View Poll Results: How many pages of math can you absorb in one day.
1-5 44 33.33%
6-10 28 21.21%
11-15 16 12.12%
16-20 8 6.06%
21-25 4 3.03%
26-30 0 0%
30+ 32 24.24%
Voters: 132. You may not vote on this poll

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How many pages of math theory can you absorb in one day?

by andytoh
Tags: absorb, math, pages, theory
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Gib Z
#37
Feb23-07, 08:09 PM
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Did you expect an even or a normal distribution?

And this is an internet forum, why in hell would anyone bother lying to other people here who they do not now, will probably never see, and are here to help them learn anyway?
mathwonk
#38
Feb23-07, 09:55 PM
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boy are you naive. we are building a totally artificial persona here that we live with in in our fantasies. E.g. I have pretended for years here to understand tensors, whereas actually they scare me to death.
Gib Z
#39
Feb24-07, 02:34 AM
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We'll perhaps I haven't reached that level yet where the mathematics im learning is too abstract for me to grasp.

and andytoh, why did you delete you post..if looks like i double posted talking to no one...
complexPHILOSOPHY
#40
Feb24-07, 09:34 AM
P: 360
I have never forced myself to remember anything, that I can recall. I only read through what I want to, when I want to and absorb whatever my brain decides to absorb. That is seriously that only way that I can learn. Forcing myself to memorize and learn things that I don't feel like absorbing, never works. I compartmentalize and organize information that I become consciously aware of during my reading (e.g. I decide it's interesting or might have a relationship with something else) and then construct my cognitive model of it. I think my memory is more cue oriented.

Does forced memorization, like what Gib Z does, work well for some of you?
mathmuncher
#41
Feb24-07, 10:31 AM
P: 12
I think it's dependent on how terse the book can be. Books with exhaustive rigor, while often long in content, can be a breeze. Rudin-like terseness could be more challenging, and necessitates more of me to absorb.
Gib Z
#42
Feb24-07, 06:08 PM
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I usually do not do forced memorisation for anything other than memorising digits lol
complexPHILOSOPHY
#43
Feb24-07, 10:51 PM
P: 360
Does it really function as an aide to have those digits memorized? I try my best to only use what I know in my head without reference to external sources (if absolutely possible) but if it is something like the digits of some number, I do not trust my head (well I do, but I know I don't make conceptual mistakes, I make arithmetic mistakes or I copy the number down wrong).

Does it help you? I can't see that helping me with doing abstract algebras or anything. Is it more for Calculation? Even then, is it really that much more helpful?

I am ignorant dude, so help me out!
Gib Z
#44
Feb24-07, 11:59 PM
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Yes its pretty much only for calculation. I own a calculator, but leave it at home and perform everything by hand. Square roots, sines, logs, you name it. But seeing as im only in year 10, The most labourous thing I calculate is sines, not so bad. It doesn't help at all when doing anything other than arithmetic.
andytoh
#45
Mar3-07, 10:13 AM
P: 363
Quote Quote by mathwonk View Post
my old algebra teacher maurice auslander used to say that if you want to understand what you are reading you need to write out at least 5 pages oer page read.
mathwonk is quite correct here. Just yesterday, I decided to add a footnote to every statement made in one page that needed further explanation. I typed out my FULL, RIGOROUS explanation for each footnote I inserted. The page had many footnotes, and my explanations for all the footnotes took up just about 5 pages.

With this thoroughness of absorption, I am now in the 5 or so pages per day category. Incidentally, each footnote I add serves as an exercise, so not only am I reading the pages with full understanding, but I am improving my fluency in the topic by doing (simple) problems.

For those in the 30+ category, are you fully absorbing everything by doing these footnote explanations (either by hand or in your mind?), or are you just accepting every single statement you read on faith?
interested_learner
#46
Mar3-07, 09:09 PM
P: 214
You can't "accept everything on faith" in math. That misses the whole point. The real point is to start with the assumptions and develop the math through the proofs. When you understand the proofs and can work the problems then you understand the math.

