This is stupid. The hard part about a Math degree is the number of hours you have to put in. If you cannot go to university full time, go part time. If you cannot go part time, you don't have enough time to actually learn any of these topics on your own.
I've done these classes. It's typically 150 hours per class and it's not something you do after coming exhausted home from work either. After those 150 hours you'll get a basic understanding of the topic. You won't be an expert by any means. That will require more exposure, more time.
The lectures themselves are not that useful, I find. The lecturers are mostly useful in guiding you along, telling you which aspects of the theory to focus on and weeding through the study material to deliver you the best bits. The problem sets are indispensable. Exams make sure you actually know the basics in depth instead of just knowing about them.
My advice: enrol part-time, take one class at a time, catch up on the lectures and do the problem sets and the homework over the weekend.
I hope it is not stupid. I won't fit inside the university system at this point. They would make me take courses on subjects I already know which is a waste. I have about 20 hours on the weekend I can use towards accomplishing a class and I will have minimal waste since my curriculum is tailored directly for me. Of course it is only because I already wasted a decade learning math poorly that I know what I want to know and what I need to know to know it ;)
Prerequisites for classes are oftentimes a suggestion, you can easily get into a class you don't meet the prerequisites for by simply signing up for the class (most class registration systems don't bar this), or by emailing the professor and getting an override. Furthermore, if you're a non-degree seeking student, the university cares very little about you, so you can skate by with a lot more freedom with classes.
Interesting, anecdotally, I went to three different universities and they all barred this from happening without an explicit override from a professor or occasionally an adviser. Just curious what experience you have that makes you say this?
Huh, I've attended classes at two universities: one for my undergraduate and one while I was in HS, and neither had a system in place to explicitly bar you from registering for a class whose pre-reqs you didn't fulfill. At best you'd get a scary message confirmation message telling asking you "You don't meet the pre-reqs, you may be dropped from the class, are you sure?".
Also, at least when I was an undergrad, the Banner student system (from ellucian company) had no system in place for barring you from registering from classes. This was frequently the point of discussion between the professors that I TA'd for.
Eh, if you're just auditing the class, maybe. When I was in college they made me retake ridiculous prereqs for the most trivial of reasons every time I transferred, allowed no exceptions to these, and personal requests to professors to get out of them were completely ignored. The prereqs were enforced by the computerized registration system - good luck getting past them without a waiver.
As one anecdote, they once told me I needed to retake intro physics. On the pretest given on the first day of class, I came within one problem of a perfect score. Didn't make a lick of difference - their syllabus differed from the last university in the most minor of ways, and despite the fact that the class never actually covered even 50% of the stuff it claimed to on the syllabus, I was made to retake the entire sequence anyway.
I'll counter your anecdote with mine: in my undergrad years, I started out as a computer science major, and discovered that I wanted to do computational astrophysics 3 years into my college career, meaning that I lacked significant physics background. The Astronomy department was adamant on me "needing" to have done the basic physics classes (mechanics, E&M) before letting me into an introductory quantum physics class, even though I already possessed a working knowledge of the basics. I emailed the professor of the quantum physics class, explaining my situation, and simply ended up taking the quantum class alongside the basic physics classes.
Although I think your situation was pretty special as well, transferring universities is usually incredibly annoying and filled with road bumps. I've found there's a lot more leniency given to students who remain within the same university.
If you are taking a degree program, it is the institutions responsibility to ensure that you have met all the requirements. If they don't have enough information on equivalence of a different institutions course, the easiest thing for them is to require you retake the sequence.
The way to get around this isn't by taking pretests (which don't mean much) it's by writing the final exams. In some institutions you will be able to do this without (full?) course fees if you are attempting to demonstrate equivalence.
That's kind of my point - they could have tested me easily by giving me some problems from a previous final, or anything else, or even talking to me for five minutes, but instead they chose the path of petty legalism by assuming since the syllabus didn't agree with their's 100%, the only way to guarantee I knew the material was to make to pay to retake the entire sequence.
