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

cepheid

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.

Gib Z

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.

Gib Z

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

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

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

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

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

I usually do not do forced memorisation for anything other than memorising digits lol

complexPHILOSOPHY

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

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

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

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

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

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

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

He said a full day of free time. How rare is that? Quite rare.

andytoh

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?