[Pmb (OP)]

Hi everyone!

I'm trying to keep myself busy and am going to create some learning material for math and physics. I would like to ask everyone what the hardest parts of their learning in math and physics was and how we can help people overcome their difficulties.

Myself, I had a terrible time memorizing the multiplication tables. Even to this day I have trouble with it. I think its because I have a very poor memory. I learned that I sucked at arithmetic but was an ace in math because arithmetic is all about memorizing things and the algorithm to calculate numbers but math was easy for me because its abstract and visual and I'm good at those things.

When it comes to physics I had a terribly hard time with statistical mechanics. I think its because one has to have a solid grasp of combinatorics and I sucked at that.

This is the kind of thing I would like to ask you good folks to share even though I realize that it’s a hard thing to do. After all who likes to put out there what we suck at. I don’t mind because I’m no longer ashamed of it. I’ve come to understand and accept that part of myself. That way I can fight it.

If you have any suggestions on how I can overcome my difficulties in the above please share. Thanks!

[yor_on]

Makes me remember a good friend from long time ago Pete. He was gifted when it came to understanding the principles behind mathematics, and I was rather poor in it So he once said that mathematics could be understood as logical symbols, even things you could hold in your hands, that you by some defined rules could twist and put together in combinations and treat one way, or the other. I don't think he ever made something from it but it stuck in my mind as a good idea. Wonder if it would be possible? To make it a game that you could give to kids to play with and from that intuitively learn maybe not all rules, but some of the hidden logic regarding mathematics, whatever form it takes?

[bizerl]

It's been a while since I've thought about Maths and I think my main problem was not studying enough, but I can remember that whenever we learned a new formula, the teacher would take the effort to go through how it was derived from basic principles. I found this really helpful and especially useful in exams when I couldn't remember the formula, but could remember how to derive it.

The problem with education is that different ways work for different people. Some people might be better at learning a few basic principles and extrapolating them out for whatever purpose, other people might do better at memorising large amounts of facts to call upon when required.

[damocles]

I have a very strong sense of pattern and spatial relationships. When I was quite young (about 5) my very wise father put up a chart on the back of the toilet door, where I would have plenty of time to contemplate it. It showed the relationships between numbers from 1 to 100 -- all of the numbers divisible by 5 were in 2 columns with an orange background shading. Those divisible by 8 were in blue squares, those divisible by 7 had a blue ring around them, divisible by 3 was a red font, by 9 a red font backed up with a red diagonal stripe, by 11 a black diagonal stripe running the other way.

This seemingly chaotic arrangement was capable of resolution into a number of patterns, especially as I was just learning to play chess at the time, and was fascinated by the knight's move. I found it expressed in the 8 times (10-2) and 7 times (20+1) tables. It started me out with a really good sense of number, based on an innate spatial sense.

[lunar11]

I recall doing Quantum Mechanics in my Physics degree. It took me 6 months to get my head around the mathematical concepts. In the end I passed but I really did not know what I was doing. It was no longer a Physics course; it became a Maths course.
One of the major problems that students have in doing the maths in the Physics course is that there must be certain prerequisites that must be achieved.

[yor_on]

He, hear what you're saying Lunar. You start with grasping some principles, then you meet obstacles confounding you, as advanced mathematics but without basic premises explained? And doing them you sort of lose sight of what you first thought of as being principles, just to come back to them after more time passed, as the mathematics suddenly starts to make sense again?

The wheel of life huh

And you must have had a good, and patient, teacher Bizerl. Myself I like finding out how people thought something up, it makes it so much easier to understand how they got their results.

[yamo]

I really hate the Monty Hall problem.  I just can't accept that changing doors makes a difference.

[damocles]

from yamo:

I really hate the Monty Hall problem.  I just can't accept that changing doors makes a difference.

What I cannot figure about the Monty Hall problem is why so many authorities say that the probability of success is only 1 in 2 if you change doors. The way I figure it is that you should try to pick the door that you are not expecting it to be behind, because if that fails (1 in 3) you will have a sure fire pointer to success (2 in 3).

