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.

[rstofer]

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.

For the purposes of this thread, there are really two approaches:  First, study math, in sequence from arithmetic up to however far you want to go just for the sake of math.  Second, use the resources to learn as much math as you need for your other interests.  For the hobbyist in electronics, algebra is enough except for a few moments in Calculus.  We have those charge/discharge curves to deal with.  In general, they can be solved with Algebra but are best understood with Calculus.

The student needs to be sure which they want to do.  Math is a very big subject and learning it can be an infinite time sink.  I have always subscribed to the second approach but college gets in the way.

[rstofer]

Regarding NancyPi and her earlier channel MathBFF:  Some of the comments on her videos are clearly over the line bordering on harassment.  At some point it seems that she slowed down on making videos about 2 years ago and has only just started up again with her own channel, NancyPi

MathBFF site has more advanced videos on Calculus presented by Nancy and now Janel has some videos on matrix math.  You can see the recording setup here:

https://www.youtube.com/watch?v=jZc76WDylEg.

I'm not sure how the split occurred, I don't imagine it is any of my business.  But Janel is pretty easy on the eyes as well.

If you want videos on Calculus, go to the MathBFF channel.

[Jasonbit]

The best place to learn math online: https://www.khanacademy.org/

Exist thousands places online but this website and story this is awesome, at least for me!

[mathsquid]

Another great youtube channel for mathematics is the Mathologer:https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg

[rstofer]

There is a problem with all of the online video series, a lack of problems for the viewer to solve.  Just because the presenter can solve the problem and you can follow along doesn't mean that you can solve the problem.

Khan Academy does have concept quizzes and this is most helpful.

Some college classes are old fashioned, they assign all the odd problems knowing that you can get help by solving the even problems for which answers are in the back of the book.  The instructor then has a chance to see your work.  It's a lot of work for the instructor or the Teaching Assistant (TA).

Increasingly, courses are moving toward the Cengage system where you have a physical textbook with problems and solutions but the course work is done on the computer.  You solve the problem on scratch paper and select from a multiple choice answer.  In the end, the program will not accept an incorrect answer but you only get so many tries before the program closes out that question.  There are often videos of the solution (with different numbers) and a link to a tutor chat.  I don't know how the chat works...

You really can't learn this stuff without solving problems yourself.  As much as I like the video presentations, they are no substitute for taking an actual class.  Checking out the local community college is probably a good start.

[james_s]

I've found that Khan Academy is quite good, however the quality of the courses varies from one to another. Some are very well presented with enough practice material to learn, others seem to gloss over too much stuff. Then with any of the coding stuff there's that "Oh Noes!" thing that pops up at the first hint of an error, often obstructing what I'm trying to type.

[TerraHertz]

It would be nice to have the time available for things like 'learning math'. Mine is pretty abysmal, and I'd like to be better. But there appears to be zero potential for putting aside the required time. And in the long run for me, just not enough time. So learning math remains just another 'unfinished project.'

As for NancyPi, in that video at least 50% of my attention gets monopolized by that ringpull. Not helping.

[bson]

I thought her name looked familiar!  Ms Oakley recently wrote a piece for the WSJ on her experience with women being discouraged from entering STEM fields.
https://www.wsj.com/articles/why-do-women-shun-stem-its-complicated-1531521789

[rstofer]

It would be nice to have the time available for things like 'learning math'. Mine is pretty abysmal, and I'd like to be better. But there appears to be zero potential for putting aside the required time. And in the long run for me, just not enough time. So learning math remains just another 'unfinished project.'

As for NancyPi, in that video at least 50% of my attention gets monopolized by that ringpull. Not helping.

As long as you have the math skills to do the projects you want to do, why worry about it?  You don't need to know the history of fire just to use a match.

[james_s]

As long as you have the math skills to do the projects you want to do, why worry about it?  You don't need to know the history of fire just to use a match.

In most cases there are many paths to roughly the same result. In some if one knows the math they may be able to reach a far better result and/or do so in far less time. There is a difference in software for example between a developer that can kludge together some code and make something work, and someone who can write elegant, easily maintainable code that uses resources sensibly and is relatively free of bugs. Knowledge also creates paths to new projects that one otherwise may not have even thought to attempt.

[2N3055]

To get back to original post, that lady didn't "rewire" anything. She explained how her whole life she didn't have any interest in math. But when she explains how she learned languages, and generally how she writes and organizes her thoughts, she reveals highly logical, pragmatic brain. She was born with "knack" for math and logical thinking. During childhood, she was not exposed or enticed to do math or STEM. If you teach math is boring, it is.
Also it is hard work ("Repetitio est mater studiorum"  repetition is the mother of learning, our math teacher kept repeating that), so if you are not highly motivated you will not put in effort. Once she got interested in a topic, she simply did it. Because she had predisposition.  She didn't rewire her brain, but finally used one she already had, for the first time... It took her years to make up for the share volume of the material. It looked like she rewired it, but she just had classic moment that it starts to make sense when you finally have all the pieces of the puzzle.

[lordvader88]

I love math/science and can usually learn most stuff. What really stops me from learning more as a hobby is the lack of text books like from highschool and early university. In those books they had worked examples, problems, etc, and were aimed a people of a certain level.

I have a ton of pdf math books, that I try to start with, and then encounter something that doesn't get explained and/or I just don't know where it came from, and I get frustrated, lazy and stop.

