I’d be interested in learning more about how he does that, if anyone knows…
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So you memorize theorems as verbal statements as opposed to equations?
Derivative of the secant and cosecant functions
Psst ( as if someone is trying to get your attention).
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Glad to hear about your interests in this. I did math, chemistry and physics starting late in college. My learning curve was straight up so I looked for every edge I could get.
My interest is in mathematics. I’m no better than anyone (by a long shot) but I’m not bored or afraid as many people are. I can tell you about the best, if any tools to focus on.
There are a couple Math-Wiz type video courses (particularly for kids- look there too) that collect fascinating shortcuts to multiplying and adding numbers. You can find these and see if any really speak to you.
One of limited interest is Vedic Math. That one has means of doing quite complicated calculations but each seem to be at the edge of a solution. That is, only for problems where the numbers are of a special form or type. Such as beginning and ending with certain digits or other restrictions: 3xxx3 times 2xx2. I’m not sure but limited.The methods are very cool but hardly apply generally and require as much effort to learn as the times table.
You would make better use (truly) of your time by memorizing a table of ratios; the decimals for 1 over 2 to 9, then 2 over 3 to 9, etc. Use no mnemonics just brute force. The results of many calculations will pop out at you if you have such things handy. At school we learned times table but not this. Print this out and leave it on the wall to see all day. It will get through to you in time.
The best thing I ever picked up is the Korean finger math system in the book called Finger Math. I think it is called Chisembop (phonetically). All I use it for is counting. It is a means of using the ten fingers to count to 99. With some practice you can do very rapid addition but need to keep in practice. The multiplication and division are only speedy because of the speed of the addition if I recall. I use it when I need to know how many letters, syllables, vowels or words are in a sentence, song, title etc.
Finger Math is worth following getting at the library.
There is an Indian version described in Brain Hacks that uses each finger to count more than one thing. I have seen this in use and it gets ridiculous complicated. Just give me my 99 fingers.
More than anything I can tell you that there are no real shortcuts apart from actual work. The best thing then is start early so you might finish on time. I said elsewhere here that problems are alike one textbook to the next. You must learn to find the general theme (Atwood machine, acceleration, emitter follower circuit, electrostatic force) and learn how each group of such problems is built. These are called problem sets and for a given chapter they only stress you out to learn how the new equation is used. Once you have seen these you should list out their variety and categorize their solutions. Then on a test you just think Where have I seen you before. This only takes work.
Almost left it out. Use pictures for everything. In Trig, make circles and waves. In Calc, draw functions. In Physics draw everything. This is the best way to internalize what the numbers are describing.
Next to that is finding an audience or friend to whom you must-must describe what you are doing. Re-relating anything serves to play it on a screen in your head that you otherwise would not have access to. My friends still don’t know what I’m talking about but without them listening (and eyes glazing over) I would rarely solve any problem.
The better way to describe it is that you must properly understand each subject. The equation for the electrostatic force of a charged particle has no use apart from such a particle. I think - Of course the charge forms a sphere and any sphere will have one over 4pi whatever it is in its description. And its going through space so of course it will involve epsilon sub zero to describe the permittivity. With this I would derive all the bits needed to work out solutions for electrostatics and got an A. For mechanics I had lovely phrases and tricks to keep the equations in mind but lacked the internal feel and problem solving practice, bad grade. You need the equations in your bones, not your head.
I think the reason I’m not much on mnemonics for these subjects is that it is a distraction. They are a tool for remembering an arbitrary list of things; digits, names, locations. If you have no idea of what the equations are for are how they are used then sure such things would help. But they will not help with the insight you need to get the equation to work. As I related with the charge of particle, there could hardly be anything less arbitrary. It makes its own Mind Map of relations and qualities.
Good luck and let us know what you end up with.
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And link for your webpage is?
Thanks Yuri. I notice that the link has disappeared. Is it current somewhere else.
Honestly, the best way to memorize a theorem and all the little caveats is to simply go out an prove the theorem yourself. All my undergrad math profs recommended math majors to do this.