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

## How many pages of math can you absorb in one day.

• ### 30+

• Total voters
115
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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JasonRox
Homework Helper
Gold Member
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.

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

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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JasonRox
Homework Helper
Gold Member
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
Staff Emeritus
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!"

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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cristo
Staff Emeritus
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)

oops, i was talking about afternoon greenwich mean time.
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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cristo
Staff Emeritus
Ahh, ok. Well that sounds better!

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

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.

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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! Lets gooooogooggogo. Also, no one is allowed to be sober in any fashion while taking this test!

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

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.

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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

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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.

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JasonRox
Homework Helper
Gold Member
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.

JasonRox killed the thread. :!!) :surprised

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

JasonRox
Homework Helper
Gold Member
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
Homework Helper
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.

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.....

The question is entirely dependant on mitigating circumstances, so it's hard to judge, but on average I can get through a text book 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
Homework Helper
Gold Member
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.

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
Homework Helper
Gold Member
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.