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

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Discussion Overview

The discussion centers around the question of how many pages of math theory individuals can absorb in a single day, considering factors such as the difficulty of the material, personal learning styles, and prior knowledge. Participants share their experiences with reading math textbooks, including definitions, examples, and proofs, and reflect on their retention and understanding of the material.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants report being able to absorb 10-15 pages effectively, while others suggest they could handle more if the material is familiar or less complex.
  • One participant mentions that reading a whole chapter does not lead to retention, emphasizing the importance of understanding over mere reading.
  • Another participant shares an anecdote about a teacher solving numerous problems in a textbook quickly, noting that this is different from learning new material.
  • Several participants agree that math learning is not fast and often requires additional thinking and reflection, which can slow down the reading process.
  • Some express that the ability to absorb material varies significantly based on the subject matter and individual circumstances, such as distractions or prior knowledge.
  • One participant highlights that re-learning material is generally easier than learning it for the first time, especially for foundational topics like calculus.
  • There is a mention of the challenges posed by proof-based texts, which require deeper engagement than non-proof-based materials.
  • Some participants question the validity of the poll options, suggesting that the difficulty of the material should be considered.

Areas of Agreement / Disagreement

Participants generally agree that the number of pages absorbed varies widely among individuals and depends on multiple factors, including the difficulty of the material and prior knowledge. There is no consensus on a specific number of pages that can be absorbed, as experiences differ significantly.

Contextual Notes

Some participants note that their ability to absorb material is influenced by the complexity of the subject matter, with more difficult topics requiring more time and effort. Additionally, the discussion reflects a range of personal experiences and learning styles, which complicates any attempt to generalize about page absorption rates.

Who May Find This Useful

This discussion may be of interest to students and educators in mathematics, particularly those exploring effective study habits and the challenges of learning complex material.

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
  • #31
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
 
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  • #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
complexPHILOSOPHY said:
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
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
Crosson said:
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
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 I am not very clear, that's just all I can say lol.

Or take Newtons Approach, 1% Genius, 99% Perserverence.
 
  • #37
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
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
We'll perhaps I haven't reached that level yet where the mathematics I am 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
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
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 I am 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
mathwonk said:
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
If I am 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
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
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
mathwonk said:
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.
 
  • #51
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?
 
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  • #52
andytoh said:
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.
 
  • #53
I'll participate in this competition for the hell of it! I'll win the grand prize, that is fer sher.
 
  • #54
JasonRox said:
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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  • #55
andytoh said:
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.

I don't think it will ever happen and it's most likely a big waste of time.
 
  • #56
It does seem a bit pointless; for example, it hugely depends on the choice of topic as to whether one would spend a day studying it. If a particular topic were picked that I didn't find interesting, then I'd get bored after about an hour and give up! On the other hand, if I enjoyed a topic, then I could study it for longer, and so would do better. Therefore, in my opinion, the people who find the particular subject interesting are bound to do better on the "test!"
 
  • #57
i for one would like to take the test, not as a competition but as a self-diagnostic--for my own good. but make it a 3 hour reading period (multiply the scores by 4 if you want to answer your poll question). in a 3 hour reading period, i don't think the people interested in the topic will have much of an advantage over the bored readers.

the questions should be such that flipping through the notes will be of no use if you didn't understand the topic well during the reading period. upload the reading material at a fixed time (e.g. 3:00 GMT), everybody then reads for 3 hours. then upload the test (6:00 GMT). then everybody has until, say, 9:00 GMT to hand in the test. like this, people can only cheat if they get help from other people. scores should be displayed without names, and your own score given privately so you can see where you stand compared to other self-learners.

i think this would be a good diagnostic test, and hardly a waste of time. what do you have to lose by participating?
 
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  • #58
That seems a good suggestion, Tom, to have a shorter period. However, that brings into play the matter of time differences! For example, I'm in the UK, and so don't really fancy learning it during the night!

I never said I wouldn't participate, by the way, it's just that if I wasn't interested in the topic, then I wouldn't be able to study it for a whole day! But yes, if I have the time, then I'll give it a go. (Good idea about the private scores as well)
 
  • #59
oops, i was talking about afternoon greenwich mean time.
start reading: 15:00 GMT
start test: 18:00 GMT
hand in test: 21:00 GMT

this should be ok for people from western us to eastern asia. if 3 hours reading and 3 hours test is still too long, make it 2 and 2.
 
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  • #60
Ahh, ok. Well that sounds better!
 

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