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

  • Thread starter andytoh
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How many pages of math can you absorb in one day.

  • 1-5

    Votes: 38 33.0%
  • 6-10

    Votes: 25 21.7%
  • 11-15

    Votes: 16 13.9%
  • 16-20

    Votes: 6 5.2%
  • 21-25

    Votes: 3 2.6%
  • 26-30

    Votes: 0 0.0%
  • 30+

    Votes: 27 23.5%

  • Total voters
    115
  • #26
Gib Z
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Well what im doing is definitely not cutting edge lol.

O btw Im pretty sure I would ace the test, if i had written it >.<"
 
  • #27
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Crosson - how old are you, and what level are you reading at?
I'm 21, and the material I am currently reading Poizat's Model Theory.

Are you reading stuff which has been around, as has been gone over for a long time, or more cutting-edge stuff, in the form of research papers?

If the latter, I don't believe you can give a full account to people in a day; ie. these papers never contain all the info you need - for this you need to research back and back, through many past references.
I absolutely agree, I think a few posts up I mentioned the difference between material that has already been thoroughly digested and other things like obscure or cutting edge research. The only research papers I read are in quantum physics/dynamical systems, but that is the difference between work and (what is for now) play.

You should study 30+ new pages everyday and become a truly great mathematician.
Unfortunately the ability to read, solve, digest, recite and perform textbooks does not a mathematicians make. I see little value in producing obscure research for the academic system, e.g. "Super-Edge Magic Graph Labelings", but in America this is what is encouraged. I think integrating the knowledge we already have is a more important goal.
 
  • #28
Do you guys have true photographic memories, or what's up? I have a pretty phenomenal memory and solid visualization skills but I can't imagine keeping up with you guys, so I imagine your memories are remarkably powerful.
 
  • #29
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By the way, if you haven't figured it out yet. People like Crosson, who can absorb 30+ per day (and hypothetically ace the test immediately after) are learning 6 times faster than the majority of us!
 
  • #30
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Do you guys have true photographic memories, or what's up? I have a pretty phenomenal memory and solid visualization skills but I can't imagine keeping up with you guys, so I imagine your memories are remarkably powerful.
Not myself, but I have a similar friend who gets the ability from his photographic memory (interestingly he cannot remember smells and tastes at all!).

Spinoza said, of the three forms of knowledge: sensory, deductive, and intuitive, that only intuitive knowledge is true knowledge. The sense in which I agree with this archaic statement is that I gain knowledge by studying the process and not the details, which is why I can remember a math text much better than a fantasy novel (ironically E.A. Poe critiqued fantasy literature as being analytical in the sense that once the rules of the fantasy realm are established it is a formulaic process to translate our world into the fantasy world according to the rules; where as mathematics is truly creative:biggrin: ).

When reading, strive to create intuitive knowledge. Don't worry about getting every detail, because that is a natural consequence of having an intuitive feel of the process. That said, until one is completely comfortable with the style of mathematical writing, the going is tough. But after this initial barrier, it becomes almost embarassingly easy.

"In mathematics we don't understand things, we just get used to them" - Von Neumann.

What the master meant is that the feeling we call understanding is actually a sensation of familiarity; this is the reason for the uniformity of style across mathematical literature: new definitions in a familiar style are immediately "understandable", with the lucidity being nearly too much to bear.
 
  • #31
quasar987
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The cool thing about Spinoza is that it is so impossible to get what the hell he's talking about that we can make him say whatever we want. :D
 
  • #32
Crosson said:
Not myself, but I have a similar friend who gets the ability from his photographic memory (interestingly he cannot remember smells and tastes at all!).

Spinoza said, of the three forms of knowledge: sensory, deductive, and intuitive, that only intuitive knowledge is true knowledge. The sense in which I agree with this archaic statement is that I gain knowledge by studying the process and not the details, which is why I can remember a math text much better than a fantasy novel (ironically E.A. Poe critiqued fantasy literature as being analytical in the sense that once the rules of the fantasy realm are established it is a formulaic process to translate our world into the fantasy world according to the rules; where as mathematics is truly creative ).

When reading, strive to create intuitive knowledge. Don't worry about getting every detail, because that is a natural consequence of having an intuitive feel of the process. That said, until one is completely comfortable with the style of mathematical writing, the going is tough. But after this initial barrier, it becomes almost embarassingly easy.

"In mathematics we don't understand things, we just get used to them" - Von Neumann.

What the master meant is that the feeling we call understanding is actually a sensation of familiarity; this is the reason for the uniformity of style across mathematical literature: new definitions in a familiar style are immediately "understandable", with the lucidity being nearly too much to bear.
Well, my friend, I understand what you mean about intuition but I can't relate to the notion of maths being embarassingly easy. That is certainly an awesome statement to be able to make.
 
  • #33
J77
1,076
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Do you guys have true photographic memories, or what's up? I have a pretty phenomenal memory and solid visualization skills but I can't imagine keeping up with you guys, so I imagine your memories are remarkably powerful.
I have the memory of a goldfish.

Being good in a field is not about learning everything which has been written about it.
 
  • #34
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Being good in a field is not about learning everything which has been written about it.
Indeed, it is a necessary but not sufficient condition:wink:
 
  • #35
cepheid
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Indeed, it is a necessary but not sufficient condition:wink:
Ouch! You just contradicted him soundly. He said it was NOT about learning everything that has been written about that field. You said that that was required AND MORE.
 
  • #36
Gib Z
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lol. My memory is not that remarkable, i remember the first 10 primes, and various mathematical constants and physical constants to about 10 decimal places, but anyone could have done that if they bothered to do what i did. Every week i would say nothing but those digits off a piece of paper, over and over. Some came easily, eg e approx 2.718281828, nice repeating 1828's. My point is, to remember all the mathematics you learn, you sort of need to learn to feeling of it. If you can remember the "feeling" of how to do it, youve got it. I know im not very clear, thats just all I can say lol.

Or take Newtons Approach, 1% Genius, 99% Perserverence.
 
  • #37
Gib Z
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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?
 
  • #38
mathwonk
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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.
 
  • #39
Gib Z
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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...
 
  • #40
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?
 
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  • #41
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.
 
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  • #42
Gib Z
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I usually do not do forced memorisation for anything other than memorising digits lol
 
  • #43
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!
 
  • #44
Gib Z
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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.
 
  • #45
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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?
 
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  • #46
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.
 
  • #47
Gib Z
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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.
 
  • #48
JasonRox
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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.
 
  • #49
mathwonk
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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.
 
  • #50
JasonRox
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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.
He said a full day of free time. How rare is that? Quite rare.
 

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