Let's suppose you have a full day, free from classes or work, and you wish to read something new from a math textbook (which is moderately paced and at your current level), reading every single definition, example, and every proof of every theorem in each page. How many pages of math theory can you absorb in one day? I have found that I can easily read a whole chapter, but the whole chapter does not really sink in, even if I read every single word. However, if I restrict myself to 10-15 pages, it all sinks in and I can absorb and remember all the content in those 10-15 pages. I'm concerned that 10-15 pages is too little. But any more, and I cannot retain it. I admit I am not a learning machine. But I want to fully, fully understand what I read, and really grasp the heart of the matter, and not just memorize definitions and results without getting a strong feel for them. So I slow down my reading intentionally. What do the others say?
depends on the subject. i've heard of someone who was going to instruct a 1st-year calculus course & to get solutions (because the answers in the back had some typos apparently) she solved every problem in every section of the edwards/penney text which was on the syllabus. that must have been about 400-500 pages or more & it only took her 4hrs. i've never tried but i think i could do that. it would get easier as i get back into it i'm sure. with something new of course it would be slower going, especially if i'm not very interested & i have to do it just because someone told me to. (if i do it at all in that case) i think i used to be able to handle a section or two per day, but with no distractions like work, classes, etc maybe i could do as much as 5 or more. maybe it would also depend on how easily things like examples come to me.
The answer to this question is extremely relative and varies from person to person. But one holds - there is no 'fast' math learning, as far as I know. Often the book/tutorial isn't enough (although it may contain numerous examples etc.) and requires from the reader to do some (!) additional thinking.
That's a bit different though, as that's not learning as such; if she's about to instruct a course, then she's got to be a mathematician who has learnt that in the past!
i guess it was all in her brain somewhere but on the other hand i think she had forgotten & had to re-learn at least some of it.
Yes, it is precisely this "additional thinking" that forces me to slow down my reading. Reading a math textbook, including all the proofs of theorems, is not like reading a newspaper and just collecting the facts. There is a lot of reflecting required. Also, many proofs and explanations have intentional holes and that you must fill in yourself to fully absorb the content. And even after filling in the gaps and understanding the entire proof, I must still reflect again (how did it work?) and understand the implications (so what does this signify?) before I read on. These are what force me to slow down my reading to 10-15 pages. Some people may read a sentence or a step, not understand it, and then say "Ah, who cares? Let's just move on." But that obviously does not qualify as ABSORBING.
Yea, I suppose so, but then re-learning is a lot easier than learning for the first time; especially if it's only first year calculus-- although she may have forgotten, experience with solving problems helps a lot! However, 400-500 pages; that's still pretty brave! I'd just get the solutions of the guy that taught it last year
11-15 is average for me but I can easily get stuck and spend a whole day on essentially one page. >.< Interesting poll though.
Remember, I said reading something NEW and at YOUR CURRENT LEVEL (or slightly above). Also, perhaps 2nd year math students or higher should only participate in the poll. I remember reading ahead chapters from high school textbooks in one day easily and absorbing everything (because there were no proofs involved).
If I read something on my own then I won't do much more than 10-15 pgs, but for classes, and I think this is probably the case with a lot of people, that each subject will require about 4-5 pgs of mathematics every day. I would be more interested to see how much physics reading everyone can do because physics readings generally demand both physical concepts and mathematics.
Depends on the topic and it depends on the day. Anywhere from being unable to do anything to being able to read a short book.
mathwonk didn't vote because there were no "under 1 page" option. :tongue2: I remember him saying it sometimes took him 1 week to plough through 1 page of Riemann's original work. I wanna know what Gib Z and Tom1992 voted.
hmmm... i never really kept track. let's see: since we can only count proof-based textbooks, i cannot count the textbooks i read up to calculus 1. after calculus 1, i read about 10 math textbooks = 5000 pages. this was done over 3 years, but take off one year because the physics textbooks i read don't count, and take off another 50% of the time spent on my other high school commitments. thats about 5000 pages in 365 scattered days or about 14 pages per day. i'm not the one who voted 30+ pages per day. perhaps that's matt grime.
let's get this right: at 30+ pages per day, that's 1 entire textbook in less than 2 weeks. and this a textbook of new material which is at your current skill level, and this is fully understanding the entire content of the book. this to me sounds like more than the completion an entire course in under 2 weeks. at this rate, you can master about 30 courses in one year so in essence finish an entire university degree in one year and also hypothetically get A+ in every course, since this poll asks about fully absorbing the content. i personally cannot learn this fast! and this is from a 14 year old in 1st year university. and why the empty gap before the 30+ category? it must be the professors who voted 30+ (i guess they have to be this good else they wouldn't have become professors, and they probably have to absorb material this fast when they do background reading for their projects), and the students the others.
My idea is how many pages of maths you can read one day depends on the difficulty of the pages. I remember when in university, linear algebra took me a lot of time, but derivative and integration did not take that much.
In this case your fallacy was the assumption that anyone would, or could, read 30+ pages in one day on consecutive days for a sustained period of time (2 weeks). In the poll I claimed to be a 30+ math reader, but this is because I only read new material when I feel up to it, which is maybe 2 days a week. One can joke of the wise old sage who ponders a single half page in a week*, but in fact reading mathematics that has already been written and solving problems that have already been solved is easy. *It is one thing to read 120+ year old works of Reimann, there the difficulty is historical as well as mathematical.
Quasar*somenumbers*: I want to know what GibZ and Tom1992 voted. I haven't voted just yet, but its easily more than 30. However, I am talking about things that I admit are relatively simple. Did anybody notice I didn't understand murshid_islams derivation of [tex]\int_{-\infty}^{\infty} e^{-x^2} dx=\sqrt{\pi}[/tex], but the next week was advising some Physics student for help with the Cross Product? I finished a Multivariable Calculus textbook in about a week (in the holidays, so i had all day), and most people here will say its pretty easy. However Im sure I still can't do every single question out of the textbook. Also note I knew about the first 2 chapters before hand. I doubt I would be able to reproduce the ...hmm, 86 pages I think it was, a day of learning with any other topic of mathematics. I already had a very strong base in single variable calculus and multivariable was merely an extension. O and maybe I should mention the pages were abit smaller, so its about 60 A4 pages I guess. Essentially: New topic to me, maybe 40 pages a day, if im free all day.
not me, i was going to say something like <1 page. 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, so reading 15 pages would require writing over 75 pages. i spend a day on one proof, or one line in one proof, like the easy proof that in a noietherian ring every non zero non unit has a factorization nito irreducibles. I know how to prove it, but I want to really understand the proof, and find the best proof. And I waNT TO CONVINCE MY STUDENTS THAT A "proof" like that in dummit foote is incomplete. But this is easy textbook stuff. If I am trying to read a paper where I am actualkly eklarning new ideas or new techniques I may spend much longer. I have spent about 20 years reading Mumfords paper on prym varieties. I did peruse Spivaks volume 2 on differential geometry in one or two days, but notice I said peruse, not learn. And I once read KodaIRA MORROW ON COMPLEX MANIFOLDS AND THE vanishing theorem in 5 straight days, but that was under pressure, no sleep, and again I did not fully grasp all that stuff.