Frankly I find it hard to absorb much math at a sitting. Unsually I have to leave it for a day or two and then come back. Then it is clear.
Gib Z
#47
Mar4-07, 04:09 AM
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If Im really interested in the problem, I will try to prove it myself. Unsuccessful, I will read a small part of a known proof, see if I can go from there. If not, next part, so on so forth. That helps me remember the proof, and therefore the theorem.
JasonRox
#48
Mar4-07, 09:23 PM
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I voted 30+ pages. I can pretty much read 30+ pages of mathematics in one day and do some questions that's for sure.

But the reality is, it hasn't fully sunk in yet. I can be pondering the ideas for a few days, and do more questions as the days go by.

To fully absorb material takes longer than a day in my opinion. Just like working out, you need to rest, and exercise again.
mathwonk
#49
Mar4-07, 11:19 PM
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I would be very interested to have some feedback on how rapidly anyone here can absorb my notes on my webpage. E.g. I have linear algebar notes there shorter than 15 pages, that cover a whole semester's linear algebra. Can anyone here read them in one day?

I have other notes on the Riemann Roch theorem, about 30-40 pages in loength. Can anyone read them in a week? I have a book of algebra there about 300-400 pages long. Can anyone master those in a month?


If not, quit kidding yourself that you can absorb 10-15-20-30 pages a day.
JasonRox
#50
Mar5-07, 12:02 AM
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Quote Quote by mathwonk View Post
I would be very interested to have some feedback on how rapidly anyone here can absorb my notes on my webpage. E.g. I have linear algebar notes there shorter than 15 pages, that cover a whole semester's linear algebra. Can anyone here read them in one day?

I have other notes on the Riemann Roch theorem, about 30-40 pages in loength. Can anyone read them in a week? I have a book of algebra there about 300-400 pages long. Can anyone master those in a month?


If not, quit kidding yourself that you can absorb 10-15-20-30 pages a day.
He said a full day of free time. How rare is that? Quite rare.
andytoh
#51
Mar5-07, 06:32 AM
P: 363
The Test

Some time in the near future, I will upload a 30 page chapter on a rare math topic (requiring only first year university knowledge to understand) that probably no student here has studied before. One day later, I will upload a test--one question for each page. See how many questions you can answer (i.e. how many pages you fully understood). The top 3 scorers will be announced.

Anyone interested in donating one day from the weekend to study a new math topic?
JasonRox
#52
Mar5-07, 07:55 AM
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Quote Quote by andytoh View Post
The Test

Some time in the near future, I will upload a 30 page chapter on a rare math topic (requiring only first year university knowledge to understand) that probably no student here has studied before. One day later, I will upload a test--one question for each page. See how many questions you can answer (i.e. how many pages you fully understood). The top 3 scorers will be announced.

Anyone interested in donating one day from the weekend to study a new math topic?
I rather have someone like mathwonk running something like this.
complexPHILOSOPHY
#53
Mar5-07, 11:11 AM
P: 360
I'll participate in this competition for the hell of it! I'll win the grand prize, that is fer sher.
andytoh
#54
Mar5-07, 01:13 PM
P: 363
Quote Quote by JasonRox View Post
I rather have someone like mathwonk running something like this.
Putting aside who administers the test, we need to first determine if there are enough students interested in taking the test. Before you announce yourself, keep in mind that:

1) You have to be willing to sacrifice a whole day to study a math topic that you probably never learned before. There is no guarantee that the topic you study will be relevant to whatever area of math you want to specialize in. To make the day convenient, it should be a weekend or a holiday. If necessary, it could be during the summer when the loss of a day should affect few or no students.

2) You also have to write the test the next day. After all, the test is to see how much you understood the topic in one day. Any late submission of your test answers cannot be accepted for this reason. Thus you have to sacrifice a whole day (to study) and the next morning (to write the test and submit it)

3) You cannot cheat. This is self-explanatory but unfortunately we will have no way to know for certain if people cheated. I believe this should include answering a question about a topic that you know you don't understand, but then read the relevant pages during the test in search for an answer. Let be said that anyone who plans to cheat in such a test is being a total moron.


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