How to Learn Advanced Mathematics Without Heading to University

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#41

Post by _asummers » Mon, Sep 05, 2016, 3:56 PM UTC

mafribe wrote: post #31

ryanmonroe wrote: post #28

Earlier quoted context omitted.

An added benefit to learning from a book that's more popular is that if you hit a wall and have a specific question about the material as it's presented in your book, you're more likely to find your question answered online. You might even be able to find course material that follows the book, whether from an official online course or just because the professor at some university didn't bother to make the course page…

book that's more popular Yet another benefit of popular books is that they won't be first edition, so a lot of mistakes that make it into the first edition will have been ironed out. Don't underestimate how much a strategically placed typo can confuse a learner. Rule of thumb: avoid first edition maths books.

I once had an analysis book that began the chapter "There exists epsilon < 0", which I found very amusing.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#42

Post by Chris2048 » Mon, Sep 05, 2016, 4:11 PM UTC

ploika wrote: post #40

Chris2048 wrote: post #35

Earlier quoted context omitted.

What about calculus etc? The main focus there seems to be to get a result. There are plenty of fields that use advanced math, but leave extending the math to academia. > If you can't prove what you know Does the Bayesian vs. Frequentist debate hold back working statisticians? Or debate wrt constructivism ( https://en.wikipedia.org/wiki/Constructivism_(mathematics) ) hold back math in general? I admit I'm a bit out of…

You won't do a calculus class for mathematicians without also heaps of real analysis and/or measure theory. It's a different story for a field like engineering, but that's not what the blog post is about. If you haven't studied the proofs, you haven't studied advanced mathematics. As for Bayesian vs. Frequentist, it's another vim vs. emacs style debate most of the time - which is most appropriate to use, as opposed t…

Isn't there a very small demand for actual, proof-writing mathematicians, versus "mathematicians" in the sense that they can use advanced math.

I'd say being able to use advanced math, even for engineering, is a suitable definition for "having studied advanced mathematics".

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#43

Post by Chris2048 » Mon, Sep 05, 2016, 4:15 PM UTC

lordnacho wrote: post #34

Chris2048 wrote: post #8

Earlier quoted context omitted.

I'm aiming to become a quant dev. I'm already a dev, but trying to catch up wrt the math at the moment :-O I'm finding there are a whole bunch of skills unrealted to most dev concerns. looking at this: http://quantjob.blogspot.com/2011/12/how-to-avoid-quantdevel... I think a lot of dev skills are "housekeeping" - VC, commenting, testing, agile, automation, standards etc. The quant dev stuff seems to be a lot more con…

But housekeeping is important! I've seen supposed quants who didn't know how version control worked. It caused productivity to plummet when people just did what they thought quants do. If anything it's knowing the plumbing that makes you productive as a dev, of any kind. You just can't get around understanding how branching works, or having some unit tests. Very little of the work ends up being the bit you think you'…

> it's knowing the plumbing that makes you productive as a dev, of any kind

Is this true of quant devs? Seems the focus is different - regular devs aren't as rare, so maybe the most important thing is producing a viable POC?

As for quants not knowing VC - did they come from a dev background?

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#44

Post by Chris2048 » Mon, Sep 05, 2016, 4:22 PM UTC

iorrus wrote: post #39

Chris2048 wrote: post #16

Earlier quoted context omitted.

You want an amazing, 21st century math tutorial? I was astounded by this: https://acko.net/blog/how-to-fold-a-julia-fractal/ Amazing intro to complex numbers.

Thanks that was incredible.

I actually emailed the author, asking if they had a tip jar since I was so impressed.

They replied "I'd be equally happy if you made a charitable donation this holiday to someone or some organisation that can use it more."

:-)

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#45

Post by Chris2048 » Mon, Sep 05, 2016, 4:28 PM UTC

paulpauper wrote: post #36

On question is: why? The examples in differential geometry can be difficult and time-consuming , unlike simple calculus, and are best done with computer, not by hand. A single tensor, as found in general relativity, may have dozens of components...writing them out would be taxing. My question is, what do want to do with this knowledge. There is value in learning complicated, abstract math to signal intellect and thus…

I don't know about differential geometry (isn't it relevant to machine learning?) but calculus and stats are used in finance with stochastic calculus.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#46

Post by karma_vaccum123 » Mon, Sep 05, 2016, 4:29 PM UTC

People don't go to university to learn, they go to university to get degrees...or to be more blunt...to buy degrees.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#47

Post by mungoid » Mon, Sep 05, 2016, 4:38 PM UTC

yodsanklai wrote: post #17

> How to Learn Advanced Mathematics Without Heading to University I wonder if it's even possible. Learning maths requires much work, time and dedication. Doing so alone must be very difficult. There are several things universities provide that are hard to replicate alone: a degree, which gives you access to a job, motivation, learning environment, and "peace of mind". What I mean by peace of mind is that, when you're…

I really hope this doesn't come across as brash. I don't mean it to, but I must disagree with your assertions (In my case at least). Learning advanced mathematics without university is completely possible. Because it is at your own learning pace. Not one of a University.

