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chroot

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If you just hate taking notes in class, you might be able to get away with just listening to the lectures, and then going home and taking notes while reading your book. Either way, Stephen is right: you can read a book or listen to a speaker and have no trouble follow along for the entire ride -- but you won't be able to remember a single thing unless you actually use it.

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i believe dr. nash didn't even go to class at all, much less take notes.

it's kinda like becoming a mechanic. there are essentially two ways. one way is to go to school where you learn how to do everything except anything new. one way is to teach yourself; that way, your only experience is what is with what is new, new to you at least.

cheers,

phoenix

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mathwonk

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Here is a compromise I recommend: Go to every class and listen in class as closely as possible. Then immediately afterwards go to the library, take out some paper and write out everything you remember in as much detail as possible. This way you think through everything again, and also produce useful notes. You also remind yourself of what you forgot, and make a note to review it somewhere. If it seems you are not able to remember much, you might need to take notes in class, or listen more effectively.

Another tactic is to read the material the night before to make effective listening easier.

Anyone addicted to memorizing formulas may be interested in viewing the play "The Lesson" by Ionesco.

The main point people are making here though is the unavoidable truth that reading notes is not nearly as effective for learning as writing notes is. When I write out an outline for my class of the material we have covered, I learn it very well by doing so. They on the other hand learn much less by merely reading my outline, so I always advise them to write their own.

Anyone who seeks to learn math by imitating the behavior of Professor Nash by skipping class however, does so at his/her own risk. It may be that Nash was more talented, and more eccentric, than some of the rest of us. At least missing class seldom worked for me, especially since I usually spent the time saved by playing "hearts".

Another tactic is to read the material the night before to make effective listening easier.

Anyone addicted to memorizing formulas may be interested in viewing the play "The Lesson" by Ionesco.

The main point people are making here though is the unavoidable truth that reading notes is not nearly as effective for learning as writing notes is. When I write out an outline for my class of the material we have covered, I learn it very well by doing so. They on the other hand learn much less by merely reading my outline, so I always advise them to write their own.

Anyone who seeks to learn math by imitating the behavior of Professor Nash by skipping class however, does so at his/her own risk. It may be that Nash was more talented, and more eccentric, than some of the rest of us. At least missing class seldom worked for me, especially since I usually spent the time saved by playing "hearts".

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JasonRox

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BasketDaN said:

I find this to be true.

On the other hand you have to take notes of important things, like definitions and what not. Examples or metaphors to help you understand the math is not necessary to write down. You should sit back and try to understand, and not take most of your time writing notes. My notes are really messy, and are barely readable, but I re-write them neatly after class.

Note: I am fortunate enough (well not really) to have a hearing disability, which isn't really noticeable when I put my hearing aid. Because of this, I went for "Help for Disabilities" for the first time this year, and they hooked me up with a notetaker. Although I'm doing fine now because it isn't anything I haven't seen before, I am doing this because later on when I see new material I don't miss anything. Basically, I listen and write sloppy notes, re-write notes, read notetakers notes, read textbook, and try exercise questions.

Also, I find that understanding the material is the only way you can succeed in math. Memorizing will get you past the first term, and then you're toast. Obviously lots of people forget the "Quadratic Formula", but those who experienced on how to deduce it themselves will remember for the rest of their lives (until alzheimers kicks in).

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StephenPrivitera said:

Exactly. One of my teachers would always say that math is not a spectator sport.

Besides, I think it would take quite a bit of work to memorize the Taylor Series of Expansions.

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If you are dead set against copying out notes then just go to class and listen, if there is something that you feel is worth remembering then copy it down, otherwise prepare to have the world's largest memory.

As for equation lists. Math, like every other subject, tends to like to make equations have insane amounts of subscripts and notations so I don't think you could pay somebody enough money to take the time to put them all in a nice neat organized order.

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phoenixthoth said:i believe dr. nash didn't even go to class at all, much less take notes.

Yes, but Princeton is its own kind of school, and the graduation rate of freshman is very high. (Ohio State was 50%.) Niederhoffer, writer ofEducation of a Speculator,said that he "Niederhoffered" Harvard, which was to say, when called upon to recite, he always said that he had not studied that yet because he was prepairing a special paper about a special project that he would present later to the class. The professors never objected to this.

