Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

So you want to study mathematics

susanrigetti.com

Post reply on HN
Print view View original

131–140 of 371 posts

Re: So you want to study mathematics

#131

Post by ChrisLomont »

paulpauper wrote: post #121

You don't need so many books. many of the old texts will cover many important college-level concepts in a single source. https://www.gwern.net/docs/statistics/1957-feller-anintroduc... this is linear algebra + combinatorics + probability + stats If you understand the material in this one book it's reasonable to say that you are pretty good at math

At a first glance that book completely fails for an undergrad lin alg course, and looks weak in other areas too.

Examples: the words nullity and kernel don't appear, rank of a matrix is not in it, and, well, every topic I can think of for undergrad linear algebra is simply not in the book.

It's equally bad for stats: no mention of many common distributions a student would learn for example.

Re: So you want to study mathematics

#132

Post by Koshkin »

joatmon-snoo wrote: post #49
brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

> within the US

All fifty states or just continental?

Re: So you want to study mathematics

#133

Post by davidmr »

mbustamanter wrote: post #13

> My goal here is to provide a roadmap for anyone interested in understanding mathematics at an advanced level. Anyone that follows and completes this curriculum will walk away with the knowledge equivalent to an undergraduate degree in mathematics. NO, NO, NO. There is no real way to go up to the real deal without having understood elementary Functional Analysis, which the article doesn't even mention. FA is roughly…

This is certainly not universally the case, even in very well-regarded departments. The University of Chicago, for example, does not require it: http://collegecatalog.uchicago.edu/thecollege/mathematics/.

Re: So you want to study mathematics

#134

Post by wizzwizz4 »

JadeNB wrote: post #125
Melatonic wrote: post #95

Earlier quoted context omitted.

Not sure I agree with that - you also have to take into account that calculus is a requirement for many other sciences. I suppose you could just of course make it a pre-req for things like that but I found that in highschool rarely did they go that deep. Physics becomes a hell of a lot easier with basic calculus for example. If anything should be dropped from a highschool level its all of the insane memorization you…

> If anything should be dropped from a highschool level its all of the insane memorization you have to do for some of the lower level math classes - I found that totally useless. You then learn some basic calculus and realize "I just wasted so much of my life" and never need to memorize those things again. What sort of memorizations do you have in mind that you no longer need to memorize once you know calculus?

s = ut + ½at²

Re: So you want to study mathematics

#135

Post by auggierose »

Koshkin wrote: post #82
k__ wrote: post #58

Earlier quoted context omitted.

I think, the problem is, proofs are what makes math useful. This might sound a bit dense, but the alternative is what 90% of programmers do every day.

I think one can get far enough by applying known mathematical facts. (Proof: elementary school math is useful.)

The problem is, usually you need to combine known mathematical facts to solve a problem. Now, how do you know that you combined them properly?

Yup. You need to know what a proof is.

Re: So you want to study mathematics

#136

Post by hintymad »

whatshisface wrote: post #88
hintymad wrote: post #46

I find it hard to believe that the author started to appreciate physics by reading The Feynman Lectures on Physics before any exposure to physics or even algebra, and in less than three years went from barely knowing high school math to enjoying advanced mathematical physics and graduate-level quantum physics. It looks this is one-in-a-million level brilliance as learning the sheer amount of requirement knowledge in…

I agree that this does not on its surface seem possible, but I can think of a few explanations. 1. I recently spent a week on one section of one chapter of a math book. I was able to follow it within an hour on the level of "these are the rules and this is the sequence of their application," but I have stuck with it since then because I wanted to understand it well enough that the proof they chose to use would seem o…

> Intelligence is equally distributed between genders, but most professional physicists are men,

Why limit yourself to gender? Why not white vs other skin color? Why not the US vs another country? Why not democrat vs republicans? Why not western culture vs whatever other culture? Seriously, this kind of categorization is just ridiculous, especially when you speculate instead of showing evidence.

No, I won't be surprised if a STEM professor is reading topology. I will be surprised if a gender-study professor is reading topology. I will be also surprised if some stranger (i.e. I don't know the background of this person) who could only do pre-algebra in high school says Topology without Tears is the first book on Topology that they read and they immediately fall in love with topology. Possible, for sure. Surprising, of course. It's just a matter of probability.

Re: So you want to study mathematics

#137

Post by joe_the_user »

ghufran_syed wrote: post #16

I went from only having done high school math 10 years ago to completing an MS in math and statistics at my local state university while working in an unrelated field. I would recommend NOT starting with calculus if you haven’t done it, instead, just learn how to do proofs - I used Chartrand “Mathematical proofs” - You don’t need to know any math beyond algebra in order to do that most of this book. If you need to re…

Well,

I feel like one can easily get a bunch of "Really you should start with X" statements concerning math. Really you should start with proofs, really you should start with problems, really you should start with these concepts. I started with concepts rather than proofs or problem and I too went to a MA and various study. I tackled both proofs and problems but I don't think I'd have done as well if I'd jumped on these immediately.

So, altogether for someone wanting to get into advanced math, I'd say to look at the variety of advice out there and follow the kind that seems to help your progress.

Re: So you want to study mathematics

#138

Post by Koshkin »

JadeNB wrote: post #126
edflsafoiewq wrote: post #123

Earlier quoted context omitted.

Calculus and linear algebra continue to dominate in applied mathematics. "How can I turn this into a problem in linear algebra?" is probably the most fruitful mathematical technique that has ever existed.

> "How can I turn this into a problem in linear algebra?" is probably the most fruitful mathematical technique that has ever existed. And, from that perspective (with which I agree), calculus itself is just another instance of trying to turn a non-linear problem into a problem in linear algebra!

True: the differential at a point is a linear map; the integral is a linear form (on the vector space of functions).

Re: So you want to study mathematics

#139

Post by [deleted] »

LAC-Tech wrote: post #127

I really don't. For many, many years I thought I did. I'd have a brief surge of interest for a few weeks, and then get completely bored of it. I'm not someone who finds it inherently easy, so boredom + difficulty = failure. When I was foolish enough to do this in university, it meant doing great in the first few assignments, and then abysmally in the exam. So my policy now is to never study maths for its own sake. On…

[deleted]

Re: So you want to study mathematics

#140

Post by wizzwizz4 »

ChrisLomont wrote: post #131
paulpauper wrote: post #121

You don't need so many books. many of the old texts will cover many important college-level concepts in a single source. https://www.gwern.net/docs/statistics/1957-feller-anintroduc... this is linear algebra + combinatorics + probability + stats If you understand the material in this one book it's reasonable to say that you are pretty good at math

At a first glance that book completely fails for an undergrad lin alg course, and looks weak in other areas too. Examples: the words nullity and kernel don't appear, rank of a matrix is not in it, and, well, every topic I can think of for undergrad linear algebra is simply not in the book. It's equally bad for stats: no mention of many common distributions a student would learn for example.

Is that such a bad thing? I'm half-convinced that the “rank of a matrix” is just an artefact of a particular algorithm for inverting matrices. And distributions aren't everything; I can look up any distribution I want on Wikipedia, just as soon as I need it, but a proper foundation in what statistics means is much harder to come by. (I have enough of a foundation to know when it's being taught very wrong, but not enough to actually be very useful in day-to-day life.)
Post reply on HN