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How to Learn Advanced Mathematics Without Heading to University

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Re: How to Learn Advanced Mathematics Without Heading to University

#61

Post by riprock »

ska wrote: post #21

The main thing to remember is that nobody learns mathematics to any significant depth by reading. The only way to learn it is by doing it. Doing it carefully, and in full detail, not falling into the trap of "and I understand it from there". So the biggest barriers to doing it on your own aren't source material (there is lots of that) it's a good source of correction. There is also the usual problem of self study, in…

> So the biggest barriers to doing it on your own aren't source material (there is lots of that) it's a good source of correction.

Does anyone have any recommendations for where I can find a "good source of correction" (private tutor) online or locally for discrete math/algorithms/college-level mathematics? I looked at WyzAnt which gave me no results for my area -- most of the tutors seem to be for SAT/high school prep.

Re: How to Learn Advanced Mathematics Without Heading to University

#62

Post by rubicon33 »

EliRivers wrote: post #15
steQ wrote: post #5

I know that many learn programming themselves but I'm curious if anyone have learn advanced mathematics this way.

I took a Masters in Mathematics with the Open University. It's not quite as brutal as simply telling you which textbook to read and see you in nine months for the exam (repeat five times), but it's not far off. It's not quite entirely by yourself, as in the webpage linked, but it worked like this: 1) Get sent problem sheets and a list of what chapters in a textbook to work through. 2) Read textbook. 3) Solve the prob…

Can you explain what steps you would take to learn a new subject? For instance, lets say you wanted to learn quantum mechanics - Where would you start? How would you study and check your work? Etc.

Re: How to Learn Advanced Mathematics Without Heading to University

#63

Post by chris11 »

thearn4 wrote: post #60
steQ wrote: post #5

I know that many learn programming themselves but I'm curious if anyone have learn advanced mathematics this way.

I guess I sort of did. I never took mathematics seriously, have a GED instead of a HS diploma, and subsequently started college in remedial HS-level algebra. But now I have a PhD in applied mathematics and work in the overlapping gray area of research that exists between the mathematics, computer science, and systems engineering disciplines. I did have some very good (and very patient) instructors early on. But at so…

What books would you recommend? I'm currently in university, and I've had some exposure to discrete mathematics. But I'm definitely not comfortable with discrete math.

Re: How to Learn Advanced Mathematics Without Heading to University

#64

Post by mathattack »

mng2 wrote: post #55
mathattack wrote: post #45

Earlier quoted context omitted.

That's my point. It was pretty much what was required for the CS degree. The UK standard is much higher.

I don't think it's just the UK. At Berkeley, for example, the Math minor requires 4 lower division courses and 5 upper div. https://math.berkeley.edu/programs/undergraduate/minoring-ma...

Yes - 9 versus 5. Is Berkeley quarterly or semester? Either way, it looks like a much more rigorous program. (I've generally been very impressed with Berkeley Math and CS grads)

Re: How to Learn Advanced Mathematics Without Heading to University

#65

Post by tanker »

lumberjack wrote: post #58

There is no reason to shun university. If you want to learn mathematics but do not have the time for a full time degree do it part time. You are most definitely not actually going to reach the same level of mastery of mathematics as even the most mediocre graduate by studying alone. It requires a huge amount of commitment and staying focused and discipled enough is very hard when you don't have a set goal and good co…

I disagree, at least at the undergraduate level.

There is no shortage of problems and solutions to check your knowledge for much of undergraduate mathematics.

As to the value of tutorial sessions for you, it is important to remember that people learn differently. Speaking with an expert is valuable, but not required in my opinion.

To really learn a subject, you have to go beyond the minimum required to get a good grade on homework and tests. You can absolutely do this in university, but I found that I was rarely willing to do so. Studying on my own, I find it easier to reach a deeper level of understanding.

Re: How to Learn Advanced Mathematics Without Heading to University

#67

Post by goc »

chris11 wrote: post #63
thearn4 wrote: post #60

Earlier quoted context omitted.

