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

[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.

 

[morphism]

Just thought I'd let you know that quotient spaces are very intuitive, and there's ample motivation behind them, in case you haven't figured this out already. It's all about identifying elements of the underlying set X via an equivalence relation ~. The resulting collection of equivalence classes X/~ is called the quotient space, or identification space. Here, a set is a collection of equivalence classes; it's open if the union of the equivalence classes produces an open set in the original space X.

Of course there's much more to say about this and where it comes from, but this should hopefully help you in knowing what to look for.

 

[andytoh]

Ah, so if Jason, who voted 30+ pages, now realizes that more like 5 pages, I wonder how many others who voted 30+ pages is also around 5 pages in reality...

 

[Lee55]

The question is entirely dependant on mitigating circumstances, so it's hard to judge, but on average I can get through a textbook in a week, I work full time, and I only have those couple of hours before I go to bed, and what I can read as I travel. I try to find time as soon as I get back from work, it depends if there's a math question I'm itching to work out.

 

[JasonRox]

Just thought I'd let you know that quotient spaces are very intuitive, and there's ample motivation behind them, in case you haven't figured this out already. It's all about identifying elements of the underlying set X via an equivalence relation ~. The resulting collection of equivalence classes X/~ is called the quotient space, or identification space. Here, a set is a collection of equivalence classes; it's open if the union of the equivalence classes produces an open set in the original space X.

Of course there's much more to say about this and where it comes from, but this should hopefully help you in knowing what to look for.

Exactly, that's the way I'm feeling now.

But at first, the idea of a quotient map... was just like, uh?

I'm really excited to see where it leads though.

 

[JasonRox]

Ah, so if Jason, who voted 30+ pages, now realizes that more like 5 pages, I wonder how many others who voted 30+ pages is also around 5 pages in reality...

I can do 30 pages.

But that's like Introductory Linear Algebra, or Calculus and things like that.

Later on, things are just different.

 

[JasonRox]

The question is entirely dependant on mitigating circumstances, so it's hard to judge, but on average I can get through a textbook in a week, I work full time, and I only have those couple of hours before I go to bed, and what I can read as I travel. I try to find time as soon as I get back from work, it depends if there's a math question I'm itching to work out.

If you read them that quickly, you should be putting Gauss to shame by now.

 

[hrc969]

Ah, so if Jason, who voted 30+ pages, now realizes that more like 5 pages, I wonder how many others who voted 30+ pages is also around 5 pages in reality...

Well who knows.

I did not vote at all. In my opinion counting number of pages is useless, meaningless, etc. I'll give you an example from Several Complex Variables since that's what I'm studying right now. You can go through two pages of Hormander's and in many cases you can learn more than going through ten of Krantz' book and it will take longer with Hormander's book. The difference is that Hormander's material is far more compressed and if you want to go through everything as thoroughly as you described it is easier to do so with Krantz's book.

So more pages does not necessarily mean you've learned more. Less pages don't mean you've learned less. Yeah, so I think your question is useless. It doesn't matter how many pages I read and it varies far too much. Even within the same subject as I said above it varies. Then it can vary depending on the field. So like Jason Rox said, some one can suck at learning one subject but be good at another.

 

[Gib Z]

Yea i was going to point that out as well. It depends on how hard the book is, how densely the information is packed, how much knowledge or deductions are assumed! 30 pages can be filled with crud, like the Australia textbooks I was talking about. Most arent A4, filled with pretty borders, nice big diagrams and abit of history surrounding the theorem. The proofs will take no calculation too easy to be assumed. This makes it much larger than say, Mathwonks 5 pages of Linear Algebra covering an entire semester!

 

[Lee55]

If you read them that quickly, you should be putting Gauss to shame by now.

I should of mentioned that this expected, as part of my current course. The textbooks are around 100 pages on average, sorry, I was about to go to bed when I wrote the last post.

 

[JasonRox]

I should of mentioned that this expected, as part of my current course. The textbooks are around 100 pages on average, sorry, I was about to go to bed when I wrote the last post.

But can you imagine reading that quickly though!

Apparently Gauss read Gauss's Arithmatica (spelling?) in two to three days!

He died at the age of 20 or so, and only started learning mathematics at like 15! And look at the work he DID! Damn those that ignored him. Ignorance and jealousy does no good!

 

[d_leet]

But can you imagine reading that quickly though!

Apparently Gauss read Gauss's Arithmatica (spelling?) in two to three days!