I really want to teach myself Lagrangian/Hamiltonian mechanics. And I have a bunch of pdf books and the internet and utube. But I still keep giving up on that for some reason.




As a math guy, I started learning some computer programing, and really got annoyed with how basic maths was done. I bet a lot of new people going back and forth between math and CS classes must really worry about mixing up the ways of writing stuff.

[In Vacuo Veritas]

No doubt the brain gets brittle and slower with age. Nothing beats youth. But you can just work harder at it and eventually you can learn.

[james_s]

There's a limit to how hard one can work, and between other life responsibilities time is finite. It certainly seems to pass much faster the older I get too. A year used to feel like a long time, now I don't know where they go. Sometimes I even look at a clock that shows seconds and it seems like it's ticking too fast.

[schmitt trigger]

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.

In my first year of high school, we had an exceedingly beautiful math teacher. She had a wonderful smile and this being in the early 70s, she wore miniskirts all the time. Like any hormone-filled pubescent teenager, I was madly (and stupidly!) in love with her.

This had an unintended consequence: I never skipped a single math class!! Not only that, but I would always complete my whole homework, and then would make a silly "mistake", such that I could stay a little after class and ask her to "help" me out.

In retrospective, she gave me the love for math, which in turn led to my decision to become an engineer.

So.... if some teenagers are watching NancyPi and learning math as a consequence, then all the power to her!
If they masturbate afterwards............well, that is only collateral damage. 

[blackfin76]

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. 

I'm a man I can do two things at once 

[In Vacuo Veritas]

I like black pen red pen.

https://www.youtube.com/user/blackpenredpen

[rstofer]

There's a limit to how hard one can work, and between other life responsibilities time is finite. It certainly seems to pass much faster the older I get too. A year used to feel like a long time, now I don't know where they go. Sometimes I even look at a clock that shows seconds and it seems like it's ticking too fast.

There's a 'math' reason for the dilation in time.  When you are young, a single year is a higher percentage of your entire life and seems to take longer than when you are old and a single year is a small percentage.

A year at 20 is 5%, a year at 72 is 1.4%.

[blackfin76]

There's a limit to how hard one can work, and between other life responsibilities time is finite. It certainly seems to pass much faster the older I get too. A year used to feel like a long time, now I don't know where they go. Sometimes I even look at a clock that shows seconds and it seems like it's ticking too fast.

There's a 'math' reason for the dilation in time.  When you are young, a single year is a higher percentage of your entire life and seems to take longer than when you are old and a single year is a small percentage.

A year at 20 is 5%, a year at 72 is 1.4%.

Maybe a little off topic but I think stimulation also has to do with it. When you get older there are less things to wonder about, so when you want to life longer, start doing something new as often as possible.

[Red Squirrel]

There's a limit to how hard one can work, and between other life responsibilities time is finite. It certainly seems to pass much faster the older I get too. A year used to feel like a long time, now I don't know where they go. Sometimes I even look at a clock that shows seconds and it seems like it's ticking too fast.

Tell my about it, time goes by way too fast.. except for the last hour of a work day, that hour always feels like 5 hours.  I don't even know where the years went by between 20 and 30.  I'm already 32 and it's only going to go faster from this point on.  I feel that I don't have time to do all the things I want to because the clock is just ticking too fast. 

[NiHaoMike]

More videos about math:
https://www.youtube.com/user/Vihart/videos
https://www.youtube.com/user/TheIntegralCALC/videos

Something I would like to see is how to efficiently implement math in computer code or digital logic. Strange how in university, they teach all sorts of advanced math but not how to efficiently use it in electronics!

[rstofer]

Something I would like to see is how to efficiently implement math in computer code or digital logic. Strange how in university, they teach all sorts of advanced math but not how to efficiently use it in electronics!

"Numerical Recipes in C"
"Numerical Recipes in Fortran"  - these two are the standards in the industry

"Solving DC and AC Circuits by Example Using MATLAB"  Matlab is a great tool for math and simulation.  There isn't too much it can't do!  They have a 'home' license deal so the cost isn't outrageous.  This is a magnificent tool.  Especially when Simulink is added.

Nobody writes new code for numerical analysis.  There are solvers like Maxima (or the windowed version wxMaxima) which I use extensively and others like Octave, Maple or Mathematica.

I write some stuff in Fortran as examples for my grandson but these computer packages are excellent.  Still, Fortran is warm and fuzzy for a guy who started writing code in 1970.

Want to integrate an indefinite integral with wxMaxima?  >> integrate(function, variable);
Want to integrate a definite integral? >> integrate (function, variable, a, b);
It just doesn't get any easier than that!

Most advanced calculators can do those calculations (including the TI-84) and I often use Symbolab.com.  If I need the graph first (area between curves), I can get that at Desmos.com or on the TI-84.

There's no lack of resources!

[Terry01]

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.

In my first year of high school, we had an exceedingly beautiful math teacher. She had a wonderful smile and this being in the early 70s, she wore miniskirts all the time. Like any hormone-filled pubescent teenager, I was madly (and stupidly!) in love with her.

This had an unintended consequence: I never skipped a single math class!! Not only that, but I would always complete my whole homework, and then would make a silly "mistake", such that I could stay a little after class and ask her to "help" me out.

In retrospective, she gave me the love for math, which in turn led to my decision to become an engineer.

So.... if some teenagers are watching NancyPi and learning math as a consequence, then all the power to her!
If they masturbate afterwards............well, that is only collateral damage. 

Very funny!