How to Learn Advanced Mathematics Without Heading to University

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

#61

Post by whorleater » Mon, Sep 05, 2016, 5:48 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…

Without proofs and rigor, aren't you just reducing mathematics to a set of rules to be memorized? Sure, you can memorize the basics of group theory, but when it comes down to constructing the Diffie-Hellman Key-exchange, you'll still the mathematical intuition derived from learning the proofs.

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

#62

Post by bitL » Mon, Sep 05, 2016, 5:57 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…

The main problem of contemporary mathematics is that it is unbelievably obfuscated to most people, unnecessarily so. So even if you a have super-simple thing, mathematicians invented ways how to completely obfuscate meaning (often unfortunately in order to achieve prestige and being considered elite as a form of intellectual pride). Imagine Dirichlet's box principle, a thing that a 5-year old should understand; now look at how is it taught in discrete mathematics. I remember myself being really upset after 5-year study of theoretical backgrounds and some things finally clicked and I realized how simple they were and how much was just a ballast to reach them. Often mathematicians invent a theory in their teens and spend the rest of their lives to fight with unexpected monsters in boundary conditions they created. Similar to making a distributed middleware backbone and then debugging it with all unexpected network error/split brain stuff coming in.

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

#63

Post by mungoid » Mon, Sep 05, 2016, 5:57 PM UTC

yodsanklai wrote: post #48

mungoid wrote: post #47

Earlier quoted context omitted.

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 :)

Thank you! I will admit that it was by no means quick or easy and there were many, many times I wish I could have had an actual person with me to explain it. Not to mention the frequent of wanting to give up when something wasn't 'clicking' and i felt i couldn't do it.

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

#64

Post by adrianm » Mon, Sep 05, 2016, 6:01 PM UTC

hal9000xp wrote: post #60

As I a software developer with no degree (working since 2009 in 3 countries), I can share my experience of attempts to learn advanced math. In 2010, I was very interested in foundations of mathematics, an extremely abstract math branches: https://en.wikipedia.org/wiki/Foundations_of_mathematics In particular I spent huge amount of time on: https://en.wikipedia.org/wiki/Nicolas_Bourbaki (Set theory) https://en.wikiped…

I don't agree with your suggestion about olympiad math since it often has little relationship to applying advanced mathematics, but there definitely is merit to the idea that you might need to put theory into practice in order to gain insight about these things.

I recommend (surprise surprise) programming. Implement fast fourier transform in C and then Common Lisp. Write a finite difference PDE solver. Try solving actual problems to motivate you. Signals analysis can be a fun way to exercise your knowledge. Try analyzing your favorite songs and figuring out what makes them sound the way they do. Maybe implement some audio filters. If that's not your cup of tea, write physics or chemistry simulations instead. Then use OpenGL to visualize them. Then make them interactive.

I can go on and on, but I'll just leave two book recommendations for those who might enjoy programming advanced mathematics.

Structure and Interpretation of Classical Mechanics : https://mitpress.mit.edu/classical_mech

Functional Differential Geometry : https://mitpress.mit.edu/books/functional-differential-geome...

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

#65

Post by hgh » Mon, Sep 05, 2016, 6:02 PM UTC

bitL wrote: post #62

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…

The main problem of contemporary mathematics is that it is unbelievably obfuscated to most people, unnecessarily so. So even if you a have super-simple thing, mathematicians invented ways how to completely obfuscate meaning (often unfortunately in order to achieve prestige and being considered elite as a form of intellectual pride). Imagine Dirichlet's box principle, a thing that a 5-year old should understand; now l…

Could you explain the principle in terms a 5-year old would understand?

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

#66

Post by _w7am » Mon, Sep 05, 2016, 6:07 PM UTC

hgh wrote: post #65

bitL wrote: post #62

Earlier quoted context omitted.

The main problem of contemporary mathematics is that it is unbelievably obfuscated to most people, unnecessarily so. So even if you a have super-simple thing, mathematicians invented ways how to completely obfuscate meaning (often unfortunately in order to achieve prestige and being considered elite as a form of intellectual pride). Imagine Dirichlet's box principle, a thing that a 5-year old should understand; now l…

Could you explain the principle in terms a 5-year old would understand?

If you have n boxes and n+1 things, then it is guaranteed that one box has more than one thing.

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

#67

Post by aluhut » Mon, Sep 05, 2016, 6:11 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…

I wish I could make the jump again. When I was a kid, I loved Math. I even got one of this badges that were so popular in my east block country, for being the best kid in Math for my whole year group. Then we moved to Germany. Math level was far below mine, I got bored, started to do other stuff and lost it when they overtook me. Growing up and work did the rest. I lost it. When I had/have to do some math I'm doing what is needed but this creative spark you need is gone. Now I find it very complicated to get even into the syntax...I fix most of my problem through the net. It's like losing a friend whose face you've already forgotten.

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

#68

Post by [deleted] » Mon, Sep 05, 2016, 6:13 PM UTC

bitL wrote: post #62

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…

The main problem of contemporary mathematics is that it is unbelievably obfuscated to most people, unnecessarily so. So even if you a have super-simple thing, mathematicians invented ways how to completely obfuscate meaning (often unfortunately in order to achieve prestige and being considered elite as a form of intellectual pride). Imagine Dirichlet's box principle, a thing that a 5-year old should understand; now l…

[deleted]

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

#69

Post by [deleted] » Mon, Sep 05, 2016, 6:19 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…

[deleted]

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

#70

Post by xamuel » Mon, Sep 05, 2016, 6:23 PM UTC

bitL wrote: post #62

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…

The main problem of contemporary mathematics is that it is unbelievably obfuscated to most people, unnecessarily so. So even if you a have super-simple thing, mathematicians invented ways how to completely obfuscate meaning (often unfortunately in order to achieve prestige and being considered elite as a form of intellectual pride). Imagine Dirichlet's box principle, a thing that a 5-year old should understand; now l…

It's like this. If you're on a C++ team where the whole team heavily uses C++'s features as well as Boost, then you should write your code accordingly. This'll make your code more concise, and clearer to the other members of the team. At the same time, it'll make it much more obfuscated to, say, a C programmer.