But, at most schools there is a lot of testing, such as Ohio State U. Thus the person has to handle this note taking question seriously because something may come up almost immediately on a short quiz. I alway felt that if I understood the freshman and sophmore material that notes were not that necessary.

But, I know people who felt the very opposite, especially by the time they were a senor, and went to the trouble of actually memorizing notes and formulas so that when the test came up they did not have to try and recall anything. I guess that could work too.

But the real important thing is not the grade itself, but whether you manage to make it to the next level, and at that point, nobody worries about how well you did on last year's tests. Remember it has been said, and is at least a half truth, "Testing is for your own benefit," and if you pass that is mostly right.

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mathwonk

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why am I not surprized this is the same guy who "forgot his book" the night before the test.

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JasonRox

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mathwonk, you burned this fellow bad. LOL.

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mathwonk

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i am very tough on this behavior because it cost me 10 years of my professional life wasted, when finally i learned better. so i am like the "repentant" sinner who goes around blasting everyone else for sinning.

even now i have work i could be doing. so my apologies to basketdan. hang in there young man. please remember however that being smart is something of a curse.

i.e. you have succeeded so far without working because you must be very bright. but there will come a day of reckoning, when the "bottom end of the curve" has dropped out of the course, and all the competition is both smart and hard working.

as my basketball coach told one guy, "do your self a favor big fellow and play hard on both ends of the court."

good luck.

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when I marvel that all my students know a vector basis is a set which is both "independent and spanning" but few know what either term means.

at least some know that a function is integrable if its "upper and lower sums" can be made arbitrarily near, but no one can define an upper sum correctly.

most know a riemann sum is a sum of products f(xi*)delta(xi) but few know what either (xi*) or delta(xi) mean.

most know the derivatives of x^2 and sin(x), but few know what a derivative is.

several can state the "limit test" for a global minimum, but none know what a limit is.

most can state the fundamental theorem of calculus (every continuous function is the derivative of its indefinite integral) but all claim that the continuous function e^(x^2) has no antiderivative, and most do not know how to define a continuous function.

some say they fully understand "the math", they just don't get the theorems, proofs, definitions, and corollaries.

it seems hard to change the things people care to learn, to include the ideas rather than just the numbers.

merry xmas!

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JasonRox

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mathwonk said:

when I marvel that all my students know a vector basis is a set which is both "independent and spanning" but few know what either term means.

at least some know that a function is integrable if its "upper and lower sums" can be made arbitrarily near, but no one can define an upper sum correctly.

most know a riemann sum is a sum of products f(xi*)delta(xi) but few know what either (xi*) or delta(xi) mean.

most know the derivatives of x^2 and sin(x), but few know what a derivative is.

several can state the "limit test" for a global minimum, but none know what a limit is.

most can state the fundamental theorem of calculus (every continuous function is the derivative of its indefinite integral) but all claim that the continuous function e^(x^2) has no antiderivative, and most do not know how to define a continuous function.

some say they fully understand "the math", they just don't get the theorems, proofs, definitions, and corollaries.

it seems hard to change the things people care to learn, to include the ideas rather than just the numbers.

merry xmas!

Thanks for the review!

Calculus I Exam next week and Linear Algebra Exam tomorrow.

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mathwonk

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you are a good man jason rox

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here is another remark prompted by giving my final: on test 4 i announced in advance a certain proof would be asked. namely i would ask the class to prove the only function f with f'=rf and f(0) = c, is f(x) = ce^(rx). I gave the complete proof, emphasizing that the first step was to prove that the quotient f/e^(rx) is constant by taking the derivative and applying the mean value theorem, which implies that any function whose derivative is zero is constant. then evaluate the constant by setting x=0.

everyone did well. then one week later, unannounced, i gave the exact same problem on the final, with the hint: first prove the quotient f/e^(rx) is constant by the usual method. it seemed no one knew what that method was nor had any idea how to proceed, even after I said "remember this is a differential calculus course and we have a special way of recognizing constant functions".

