Help with learning math and science

[Propianotuner]

I've always had a keen interest in math, chemistry, and physics, but it's been largely inaccessible to me on account of how poorly I did in a school environment and not having other resources readily available. Now as an adult I'm profoundly disappointed about the matter because I understand that had I been more able to pursue those interests during development I'd be in a much better position now to enjoy math and use it to more easily comprehend awesome subjects in physics related to Maxwell, Fourier, and Bell's equations.

However this hasn't deterred me from beginning to struggle through algebra again on Khan Academy and I've always had a natural knack for math when all of the logical principles are clear to me. It's much easier to remember and use formulas and equations when I'm able to understand and associate them using simple logic.

Given all of that, I guess what I'm asking for from this thread is people freely sharing with each other good book and internet resources, but most especially book resources, for learning math and the sciences most heavily related to math. How does one go about acquiring familiarity with all of the symbols a person typically runs into outside of a college math or physics class setting?

 

[Observant]

How to Solve it by George Polya
https://online.stanford.edu/courses/hstar-y0001-introduction-mathematical-thinking

And definitely this:
https://www.amazon.com/How-Prove-St...id=1525321295&sr=8-4&keywords=how+to+solve+it

"How does one go about acquiring familiarity with all of the symbols a person typically runs into outside of a college math or physics class setting?"

Can you expand on this?

 

[countzero1984]

Hi, I'm in the same boat. I started off with Khan Academy. I found Sal to be very helpful because he has the same kind of Autism-Spectrum wandering mind. The way he keeps himself focused when he's teaching his lessons I found very helpful. I played his videos at 1.5X speed. This made it a whole less boring and helped my mind think faster!

The problem with math and physics is that they are taught so poorly. The Establishment teaches things in a formal way that only work with a disciplined mindset. I.e., people who can memorize large bodies of arbitrary information: like doctors and lawyers.

They don't want to explain it in a simple way because that might cause a knowledge explosion among the little people and suddenly they are no longer the priests of math and science – like the reason why the Catholic Church suppressed early-Modern-Period science. (All this, of course, is my opinion.)

The best way to learn, IMO, is to follow the some of the great A-S thinkers in history: Newton and Einstein.

Newton would wander from subject to subject to subject. You have to let the spirit move you. Your subconscious mind will lead you to crazy places, but you gain incredible depth and insight through experiential learning. (As opposed to mnemoic, by-rote, conditioned knowledge – which isn't as interconnected. And also painfully boring.)

Einstein would boil things down to simple thought experiments. Like he imagined travelling on a motorcycle along side a beam of light. Then he thought, the light beam would just pulse up and down and therefore nullify Maxwell's 4th equation that predicts light (EM radiation) travels at a constant speed: c. Ergo, the speed of light must always be the same in all inertial frames (i.e., comprised of objects with zero relative velocity.) Also means measurements of space and time remain the same in your own frame: x = ct

Long story short: there is no one book that will explain things very well. Just dive into some topic. Watch YouTube videos and lectures at different levels of depth. Get the transcripts and take notes. Use a screen-image grabber. Then do internet searches to find out what other people are saying about a particular subject. Like HyperPhysics is a great source.

I also found using a Wacom tablet and Paint as a giant Whiteboard is very helpful in trying to get a better understanding of ideas you're working on. The best way to learn: try teaching yourself a topic you're studying.

3Blue1Brown and Minute Science do an incredible couple of videos that explain everything about Bell's Inequality.

3Blue1Brown has a lot of other videos on topics like Fourier Transformation, Essense of Calculus and Essense of Linear Algebra.

Physics Videos by Eugene Khutoryansky are also very good at explaining things. Incredible graphics. A 3D graph is worth a thousand words squared! (You can learn Python and start creating your own 3D graphs.)

Michel van Biezen has an incredible number of lectures on YouTube. The man is a lecture machine!

A lot of learning is just getting your feet wet. Just being immersed in the subject. You don't understand a lot of it at first. It takes a while for your subconscious to recognize the patterns. Then one day it just clicks.

Work hard and play hard. You actually learn while you are distracted.

 

[Progster]

I've never been strong at maths. At one point, I decided that I would get back into mathematics, and tried the Khan Academy. I thought it was excellent, but still struggled a lot with algebra, though, and there were some topics such as nested equations that I could never master. The problem was that it's something I can't visualise. The methos is excellent and Sal does explain it in his tutorial videos, but unless the problem I am trying to solve is exactly the same as the one he is presenting, I can't solve it, because I can't 'see' it, only copy the method, and not matter how hard I try I keep making mistakes without any feedback or understanding of why my answer was wrong. I felt that I needed to have it explained in a different way that I could visualise, or grasp, but I didn't have that option. My constant mistakes and lack of progress just caused me to have terrible frustration meltdown, so I stopped - I got up to about 48% - it was getting to the point where instead of being a pleasurable past-time, it was causing me harm.

Perhaps the Open University has some free materials?

 

[countzero1984]

The best way to learn math is to learn physics. Then you have the visualization. You're outside the realm of pure abstraction.

Learning math is not a linear process. That is a patriarchal construct. The realm of math is web of inter-related knowledge. Most of this knowledge comes from studying physical processes.

I think it's best to start with quantum mechanics, because there's no acceleration. Just a direct transfer of energy in an event. Makes it much simpler.

It's like "eating the elephant." If you try a systematic approach, you will make it even less appealing. Just take a bite here, a bite there and then you get a feel for how it all comes together.

Autism-Spectrum people think differently than patriarchs. So taking the patriarchal, disciplinarian, by-rote approach to learning is almost certainly doomed to failure. Just fool around with it for the love of it.

 

[Observant]

Visualization certainly helps with me. It's also easier to learn Mathematics when you have a problem that you can compare. A simple example of this from algebra is that I see a function as a machine that turns useful raw materials into something I want.

Like countzero stated, learning Math isn't linear, and you really do have to explore it piece-by-piece in order to understand it. Pretty soon fractions will start to resemble an odometer, and functions start to look like an assembly line in a factory. Your understanding of Math will creep into everyday life. It really has become part of how I experience the world around me.

 

[Aeolienne]

Check out this documentary about Eddie Woo:

Here's his official website.