He died at the age of 20 or so, and only started learning mathematics at like 15! And look at the work he DID! Damn those that ignored him. Ignorance and jealousy does no good!

You don't mean Gauss here, do you? Figuring as Gauss lived to around 80 or so, did you mean Galois?

 

[JasonRox]

You don't mean Gauss here, do you? Figuring as Gauss lived to around 80 or so, did you mean Galois?

Yes, I meant Galois! Ooops, my mistake!

 

[mathwonk]

Lee 55 please read my graduate algebra textbook from my webpage, and let me know next week when you finish, including the exercises.

 

[mathwonk]

according to my best teacher, maurice auslander, a world famous algebraist, he knew only one mathematician (paul cohen, fields medalist) who could learn math by reaDING WITHOUT WRITING 3-5 PAGES PER PAGE read. so anyone who thinks they have learned 30 pages should have written 90 pages-150 pages.

 

[Gib Z]

How large is our handwriting allowed to be?

 

[mathwonk]

as my 8th grade teacher used to say, don't laugh, you only encourage him.(on a somewhat related note, it is sort of amazing how much one used to learn in 8th grade, based on the number of times since then i have heard myself say, "we learned that in 8th grade.")

 

[mathwonk]

hrc969, note that the first short chapter of hormanders book covers all of one variable complex analysis, and more, since it proves the singular integral version of cauchy's theorem.

soon after, as i recall, he solves the mittag leffler problem in several variables, by showing every non negative "divisor" on C^n is the divisor of a global holomorphic function.

i.e. in sheaf language he computes H^1 (O) = {0}. and this is just the beginning. (it was 30 years ago i read this stuff, and since it is not my specialty, I never did finish it all.)

of course note too that when he gets to the commutative algebra chapters, where he is not an expert, he slows down to snail crawl, as if he thinks that mickey mouse stuff is somehow dense or hard for analysts!

so for me personally the number of pages wirtten per page read of hormander, goes from way more than 5 at the beginning, (as high as 10-20 pages per sentence ocasionally, or even per word, for one famous "hence" as I recall) to about Auslanders number nearer the back of the book.

 

[mathwonk]

notice on this forum, when we tell people that a manifold is a top sopace locally homeomorphic to R^n they believe it, but when we tell them to understand math you have to do some work, some people don't want to hear us.

 

[JasonRox]

notice on this forum, when we tell people that a manifold is a top sopace locally homeomorphic to R^n they believe it, but when we tell them to understand math you have to do some work, some people don't want to hear us.

Why do all that work when you can use Wikipedia?

 

[ehrenfest]

A lot of math books include lots of commentary and redundancy and the "motivation" behind the theory in order to guide you through a complicated subject. Rudin's Principles of Mathematical Analysis has none of that. In terms of Rudin's pages, I said 15.

 

[mathwonk]

see how long it takes you to read and understand my 13 page primer of linear algebra on my webpage, which goes from definition of vector spaces through jordan canonical form.

thats right, 13 pages. so one day for some of you 15 page per day guys on that. then spend the next 4 days reading my 53 page notes on riemann roch theorem.

then check back in here with a progress report, and take the quiz.

i would think you would do well to finish those in a semester.

 

[BryanP]

Depends on the math.

Some come really intuitively to me and I can read many pages and understand it (meaning more than 10 pages a day).

 

[Crosson]

see how long it takes you to read and understand my 13 page primer of linear algebra on my webpage, which goes from definition of vector spaces through jordan canonical form.

thats right, 13 pages. so one day for some of you 15 page per day guys on that. then spend the next 4 days reading my 53 page notes on riemann roch theorem.

then check back in here with a progress report, and take the quiz.

I will accept this as a challenge, and within the next week or so I will find a day for each of these sets of notes. It would be nice if I had a copy of the test available in the digital equivalent of a sealed letter on my desk. That way I can read through the notes then put them away and "open" the test and write it that same day.

As for the Linear Algebra, I already have some familiarity with that subject, although your notes look interesting for many reasons, among which are their brevity.

The Reimann-Roch theorem, however, is not something that I have ever encountered (I am a physicist by profession). Therefore I for one will consider it to be a stronger test. Also, 54 pages in one day will exceed the number of pages in the original claim.

Furthermore, the total number of pages will increase by my reviewing / learning for the first time the things that you will in some cases assume as prerequisites. In other words I am asking permission to use the simultaneous use of supplementary readings to help myself learn your notes; in any case I will take the tests with all books closed and away if that is to be set as a condition of the forum challenge.

i would think you would do well to finish those in a semester.