I failed to mention I'd also already spent three years as a physics major and had already taken classical mechanics, electrodynamics, and quantum mechanics - so being told to retake the intro physics sequence was quite silly indeed.
It's not exactly petty legalism, they can lose their ability to grant degrees over stuff like this. This is one of the reasons that if you are transferring institutions, as a student it is your responsibility to check transfer credits. After all, it certainly isn't true that all undergraduate curriculum are equivalent.
It's a bit of a pain, but the point wasn't that they should give you some questions from the old exam but that you should actually sit the new one, under exam conditions. That resolves the problem for everyone without you having to spend the time repeating lectures etc. In the best case you don't pay full rate either.
Having taken Algorithms at both undergrad and graduate levels and read through many books to prep Google/Facebook/etc interviews, I would flip out if anyone ever makes take an Algorithms class again.
> They would make me take courses on subjects I already know which is a waste
Then find a lower-tier university. In any densely populated region there will be at least one that's happy to take your tuition money to let you enroll in a non-degree-earning course of study.
You'll only have an issue if you want a degree which, BTW, is typically intended to be broader than a narrow course of study in a particular area of expertise.
>It's typically 150 hours per class and it's not something you do after coming exhausted home from work either.
Assuming you can only invest, lets say, 5 hours on the weekend, it will be 30 weeks per class, summing up to ~1.5 classes per year year.
I'd say that if someone can keep that up for 10 years, theirs understanding of math will be far above the average population...
I have studied a lot of mathematics on my own. I did study physics as an undergrad.
But, I went back and studied Real Analysis, Measure Theory, Combinatorics, Topology, and Stochastic Calculus.
I have found, though, that while I have a decent grasp of the concepts my understanding and ability to solve problems isn't as strong as the math grad students who studied these topics deeply.
I have found the knowledge useful, but I would agree that it would be hard to achieve the same results.
I don't see anything stupid about learning advanced mathematics on your own if you have previously followed a rigorous undergrad in physics or compsci.
Lots of mathematicians switch to a different subfield within their careers. And they do so by self studying, obviously.
If your compsci or physics undergrad provided you with a decent degree of mathematical maturity, it should be doable. The problem here is that compsci is still young, and there is a lot of variability. So diving into differential forms after attending a Java school sounds like a bad idea.
I disagree. I've been studying advanced math on my own for years with some success. I didn't have any rigorous undergrad experience, I don't even have a degree. But I also don't learn the same way most would, classrooms were never my forte, and I've found the way that advanced math is taught even just in textbooks lacks creativity.
Humans are capable of great things, don't discourage someone from trying.
This course of study seems to take just as much, if not more, time than a math ugrad+master's at a typical uni. The people who could really benefit from having a path of textbooks like this fall into two categories: those who don't have access a university (due to poverty, rural location, and/or being a shift worker, for example), and high school students.
And I think the latter category is more important than people realize. When I was a high school student, I benefitted greatly from t'Hooft's theorist.html (like this, but for physics, and put together by one of the Greats of the field). It's part of what got me really interested in physics, it was a whole lot of fun, and it actually did a pretty good job of preparing me for graduate-level coursework. Eventually I left physics and math for CS (I'm in PL, so this is even less drastic of career change than one might think), but I still have warm memories of working along t'Hooft's guide and checking off topics as I finished the problems in each textbook.
Sometimes the issue isn't time - it's money and access to schooling. Just because you've had the access, doesn't mean others do - and there are many, many who don't.
> Just because you've had the access, doesn't mean others do...
I don't think that the author of the post you're responding to is making any sort of normative claim.
> Sometimes the issue isn't time - it's money and access to schooling
I think the author is suggesting that if you have that kind of free time, then you either a) must be independently wealthy, or else that b) trading some of that free time for cash you can use to buy credit hours is a net positive because the guidance is worth it (again, assuming your goal is to learn math as opposed to eg obtain a uni degree).