[yor_on]

That's a weird one alright. Saw someone explain it with a hundred doors instead, suddenly making it make sense. You have a hundred doors to pick from, you pick one of them. Then the game leader opens 98 of the other doors showing you nothing in them but goats. Now the question becomes one of keeping your original one that you picked randomly out of a hundred, not opened, or use the last door out of 99 that the game leader opened? It's a question of odds, and you picked one randomly from a hundred closed doors, but the 'other side' of it is the one where 98 doors was opened to find nothing, one left. It's like two games, the one you had from the beginning being the hardest to guess, wheres the one the game leader had being the 'foolproof' one. In reality it can't be foolproof as it could be your door too, but imagining it as two separate games makes it easier to see the reasoning.

and it is weird as you could imagine yourself not choosing any of those doors, waiting until the game leader opened 98 of them, then having two doors left to choose between. In that case you would have a 50/50 % probability of getting the right one, as I see it. Statistics as magic?

[damocles]

Thankyou Yor_on! your example just highlights my reasoning! Because you only had a 1 in 100 chance of getting the first door right, then you are 99% sure if you change doors that you will be right after the game leader has opened 98 of them

[yamo]

Could an analogy to superstates be used?  Rather than measuring where the Big Deal is, collapsing the function, we are measuring where it is not.

[CliffordK]

If a cat can be half dead, and half alive,

Does it still need to be fed?

[syhprum]

What I find difficult about maths is what do all the strange symbols represent I understand about half of them and have recently learnt about Bras and Kets but am always quite defeated by matrix's.
Arithmetic is no problem having grown up with the strange imperial units and £.S.D  money which hones ones skills.

[Bored chemist]

On a good day, with a following wind, I can do the maths for calculating angles in 512 dimensions (and, with the aid of a computer, I used to do it a lot).
But I have no real idea what it means.

[dlorde]

If a cat can be half dead, and half alive,

Does it still need to be fed?

If it's Schrodinger's cat, it's both dead and alive, so you only need to feed the living version. You bury the dead version.

I once learned how to mentally calculate the day of the week of any given Georgian calendar date. It was too complicated and wasn't useful enough, even as a party trick, to remember once the novelty wore off (on a Thursday).

[yor_on]

heh
I seriously think we're all in the galactic teapot, best described by the hitchhikers guide to the galaxy.
We should present it to the UN. I'm sure they could use it..

[yor_on]

About the Monty Hall problem.

1. we have differently sized infinities defined mathematically. Would now this reasoning give me a better probability of finding something in a lesser infinity, as you can see that as open and then taking aways 'some room'

2. Imagine i have two doors to choose between. Somebody tells me that there was three doors before I got there, but one got taken away containing a goat, to the right side. Will this guarantee better odds for me if I too pick the right side? If it does, isn't this a hidden parameter? Information?

[dlorde]

About the Monty Hall problem.

1. we have differently sized infinities defined mathematically. Would now this reasoning give me a better probability of finding something in a lesser infinity, as you can see that as open and then taking aways 'some room'

Sorry, I don't understand what you're asking here.

2. Imagine i have two doors to choose between. Somebody tells me that there was three doors before I got there, but one got taken away containing a goat, to the right side. Will this guarantee better odds for me if I too pick the right side? If it does, isn't this a hidden parameter? Information?

No, the probability of you choosing the prize depends on the choices currently available to you. If you have two options and one has the prize, your chances are 1 in 2 (50:50). If there had been a hundred other options removed before you got there, it would make no difference, your chances with the two choices left are still 1in 2.  But if you'd chosen from the options before any were removed, your chances would clearly be 1/number of options, and by switching after the 'dead' options were removed, you'd improve your chances to 1 in 2.

[yor_on]

Why wouldn't it give the same odds?
the situation is the same as if I stood before those three doors, seeing him open the one to the right, finding a goat? Instead of being there I get informed of what door that was. Ahh, I think I see, I didn't make that choice before getting informed

Then we do 2. again, this time me picking one of the other doors, before getting informed of what door he opened, before removing it, finding that goat. Would my chances now increase in a switch?

[yor_on]

Alternatively getting informed of which door he opened to then remove, leaving two choices for me in which I first choose one door of two, to then switch it. Would my chances improve?