That takes the pressure off somewhat, and would make success feel even better. I just want to say, regardless of any friendly forum challenge, that I really appreciate your contribution to the forums, Mathwonk. And I have a lot of respect for the details of your career; especially that postdoc at Harvard sounds fun :)

 

[daveyinaz]

I'll read the notes as well. Not that you guys know me or anything but still..

 

[tronter]

crosson did you read quickly in undergrad as well? Or only after gettinga PhD?

 

[Crosson]

crosson did you read quickly in undergrad as well? Or only after gettinga PhD?

Yes, I started doing self-study in my sophomore year at university.

Even before that I never felt the need to do exercises. And despite this, in school I always got top grades in math and a lot of respect. This is why I must do everything I can to fight the oppressive idea that exercises are a necessary part of learning mathematics.

Soon someone will say "but if he doesn't do the exercises, then he is only fooling himself in saying that he has learned the material." But this just stubbornly assumes the very proposition I am fighting against! Mathematics for me is more like washing dishes; if someone wants to give me an exam in the form of a sink full of dirty dishes, it is not necessary that I prepare by washing each type of cup and plate repetitively.

I have thought a lot about what it means to learn a part of mathematics. I don't think it is enough just to do well on exercises and exams. Nor is it enough to teach the subject at the university level. Ultimately, I think the necessary and sufficient condition for having learned a part of mathematics is to publish major research in that area. And if that is the standard, then I must I do not know any mathematics, unlike mathwonk. I may have absorbed a lot, and I can recall it quickly to pass any exam or teach a student, but I have no plans of doing major research in these areas.

That is why my original answer to this thread should have been "http://en.wikipedia.org/wiki/Mu_(negative)" ."

 

[uman]

So read Mathwonk's pamphlet in one day and I'm sure he will be able to test your knowledge of it afterwards.

 

[tronter]

Yes, I started doing self-study in my sophomore year at university.

Even before that I never felt the need to do exercises. And despite this, in school I always got top grades in math and a lot of respect. This is why I must do everything I can to fight the oppressive idea that exercises are a necessary part of learning mathematics.

Soon someone will say "but if he doesn't do the exercises, then he is only fooling himself in saying that he has learned the material." But this just stubbornly assumes the very proposition I am fighting against! Mathematics for me is more like washing dishes; if someone wants to give me an exam in the form of a sink full of dirty dishes, it is not necessary that I prepare by washing each type of cup and plate repetitively.

I have thought a lot about what it means to learn a part of mathematics. I don't think it is enough just to do well on exercises and exams. Nor is it enough to teach the subject at the university level. Ultimately, I think the necessary and sufficient condition for having learned a part of mathematics is to publish major research in that area. And if that is the standard, then I must I do not know any mathematics, unlike mathwonk. I may have absorbed a lot, and I can recall it quickly to pass any exam or teach a student, but I have no plans of doing major research in these areas.

That is why my original answer to this thread should have been "http://en.wikipedia.org/wiki/Mu_(negative)" ."

Surely you must find something difficult? Edward Witten did all the exercises in a book when he studied. It builds work ethic right? Then how do you read a math or physics book? Do you read it like a novel, then read another book on the same subject like a novel? Problem solving can only be gained through practice. Or do you do the problems in your head?

 

[Crosson]

Surely you must find something difficult?

Don't get me wrong, math is difficult and it consumes a lot of effort. But I am able to read and comprehend quickly because:

1) I spent a lot of effort studying symbolic logic.

2) In general I am good at learning the rules of language-games, e.g. the modern mathematical style of exposition.

3) I have the sort of memory that can recall important phrases and sentences with high precision.

But problem-solving is a different and related skill from reading and comprehending. All I know with respect to math is that I can solve book problems, because as I said I have not done research in pure math. I am not sure if I could meet my own standard of a worthy publication in those areas.

Do you read it like a novel, then read another book on the same subject like a novel?

Yes and no. I read math like I read a newspaper, but that only means that I read math relatively quickly and I read the newspaper relatively slowly.

As far as novels are concerned, I can't stand to read fiction and I have not done so since the 10th grade.

Problem solving can only be gained through practice.

Either

1) show me a rigorous proof of that claim

2) call me a liar

3) get my university on the phone and have my degrees revoked

or (recommended)

4) accept the fact that I am a counter example to that claim.

 

[uman]

Everyone will believe you when you learn linear algebra from Mathwonk's notes in one day.