I could not understand how anyone could have forgotten in only one week a simple idea like taking the derivative to show a function is constant, especially since we had emphasized it all semester. worse yet, to forget a proof which had been learned correctly one week earlier. i guess the only way is if someone just memorized the proof the first time without bothering to do any thinking at all about what the argument meant.

it is almost as if many students are dragging their feet so hard, trying not to do any thinking at all, that it is really challenging as to how to get them to benefit from what they do as exercises. so the main thing to remember is that as a student one must always work on oneself to try to understand the idea behind the discussion at hand. the whole point is to use a few sample problems that one solves in class as models for a wider class of problems that one will meet elsewhere. this cannot be useful unless one sees how to generalize the idea behind the given exercise to use it in a new situation. this is the goal of all exercises, not just to do as little as possible to slide by the course.

everyone did well. then one week later, unannounced, i gave the exact same problem on the final, with the hint: first prove the quotient f/e^(rx) is constant by the usual method. it seemed no one knew what that method was nor had any idea how to proceed, even after I said "remember this is a differential calculus course and we have a special way of recognizing constant functions".

I could not understand how anyone could have forgotten in only one week a simple idea like taking the derivative to show a function is constant, especially since we had emphasized it all semester. worse yet, to forget a proof which had been learned correctly one week earlier. i guess the only way is if someone just memorized the proof the first time without bothering to do any thinking at all about what the argument meant.

it is almost as if many students are dragging their feet so hard, trying not to do any thinking at all, that it is really challenging as to how to get them to benefit from what they do as exercises. so the main thing to remember is that as a student one must always work on oneself to try to understand the idea behind the discussion at hand. the whole point is to use a few sample problems that one solves in class as models for a wider class of problems that one will meet elsewhere. this cannot be useful unless one sees how to generalize the idea behind the given exercise to use it in a new situation. this is the goal of all exercises, not just to do as little as possible to slide by the course.

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JasonRox

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mathwonk said:here is another remark prompted by giving my final: on test 4 i announced in advance a certain proof would be asked. namely i would ask the class to prove the only function f with f'=rf and f(0) = c, is f(x) = ce^(rx). I gave the complete proof, emphasizing that the first step was to prove that the quotient f/e^(rx) is constant by taking the derivative and applying the mean value theorem, which implies that any function whose derivative is zero is constant. then evaluate the constant by setting x=0.

everyone did well. then one week later, unannounced, i gave the exact same problem on the final, with the hint: first prove the quotient f/e^(rx) is constant by the usual method. it seemed no one knew what that method was nor had any idea how to proceed, even after I said "remember this is a differential calculus course and we have a special way of recognizing constant functions".

I could not understand how anyone could have forgotten in only one week a simple idea like taking the derivative to show a function is constant, especially since we had emphasized it all semester. worse yet, to forget a proof which had been learned correctly one week earlier. i guess the only way is if someone just memorized the proof the first time without bothering to do any thinking at all about what the argument meant.

it is almost as if many students are dragging their feet so hard, trying not to do any thinking at all, that it is really challenging as to how to get them to benefit from what they do as exercises. so the main thing to remember is that as a student one must always work on oneself to try to understand the idea behind the discussion at hand. the whole point is to use a few sample problems that one solves in class as models for a wider class of problems that one will meet elsewhere. this cannot be useful unless one sees how to generalize the idea behind the given exercise to use it in a new situation. this is the goal of all exercises, not just to do as little as possible to slide by the course.

I barely study for exams at all. For now, everything is pretty easy. I'll go through the theorems and proofs again, but I understand everything.

One of the coolest things I think, for a Calculus I course, is how you can prove that if something is differentiable at point x, it is also continuous at point x. You can prove it directly through the definition of the derivative, which is kind of neat.

Yes, students don't think and don't like to think. That's not good for me because I like to just talk math/physics, but unfortunately no one else does.

I don't know if it was like this before, back in the day, but I do know that it really sucks today.

Math club... in your dreams.

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It follows that deltay converges to L times the limit of deltax, i.e. zero, hence f is continuous.

this is nice, but there is a lot more going on than this level of argument. if this is what impresses you now, you have not even scratched the surface. you could get a lot deeper with some effort.

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mathwonk said:

everyone did well. then one week later, unannounced, i gave the exact same problem on the final, with the hint: first prove the quotient f/e^(rx) is constant by the usual method. it seemed no one knew what that method was nor had any idea how to proceed, even after I said "remember this is a differential calculus course and we have a special way of recognizing constant functions".

