Learning Math as an Adult

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I found this article interesting and more than a little inspiring. I actually don't specifically know what kind of topic I am trying to start here, so I'll just be blunt: I was searching google for articles relating to learning higher math as an adult, and came across this article. I read it and it really resonates with me a lot, and I wanted to share because members here often have great insight. So, the thread title doesn't match the article, but there it is nonetheless.

http://nautil.us/issue/17/big-bangs/how-i-rewired-my-brain-to-become-fluent-in-math

[gildasd]

I read diagonally (a bit busy), but I totally agree with the premise, you must exercise A LOT to become good at maths as a adult.

[Zucca]

Just watch "3blue1brown" on youtube.

[frozenfrogz]

Stumbled upon this site: https://brilliant.org/
Did not really have time to check it out in depth, but looks interesting.

[RoGeorge]

Stumbled upon this site: https://brilliant.org/
Did not really have time to check it out in depth, but looks interesting.

That site requires a monthly fee, and it looks like it's made for kids.

[frozenfrogz]

That site requires a monthly fee, and it looks like it's made for kids.

There seems to be the same freemium approach as with https://www.codecademy.com/ - I made an account and did not pay anything, but as I said, I did not check it out in depth. If it is a shit recommendation on my part I apologize.

[HighVoltage]

Best way to learn math is to teach, no matter at what age!
It is also a good way to retain your math knowledge.

[GK]

I think she's talkin' 'bout math, but I can't concentrate much for some reason. I literally heard "rational erection" on the first watch.

[The Soulman]

If you don't feel like reading the entire personal story this says it all imho:

There is an interesting connection between learning math and science, and learning a sport. When you learn how to swing a golf club, you perfect that swing from lots of repetition over a period of years. Your body knows what to do from a single thought—one chunk—instead of having to recall all the complex steps involved in hitting a ball.

[RoGeorge]

That site requires a monthly fee, and it looks like it's made for kids.

There seems to be the same freemium approach as with https://www.codecademy.com/ - I made an account and did not pay anything, but as I said, I did not check it out in depth. If it is a shit recommendation on my part I apologize.

There is no need to apologize. Indeed, there is a free 'demo' account, but only a few and very low level (by low level I mean very basic, as in introductory) classes are free. For the rest of the classes, brilliant.org needs a monthly fee.

[rstofer]

Community College is one approach up to the level of an AS degree.  The program for, say, Mechanical Engineering, consists of 4 semesters of math beginning with Calculus.  The thing is, most people don't have the Algebra and Trigonometry skills to start Calculus.  So there is another 2 semester Pre-Calculus course that is usually required (it is here).  Suddenly the 2 year Community College is stretched out to 3 years.

Hint:  Don't try to take a Pre-Calculus course during the short summer semester.  There's a reason for saying this...  It worked out but, damn, it was a lot of work in a short period of time.

But simply getting the right answers to problems is pretty meaningless.  It is only in applying the math to real-world problems that it is useful.  Word problems!  Everybody hates them but they are the only meaningful way to evaluate understanding.  Lots of word problems!

Big hint:  Draw a sketch!  Engineers can't even talk without a pen in their hands.  Always sketching...

Calcworkshop.com (fee required) is EXCELLENT with all the lower division math up through Differential Equations.  This program is worth every penny!  Watch the free demo on "Limits".  This isn't my favorite topic but it turns out to be useful later on.  And it is required early on...

Remember, I said 'lower division' - the first two years of a 4 year program that will probably extend to 6 years.  There will be more math in the upper division courses.  Field Theory comes to mind for the EE program.  And, yes, Differential Equations is a lower division course!

Khan Academy, 3blue1brown, NancyPi, and a host of other YouTube channels are also very helpful.  For actually solving problems, desmos.com (graphing) and symbolab.com (solving) are bookmarked on my computers.  There are so many resources it is simply unbelievable.

The stuff above is current; it's my grandson's program.  I'm riding along to relearn what I thought I used to know but, damn, 45 years is a long time.  As it turned out, I never used my EE education for very much.  I had better ways to make a living.

We didn't have the elegant tools back in the early '70s so the courses were probably a little more shallow.  Things like Fortran and Matlab make the courses more approachable.  Don't overlook the fun of coding up Riemann Sums in Fortran - if you are a very old Fortran programmer.

It is absolutely possible for older people to learn math.  In fact, we probably should!  We need to keep our brains engaged.

[RoGeorge]

Khan Academy, 3blue1brown, NancyPi

I didn't know about NancyPi before, watched only two of her videos so far, but totally agree with GK. While she is 100% correct from a mathematically standpoint, there is so much sexual innuendo in her videos that I couldn't follow the math at all, too.
I know it's the year of 2018, with all the PC, yet her semiotic and body language totally derails any straight male, IMO. 

[rstofer]

Khan Academy, 3blue1brown, NancyPi

I didn't know about NancyPi before, watched only two of her videos so far, but totally agree with GK. While she is 100% correct from a mathematically standpoint, there is so much sexual innuendo in her videos that I couldn't follow the math at all, too.
I know it's the year of 2018, with all the PC, yet her semiotic and body language totally derails any straight male, IMO. 

Guys, if you have to do math, you might as well enjoy the view.  She is absolutely beautiful but I can get by that to watch the math.  Barely...

At my age, I don't do PC.  People can write me off as a doddering old fool and I'll just smile and wave.