I agree that's not necessarily a good assumption globally, but it's probably a decent assumption for almost everyone in the west, both in terms of self-learning capabilities and in terms of available funds.
I don't think it's a decent assumption for "almost everyone" in the west. I'd say it often is the case that you won't have enough free time for such studies unless you trade cash (income) for the free time. At which point you may not have much after paying the bills. Or you're unemployed and, well, don't have the cash. You suggest trading some of that free time for cash, as if unemployment were something people solve by snapping their fingers and choosing to make a trade. That sounds a bit insulting towards all the people (who are many) that struggle with unemployment in western countries.
> You suggest trading some of that free time for cash, as if unemployment were something people solve by snapping their fingers and choosing to make a trade
Not at all; I meant in the form of a loan, where free time is time you would otherwise spend retired.
And I was also assuming that you already have a decent job that allows you to work 40 hours or so and make a comfortable enough living to consider spending your free time learning math.
Frankly, I can't possibly imagine trying to do something like learn advanced mathematics while also struggling with un- or under-employment. I grant that there are probably people far more motivated and resilient than I assume :-)
Of course. I hate the higher ed situation in the US as much as the next guy and wish we could move closer to the systems available in much of Europe, especially Germany
(perhaps without the pre-high school bifurcation).
I interpreted this thread as being about advice to a typical person interested in learning math who exists in the society we (specifically, Americans) live in today. For the exceptional, the appropriate advice is of course different.
Its it stupid at all. I taught myself Triginometry from a book for fun. Sure, not everyone's idea of a good time but I don't see the need to take a University or College course for lots of money when in fact I only spent about AU$34.95 on a good book and I didn't need to feel rushed in getting to grips with the concepts.
I learn different things at different speeds, a course makes me go at a speed I don't enjoy. This is perfect.
You think trigonometry is taught in primary school?
You miss the point also: I was taught trig in high school, and I remember SOHCAHTOA, etc - but until I looked at lines drawn on a unit circle and worked put what secant, sine, tangent and their corresponding ratios meant I didn't really understand trig.
Many textbooks provide much the same structure as in universities. However, I have had a lot of success in attempting to read far above my level, and satisfying the dependencies that I need along the way.
From a third world perspective, it is taught in high school but I rarely know anyone who gets interested in it after graduating, much less retain the knowledge that they learned.
I would partially agree. Yes, it's stupid if you have enough time "and" money to go to university and study math. Otherwise, if you have enough time, this plan might work for you. But, I wouldn't consider it a wise move, because science/math graduates are already struggling to find jobs in/out-side the academia, and a math degree from a decent university goes a long way in landing you a job.
I think, math, unlike CS, is not a "skill" you use in your everyday work. Whoever does math/science has to dedicate much of their life to it. CS you can learn on the internet, by MOOC's, or just by reading books about it. Math on the other hand, simply doesn't work like that.
To be clear, by math, I mean "advanced" mathematics as the title indicates. Elementary (and intermediate) math is required to learn no matter what.
> If you cannot go to university full time, go part time. If you cannot go part time, you don't have enough time to actually learn any of these topics on your own.
Going to university part time eats up more time than reading a textbook at home or wherever you are in your spare time. It also locks you in to the specific pace that the class is at which is not optimal for most people, because people learn different things at different paces. There is also the cost of university to consider.
I've done these classes. It's typically 150 hours per class and it's not something you do after coming exhausted home from work either. After those 150 hours you'll get a basic understanding of the topic. You won't be an expert by any means. That will require more exposure, more time.
The lectures themselves are not that useful, I find. The lecturers are mostly useful in guiding you along, telling you which aspects of the theory to focus on and weeding through the study material to deliver you the best bits. The problem sets are indispensable. Exams make sure you actually know the basics in depth instead of just knowing about them.
My advice: enrol part-time, take one class at a time, catch up on the lectures and do the problem sets and the homework over the weekend.