I could not understand how anyone could have forgotten in only one week a simple idea like taking the derivative to show a function is constant, especially since we had emphasized it all semester. worse yet, to forget a proof which had been learned correctly one week earlier. i guess the only way is if someone just memorized the proof the first time without bothering to do any thinking at all about what the argument meant.

it is almost as if many students are dragging their feet so hard, trying not to do any thinking at all, that it is really challenging as to how to get them to benefit from what they do as exercises. so the main thing to remember is that as a student one must always work on oneself to try to understand the idea behind the discussion at hand. the whole point is to use a few sample problems that one solves in class as models for a wider class of problems that one will meet elsewhere. this cannot be useful unless one sees how to generalize the idea behind the given exercise to use it in a new situation. this is the goal of all exercises, not just to do as little as possible to slide by the course.

This is exactly why I dislike studying the way its done now. People study to pass an exam, not to know material, and I think the latter is so much more valuable.

Tests arent effective in guaging a students understanding for that reason.

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well, if people were doing well on tests and then not really understanding later i would agree with you, but as it is, many students are not even doing well on exams when told in advance what to expect.

so i am saying the threshold is extremely low and many people are still stumbling over it. moreover my experience shows that studying to understand the material is the most effective way to prepare for an exam, but many people refuse to accept this.

For example, even without preparing, and over material I have not seen or taught for decades, and not in my area, I still outperform almost all PhD prelim takers every year on the PhD prelims written by others.

I.e. when I have to grade a prelim, I just sit down and take it myself first, even in real analysis (my worst subject) or complex analysis, or topology, or algebra, even if i have not studied it for years and years. I almost always significantly outperform all takers of the test, who have prepared for months and months on that specific topic. In particular I always pass, whereas most students fail. It is precisely because i understand the concepts and can apply them in various settings.

so i am saying the threshold is extremely low and many people are still stumbling over it. moreover my experience shows that studying to understand the material is the most effective way to prepare for an exam, but many people refuse to accept this.

For example, even without preparing, and over material I have not seen or taught for decades, and not in my area, I still outperform almost all PhD prelim takers every year on the PhD prelims written by others.

I.e. when I have to grade a prelim, I just sit down and take it myself first, even in real analysis (my worst subject) or complex analysis, or topology, or algebra, even if i have not studied it for years and years. I almost always significantly outperform all takers of the test, who have prepared for months and months on that specific topic. In particular I always pass, whereas most students fail. It is precisely because i understand the concepts and can apply them in various settings.

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For example, I got A's in all my E&M exams, and I cna honestly say I blow at E&M. The fact that I could get by without knowing this stuff is so wrong.

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mathwonk

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you are right. we are penalized for having too many students withdraw from our classes, so we make them easier and easier every year.

but the students can always drag their feet even more.

but to be fair some are woefully unprepared from high school, and have no clue what ti means to study or try hard at all.

most of my students wanbt to do well, and want to do what ia sk, they really have no clue how to proceed. the high schools are apparently teaching nothing at all in many cases.

so in college calculus i cannot assume algebraor trig, or geometry, or how to read a sentence, or how to reason, much less how to amkke a proof.

my favortite criticism of my teaching was "I can't understand him at all, he teaches with WORDS!":

but the students can always drag their feet even more.

but to be fair some are woefully unprepared from high school, and have no clue what ti means to study or try hard at all.

most of my students wanbt to do well, and want to do what ia sk, they really have no clue how to proceed. the high schools are apparently teaching nothing at all in many cases.

so in college calculus i cannot assume algebraor trig, or geometry, or how to read a sentence, or how to reason, much less how to amkke a proof.

my favortite criticism of my teaching was "I can't understand him at all, he teaches with WORDS!":

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If you were to make those assumptions on algebra and trig, and assigned an exam based on perfect understanding of these elements, its no doubt that many more students will fail the exam. For example, in Calc 2, partial fractions is taught as a method to evaluate certain integrals. Should they really have to teach this? It should follow immediately from their workings in algebra courses that the integrand is expressible in simpler terms and it should be intuitive for the student to make that judgement and solve the problem on their own.

STudents are instead dumbed down and are retaught things that they should already know, and the students see this as "If I need it, theyl'l show me it next time", and when that next time doesnt come, they get overwhelmed.

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