[Red Squirrel]

I've been playing a bit with electronics but been wanting to get into it more, especially power electronics, but the one thing that makes it hard for me is I've never been good at math.  Funny thing is science, engineering, all that stuff has always interested me and I can know the general concepts behind things, but ask me to calculate anything and I'll be at a loss.   I feel this article totally applies to me.  I may need to work harder at trying to rewire my brain too, so I can enjoy the hobby more and actually perhaps get somewhere with it.  When I read up on stuff I just get discouraged once they start throwing lot of math as I just get lost.

In school I did have trouble with the idea of not knowing the purpose of a math concept.  If I don't know the purpose or how to apply it, it's much harder to understand.  I was ok with basic stuff like how to calculate the area of a shape, because I understood the purpose.   You have a floor that's 10 by 10 and you want to lay tiles that are 1 x 1, I can visualize it as a grid and I know that I need 100 tiles. I did not have to try to memorize the "formula" to calculate the area, I just know it because it's logical to me.  If it's a right angle triangle I know that if I had two of those triangles it would make a square, so one triangle is half.  Concepts like that I was good at because they have a purpose and I can visualize it.  The other math had a purpose, they just never taught it in a way that you know what the purpose is, or in a way that you can visualize it.   So that I always had trouble with.

[rstofer]

I've been playing a bit with electronics but been wanting to get into it more, especially power electronics, but the one thing that makes it hard for me is I've never been good at math.

The only way you will get up to speed on math is to work with it.  So much of electronics is based on Ohm's Law and Kirchhoff's Laws that simple algebra is all you need.  I'm talking 1st semester Algebra.  You can go a long way with just this level of knowledge.

Kirchhoff's Laws will inevitably draw you into matrix math.  Node and mesh equations require matrix math.  But YOU don't have to solve the matrix, just write the loop or node equations.  There are plenty of matrix solvers on the Internet or, if you want, you can get into something like Matlab or one of the clones like Octave.  I'm not saying that writing out the equations is trivial, it isn't.  It takes time and patience to get the signs correct.  But, having written them, don't get bogged down in trying to solve a 4x4 matrix by hand because it likely isn't possible.  Technically possible, practically impossible.  3x3s are hard enough.  Use a computer!

AC circuits will add to the complication by bringing in complex numbers, vectors and phasors.  In terms of Kirchhoff's Laws, Matlab and all the others can do complex numbers without a hiccup.  They will also graph the results of almost anything you can come up with.

The tools are all out there.  The Home version of Matlab is kind of affordable until it comes time to renew but it's just a cost of doing business.  Maybe that's why Octave is so popular.

Khan Academy has an Electrical Engineering track.  I haven't spent any time with it but I have watched a bunch of the Calculus videos.  Digilent also has an EE program called "Real Analog".  It's very good!

https://learn.digilentinc.com/classroom/realanalog/

https://www.khanacademy.org/science/electrical-engineering

For most hobby work, it isn't really necessary to get too deep into the math.  You need Kirchhoff's Laws in order to deal with Op Amps and you need Ohm's Law for everything.  Beyond that, well, you better strap in because there can be a LOT of math.  Mostly involving e and sin() or cos().  Lots of exponentials and trigonometry.

And then there is simulation using something like LTSpice...  It can solve all those node and mesh equations in a blink.  A very nice tool!

[HighVoltage]

I did not know about NancyPi before this thread.

But ... how does she do the videos with her writing ?

[rstofer]

This has been asked many times and there are a number of responses on Google.
This particular response suggests using the video editing software to flip the image on the glass.
Seems right...

https://video.stackexchange.com/questions/16454/how-to-make-a-video-where-an-actor-writes-facing-the-camera

[GK]

She is absolutely beautiful

If she begged me for it I'd do her the favor.

[NiHaoMike]

I did not know about NancyPi before this thread.

But ... how does she do the videos with her writing ?

I'm going to guess writing on glass and then flip the video so the writing is the right way around. Another possible explanation is some sort of digital effect, but that's a lot more complex so I consider that unlikely.

I never really liked math until I found out about cryptocurrency and got recognized by many of my friends for doing something great with it. Now I'm quite fascinated with cryptography, although I don't understand the details very well.

[Zaphod1]

I’d be able to concentrate on the maths much more if she was facing the board she was writing on with her back towards me

[rhb]

Whether old or young, you only learn math by doing it a lot.  It's just like playing a musical instrument.  And if you don't keep in practice, it all goes away.

[NiHaoMike]

I’d be able to concentrate on the maths much more if she was facing the board she was writing on with her back towards me

Then everyone would be complaining about the blocked view.

Come to think of it, flipping the image around could be done with a simple mirror. Might even make a (small) difference in video quality since I'm not sure if h.264 or whatever can be losslessly flipped.

[The Soulman]

I’d be able to concentrate on the maths much more if she was facing the board she was writing on with her back towards me

Then everyone would be complaining about the blocked view.

Come to think of it, flipping the image around could be done with a simple mirror. Might even make a (small) difference in video quality since I'm not sure if h.264 or whatever can be losslessly flipped.

I'm fairly sure it can.

[The Soulman]

speaking of (a) beauty in maths:

[Buriedcode]

How is learning mathematics as an adult any different from leaning as a child?  With the possible exception of smaller font and less primary colours?  Also, whilst this isn't a platform for my rants - I hate the phrase ("rewiring the brain") because it implies that's how the process works, also used to imply there are quick "shortcuts" to "hack" learning.  There isn't - its just practice.