at 1:58 PM on December 11, 2013

posted by Nomyte at 1:58 PM on December 11, 2013

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Write every formula on a note card, dude names on one side and formula on the other. Go through the note cards backwards and forwards like it's your job, trying to recite the formula if you are looking at dude names and calling out dude names if you are looking at the formula. Stop on any you get wrong and repeat it out loud a few times. Shuffle cards. Repeat until you can do it all perfectly.

Also, start with only a couple note cards, and do those perfectly. Then add in a couple more. Then a couple more. Until you can do them all perfectly.

Always worked for me. Maybe not the most efficient, but got the job done.

posted by 3FLryan at 7:15 AM on December 11, 2013 [1 favorite]