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

[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 I am not very clear, that's 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 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...

 

[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 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.

 

[andytoh]

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]

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 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.

 

[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]

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]

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]

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]

I'll participate in this competition for the hell of it! I'll win the grand prize, that is fer sher.

 

[andytoh]

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.

 

[JasonRox]

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.

 

[cristo]

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!"

 

[Tom1992]

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?

 

[cristo]

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)

 

[Tom1992]

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.

 

[cristo]

Ahh, ok. Well that sounds better!

 

[Gib Z]

Well include me in the test, but perhaps arrange it so that I don't have to start at 1 a.m..

 

[andytoh]

hmmm... well that's 5 people so far interested in the test, but I think we need to know what time zone you live in as well. Gib, I recall you live in Australia, which unforutunately is opposite to where most people live, which I believe is between Pacific standard time to Greenwhich time.

Also, to make this test a reality, we need a volunteer to administer the test (and grading it as well--which shouldn't take to long, because I don't think we'll have more than 15 people writing it). It should be someone who has already graduated, ideally a professor. I think we agree that the reading peoriod should be 3 hours, and the test 3 hours immediately following (with no late hand-ins accepted). The prerequisite knowledge should perhaps be just calculus and under so that no one will have a big knowledge advantage. All mathematical knowledge beyond calculus should be developed ab initio in the reading period, and not already taught in university courses.

And yes, this test should be looked at as a self-diagnostic rather than a competition.

 

[complexPHILOSOPHY]

Well, I am still learning Calculus but I will learn the relevant Calculus in conjunction with this and then shoot myself in the face with excitement.

Actually, I will just take the test and quietly hand it back in! Let's gooooogooggogo. Also, no one is allowed to be sober in any fashion while taking this test!

Seriously though, I am down for this test. I want to see what I can do with a limited understanding of Calculus.

 

[andytoh]

Complexphilosophy, if you're double majoring in math and physics, shouldn't you already know calculus?

Actually, the topic might not even require calculus. For example, if the topic were von Neumann–Bernays–Gödel set theory, which I don't think is taught in any undergraduate university course, all you need to get started is to know the basics of set theory taught in high school. Or a rare and narrow topic like convex polytopes, all you need to start from scratch is high school geometry.

 

[complexPHILOSOPHY]

Complexphilosophy, if you're double majoring in math and physics, shouldn't you already know calculus?

Actually, the topic might not even require calculus. For example, if the topic were von Neumann–Bernays–Gödel set theory, which I don't think is taught in any undergraduate university course, all you need to get started is to know the basics of set theory taught in high school. Or a rare and narrow topic like convex polytopes, all you need to start from scratch is high school geometry.

I just learned what $$y=mx+b$$ was about 7 months ago. The highest math that I learned was in my (american) high school, algebraic arithmetic (Algebra I and Geometry). I hated math so I took this course three times because I failed it twice, simply because I would hand in my tests, blank. My cumulative, graduating GPA was a 1.2 and I finished in the bottom 10 of my high school class. Once I started college, I had to take a course on Algebra and Geometry. This time, I finished the book in a day and decided that I might not be so bad at maths. I taught myself trigonometry over the next week and then taught myself what is considered, Calculus I, at my college. Granted, most of you here taught yourself Calculus at like 11 (or atleast I feel that way). Right now, I am in Calculus II but I have worked through about 1/4 of Herstein's Topics in Algebra, doing all of the proofs and problems anbd having them checked on here and I haven't had any problems yet (it's still easier stuff right now, his book gets harder, for me atleast).

So, I want to do pure maths and physics and I have a transfer agreement with UCSD-Revelle (I transfer into tht University after 64-units). I correspond with one of the professors at UCSD doing research in Supermanifolds and Supervarieties and he gives me academic advice to help make sure I have a smooth transition into UCSD. So assuming that everything continues in this fashion, I will declare a double-major in maths and physics and according to the provost, as long as I continue to work on my maths, there is no reason why I won't be able to complete both of those majors.

Other than that, I am pretty much mathematically ignorant. That is why I was interested in doing this, I wanted to see if I was any good at maths or not.

Sorry for the long explanation but that is why I can't do calculus! lol

 

[andytoh]

Even with your high school algebra background, you would more or less be on par with everyone else with a narrow topic like the Cayley-Dickson construction of Quaternions, which no other student here has learned, and only requires basic algebra to learn from scratch.

And you made a good point, this test should give you an idea of whether you can self-learn efficiently enough to be able to soar to great heights in the future.

 

[JasonRox]

And you made a good point, this test should give you an idea of whether you can self-learn efficiently enough to be able to soar to great heights in the future.

Not really.

You can suck at learning Analysis but awesome at learning Group Theory.

 

[complexPHILOSOPHY]

JasonRox killed the thread. :!)

 

[andytoh]

Yeah, I just came back from my latest alien abduction, and I noticed that the 10 posts prior to his were pretty enthusiastic.

 

[JasonRox]

It's reality.

Anyways, I think I should go back on my word.

I think on a good day I can probably absorb 5 pages of a single subject and fully understand it. I was just reading about Quotient Topologies and Quotient Spaces and I had to stop after 3 pages simply to really think about it. I had an extra hour or so before bed time. I chose to relax, and let it sink in. I'll read more about it later though. It's just so out of the ordinary to create such a topology. It'd be very interesting to see where the motivation came from.

Anyways, cheers.

Note: It might be 5 pages now, but I'm betting it will be 1-2 pages in about a year or two. Maybe less. :surprise:

Note: Now that I let it sink in, and gave myself some examples of quotient maps and how they work. I'm ready to move with it. If I would have kept going, I wouldn't have understood a thing because I didn't even create a personal picture of quotient spaces.