I graduated several years ago with a BS in Computer Science, with a Focus on Networking. And during that time, I held 3 part time jobs while also being a math tutor. Almost none of the math I use today as a physics developer was learned from schools. I also never had that piece of mind you mentioned, because I was constantly juggling several things at once while going to school. My knowledge of advanced mathematics at the time of my graduation was pretty non existent. I think the most advanced math I had was Algebra 2 or something like that, and the Professors just basically read verbatim from the book.

A few years after Uni, I started teaching myself Calc, Trig, Vector maths, Diff Eq and Physics strictly from what I have found on various sites, software and books. Because of that, I ended up getting a physics simulation developer position at a software company. Because in my companies view, being able to teach yourself all that math is much more impressive than being taught from a University.

I hated math during High School and College, but since then, I have found that I absolutely love math, and I will never stop trying to learn or do new things. My degree was two small lines on my CV, while about 50% of what I had on my CV was all learned on my free time, by myself.

So learning math without a College or University is totally possible, and in my situation, worked way better. Sites like Khan Academy, Wolfram, Youtube, etc. all give you the resources and leave it up to you to progress at your own pace, for free.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#48

Post by yodsanklai » Mon, Sep 05, 2016, 4:47 PM UTC

mungoid wrote: post #47

yodsanklai wrote: post #17

> How to Learn Advanced Mathematics Without Heading to University I wonder if it's even possible. Learning maths requires much work, time and dedication. Doing so alone must be very difficult. There are several things universities provide that are hard to replicate alone: a degree, which gives you access to a job, motivation, learning environment, and "peace of mind". What I mean by peace of mind is that, when you're…

I really hope this doesn't come across as brash. I don't mean it to, but I must disagree with your assertions (In my case at least). Learning advanced mathematics without university is completely possible. Because it is at your own learning pace. Not one of a University. I graduated several years ago with a BS in Computer Science, with a Focus on Networking. And during that time, I held 3 part time jobs while also be…

Congratulations, and I'm glad you proved me wrong :)

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#49

Post by heimatau » Mon, Sep 05, 2016, 4:56 PM UTC

Chris2048 wrote: post #20

yodsanklai wrote: post #17

> How to Learn Advanced Mathematics Without Heading to University I wonder if it's even possible. Learning maths requires much work, time and dedication. Doing so alone must be very difficult. There are several things universities provide that are hard to replicate alone: a degree, which gives you access to a job, motivation, learning environment, and "peace of mind". What I mean by peace of mind is that, when you're…

What I actually need is "learning math in a short time", With a few, minimal yet illustrative examples (ala katas), plenty diagrams/illustrations and other mental aids, an no rigour - not a single bit of set-theory! The proofs and rigor can come later... Incidentally, I'm a dev in finance, looking to move into quant dev. I have a math degree (completed 2007) and I'm doing a "CQF" to catch up with the relevant quant k…

I agree with this sentiment. I'm currently pursuing a Bachelor's in Pure Mathematics (or called 'Theoretical Math', eventually I'd like to go far as a PhD in it). I think the ideas of Math could be taught in a condensed way. Maybe it's already done but...education needs to be disrupted in order to do this.

My current idea is that Math could be taught as a language and taught as a critical thinking class. A condensed class would like like 'this is an equation...here is what we can do with it (derivatives, areas/3D/4D, etc)...but...99.99% of you won't need to know it this way. You need to use math in a way that indirectly teaches you how to creatively look at problems in life.'

I'm not sure why everyone is forced to learn math without knowing WHY they are forced to know it. Creative problem solving is one of the best takeaways, imho, for the masses.

As for Adv. Math...I think it's not effective for most people's career paths and skillset they will require in the real world.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#50

Post by lordnacho » Mon, Sep 05, 2016, 4:59 PM UTC

Chris2048 wrote: post #43

lordnacho wrote: post #34

Earlier quoted context omitted.

But housekeeping is important! I've seen supposed quants who didn't know how version control worked. It caused productivity to plummet when people just did what they thought quants do. If anything it's knowing the plumbing that makes you productive as a dev, of any kind. You just can't get around understanding how branching works, or having some unit tests. Very little of the work ends up being the bit you think you'…

> it's knowing the plumbing that makes you productive as a dev, of any kind Is this true of quant devs? Seems the focus is different - regular devs aren't as rare, so maybe the most important thing is producing a viable POC? As for quants not knowing VC - did they come from a dev background?

> As for quants not knowing VC - did they come from a dev background?

No, and that was the problem. The more you venture into this field, the more you realise how much of it is coding. New idea about how price series X relates to Y? No use unless you can pull the data, do the transformations yourself.

Another critical problem is that when you're unproductive, you make contortions to make your results "real". You make rationalizations that don't hold up, because OMG it's a lot of work to test some more ideas.