I guess I sort of did. I never took mathematics seriously, have a GED instead of a HS diploma, and subsequently started college in remedial HS-level algebra. But now I have a PhD in applied mathematics and work in the overlapping gray area of research that exists between the mathematics, computer science, and systems engineering disciplines. I did have some very good (and very patient) instructors early on. But at so…

What books would you recommend? I'm currently in university, and I've had some exposure to discrete mathematics. But I'm definitely not comfortable with discrete math.

To start from absolute zero, check out Suzanna Epp's Discrete Math[0]. I believe even a motivated high school student could get started with it and even finish it. If your proof-writing is shaky, the book provides a very good workout. From there it will be easy to choose the areas of discrete math to specialize.

[0] http://www.amazon.com/gp/product/0495391328?keywords=susanna...

Re: How to Learn Advanced Mathematics Without Heading to University

#68

Post by chris11 »

goc wrote: post #67
chris11 wrote: post #63

Earlier quoted context omitted.

What books would you recommend? I'm currently in university, and I've had some exposure to discrete mathematics. But I'm definitely not comfortable with discrete math.

To start from absolute zero, check out Suzanna Epp's Discrete Math[0]. I believe even a motivated high school student could get started with it and even finish it. If your proof-writing is shaky, the book provides a very good workout. From there it will be easy to choose the areas of discrete math to specialize. [0] http://www.amazon.com/gp/product/0495391328?keywords=susanna...

Thanks, I'll check it out. My proof-writing is definitely shaky. I can clearly see the relationship between programming on writing proofs, but I can't get immediate feedback on the validity of my mathematical proofs like I can with code.

Re: How to Learn Advanced Mathematics Without Heading to University

#69

Post by hexagonc »

ska wrote: post #21

The main thing to remember is that nobody learns mathematics to any significant depth by reading. The only way to learn it is by doing it. Doing it carefully, and in full detail, not falling into the trap of "and I understand it from there". So the biggest barriers to doing it on your own aren't source material (there is lots of that) it's a good source of correction. There is also the usual problem of self study, in…

The only way to learn it is by doing it. Doing it carefully, and in full detail, not falling into the trap of "and I understand it from there".

This. So much this. A lot of people think there is some big difference between mastery from a physical versus intellectual level. No one who is serious about learning to play a musical instrument will only play a song up to a point and then stop, saying "... no need to go further, I already know how to play the rest." I think the way the brain consolidates high level learning into long term memory is essentially the same as for "muscle memory". This is like when you learn to drive. At first, you have to think consciously about every little detail but with practice, your unconscious mind takes those over and your conscious mind is left to operate on higher and higher level concepts. Mathematics is hard and the sooner you can offload the details to your unconscious mind the better. And the only way to do that is by practice.

I consider myself to be a smart but sometimes intellectually lazy person and had to struggle to develop the habit of working problems out rigorously and completely when learning new material. The belief that you can learn material by just reading is seductive because it feels like you're saving time and getting to the interesting topics faster. But in all likelihood, this belief is false and will be proven as false the moment your understanding is put to the test, either in a real test, or when subsequent material requires a solid understanding of older material. Sure, you may indeed be understanding it at the moment you're reading and in the flow of the material. But what makes your knowledge solid and reliable even under adverse circumstances (e.g., when you're distracted or learning a difficult new subject that builds on that knowledge) is practice and repetition. This applies not just to mathematics but to learning a new framework or programming language.

Re: How to Learn Advanced Mathematics Without Heading to University

#70

Post by Retra »

thegenius2000 wrote: post #49
chatmasta wrote: post #30

Earlier quoted context omitted.

This is probably the reason why there are so many more autodidact programmers than mathematicians. When programming, you know if you made an error as soon as you try to run your code. The program, by definition, must be "correct" in order to execute. The "source of correction" is the error detection built into any programming language runtime or compiler. No such "source of correction" exists for mathematics, and tha…

Good point and great analogy, though I think EWD might be turning over in his grave. While the error detection built into compilers and the testing process are, in general, indispensable tools for developing stable software, a program that executes without any evidence of error is a great distance from a program that has been shown to be correct.

It's still easier to build up an understanding of computers under that environment. You may not be proving your programs correct, but you are probably proving them useful.
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