[RD] Learning math as an adult.

[Ferocitus]

You don't need to be good at math to be good at statistics.

Completely and utterly wrong.
Statistics is a very difficult, specialised mathematical field.
Have a look at the entry for Statistics on arxiv.org. It's not
what they teach 1st year psychology students.

https://arxiv.org/

 

[Hygro]

statistics is kind of different though

 

[Synobun]

Completely and utterly wrong.
Statistics is a very difficult, specialised mathematical field.
Have a look at the entry for Statistics on arxiv.org. It's not
what they teach 1st year psychology students.

https://arxiv.org/

Your counterargument doesn't support your initial refusal of what I said. Being good at math will help you with statistics, but proficiency in it isn't necessary for a proficiency in statistics.

 

[Ferocitus]

This way of teaching math worked the best for me:

1. A new algorithm is presented
2. The new algorithm relies on a related theorem (or theorems)
3. The entire class is spent proving the theorem rigorously
4. Once you have proved the theorem you can then proceed to use the related method, to solve problems

On midterm and final exam tests, as well as assignments, we were asked to use the method we learned in ways we haven't seen before. We were also often asked to prove similar theorems (that we hadn't seen before either), for example with 1 extra dimension.. i.e. similar idea, different details

Since you couldn't predict what sort of stuff you would see on midterms and final exams, you had to actually understand the theorems and how they work. You had to understand the principles behind what was going on, so that you could apply them in situations that you've never seen before. The best way for learning this was to prove everything, and understand why things were proved the way they were, and what the thinking behind every step was. It forced you to eventually see the big picture, which is vital.

Good advice, warpus!

I found that having a definite problem to work on was essential.
For me it was computer modelling of certain types of wind turbines.
That required a variety of mathematical techniques, fluid dynamics,
and computer programming. I was lucky that it also led to enough
publications so that I could bypass the under-grad degree.

Giving you a formula and asking you to apply it over and over...

That's like the attitude of "just learn these scales" and you're well on your way to being a musician.

 

[Ferocitus]

Your counterargument doesn't support your initial refusal of what I said. Being good at math will help you with statistics, but proficiency in it isn't necessary for a proficiency in statistics.

Higher statistics requires a lot of mathematics.
Don't judge it on what can get you through an under-grad statistics course.

 

[Synobun]

Higher statistics requires a lot of mathematics.
Don't judge it on what can get you through an under-grad statistics course.

Mathematics that you learn within the context of statistics.

 

[Ferocitus]

Mathematics that you learn within the context of statistics.

That you learn.
The best statisticians weren't one trick ponies.

Andrey Kolmogorov

At the Moscow State University, Kolmogorov occupied different positions,
including the heads of several departments: probability, statistics, and
random processes; mathematical logic. He also served as the Dean of the
Moscow State University Department of Mechanics and Mathematics.
https://en.wikipedia.org/wiki/Andrey_Kolmogorov

 

[Synobun]

That you learn.
The best statisticians weren't one trick ponies.

Andrey Kolmogorov

At the Moscow State University, Kolmogorov occupied different positions,
including the heads of several departments: probability, statistics, and
random processes; mathematical logic. He also served as the Dean of the
Moscow State University Department of Mechanics and Mathematics.
https://en.wikipedia.org/wiki/Andrey_Kolmogorov

Somehow I doubt Mouthwash seeks to be an innovator within the field of statistics.

 

[Ferocitus]

Somehow I doubt Mouthwash seeks to be an innovator within the field of statistics.

Who knows.
Once he is exposed to areas of maths that he doesn't even know exist,
he could fly off in any direction.

 

[Kyriakos]

^Pandora's hypercube should not be opened at random

 

[dusters]

^Pandora's hypercube should not be opened at random

I think it should. Because when someone is like 4-5 years old, world is full of wonders. If you still think there are wonders in this world when you are approaching 35 or 40, you are one lucky human being.

What i get from this thread is that to further unlock the hypercube Mouthwash needs some mathematical tools.

 

[Ferocitus]

I think it should. Because when someone is like 4-5 years old, world is full of wonders. If you still think there are wonders in this world when you are approaching 35 or 40, you are one lucky human being.

He can open the box, but the only wonder he will get out of it is how completely
opaque the language is. For example:

Let M be a closed oriented three-manifold, whose prime decomposition contains
no aspherical factors. We show that for any initial riemannian metric on M the
solution to the Ricci flow with surgery, defined in our previous paper
math.DG/0303109, becomes extinct in finite time. The proof uses a version of
the minimal disk argument from 1999 paper by Richard Hamilton, and a
regularization of the curve shortening flow, worked out by Altschuler and Grayson.

That abstract is from a paper by Grisha Perelman which ultimately won him a million
dollar prize, and which he refused to accept.

What i get from this thread is that to further unlock the hypercube Mouthwash needs some mathematical tools.

Sage observation and advice, Dusters!

 

[civvver]

It depends on what you are trying to do. If you just say I need to take some math test to get into school, that's very vague. What level is the test? What proficiency do you need? Are you going to take math classes in school after? Can you study just for the test or do you need to retain after?

The truth is unless you use the stuff on a daily basis you'll forget it in a few months. I took algebra and trig and some pre calc in high school, then did three classes of calculus in college, plus differential equations, stats and probability, and three semesters of physics. I got A's in everything and now ten years later I don't remember any of it. I think I could do some very simple derivatives and that's it. Prob and stats is probably the most real life useful of all those classes and even that I can't remember how to do stuff like how many permutations of pick 4 from 10 things without looking up the formula.

And same thing applies to pretty much any discipline. I write computer code for a living and I honestly can't tell you how to write a java applet from scratch off the top of my head. Why? Cus when you need to make a new one, you cut and paste the outline from a previous program or use a wizard that puts in the framework init calls for you cus it's so trivial, why memorize how to do it? For most people what's more important is the concepts and that they can grasp what's going on behind the scenes and understand the fundamentals of program architecture.

 

[dusters]

It depends on what you are trying to do. If you just say I need to take some math test to get into school, that's very vague. What level is the test? What proficiency do you need? Are you going to take math classes in school after? Can you study just for the test or do you need to retain after?

The truth is unless you use the stuff on a daily basis you'll forget it in a few months. I took algebra and trig and some pre calc in high school, then did three classes of calculus in college, plus differential equations, stats and probability, and three semesters of physics. I got A's in everything and now ten years later I don't remember any of it. I think I could do some very simple derivatives and that's it. Prob and stats is probably the most real life useful of all those classes and even that I can't remember how to do stuff like how many permutations of pick 4 from 10 things without looking up the formula.

And same thing applies to pretty much any discipline. I write computer code for a living and I honestly can't tell you how to write a java applet from scratch off the top of my head. Why? Cus when you need to make a new one, you cut and paste the outline from a previous program or use a wizard that puts in the framework init calls for you cus it's so trivial, why memorize how to do it? For most people what's more important is the concepts and that they can grasp what's going on behind the scenes and understand the fundamentals of program architecture.

This is why not everyone who is expert in the field is also a great professor. People who are great scientists can come up with innovations using given framework given to them, but to teach math/physics you have to be able to explain everthing from scratch at any given time.

Of course, if you teach in university, you assume pupils know everything taught in high school, but realistically this assumption is naive.