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Relearning math as an adult

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Re: Relearning math as an adult

#171

Post by globalnode »

dcw303 wrote: post #8

I've been doing similar for about a year. My target is to learn the math needed to make 3d games, so basically algebra, geometry, calculus and linear algebra. I started with brilliant.org, and while I liked the level of polish in the interactive lessons, I found the lesson structure to be out of sequence, often referring to things that haven't been covered yet. They didn't seem to have put as much thought into pedago…

i was motivated by the exact reasons you are but after a few years of maths i started to like that more than the 3d games and programming :(

Re: Relearning math as an adult

#172

Post by DeathArrow »

mjburgess wrote: post #117

The "math" used in ML/AI papers is usually just a sort of 'whiteboard math' which is a domain-specific mishmash of linear algebra, calculus, set theory and statistics. If you could find a book just going through the relevant bits you wouldnt really have to "learn math again", it can be translated into english straightforwardly -- very very few ML papers relevant to industry have extended proofs, etc. that require eg.…

>If you could find a book just going through the relevant bits you wouldnt really have to "learn math again"

Hard to find a book or a course doing applied math just for AI and ML. I was interested in learning the math needed to understand quantitative analysis and I was lucky to find some resources doing just that.

Re: Relearning math as an adult

#173

Post by indigochill »

zelphirkalt wrote: post #161
hiAndrewQuinn wrote: post #119

About a year ago my wife and I made the joint decision to get her into college for a bachelor's degree in either English or computer science. Here in Finland, university admissions are based around how well you did on various end of school exams, and she fortunately did quite well on all of them a decade ago - except for math. She bombed math due to health and family problems as a teenager decimating her ability to p…

It is truly amazing, what some people can do, when they are enabled. Now imagine, if somehow we could get this for more people, as a society, not just on a partner/SO level. How much more human potential we could unlock.

A society is just a collection of individual human relationships. We need to teach not just knowledge but character.

Re: Relearning math as an adult

#174

Post by gmadsen »

tux3 wrote: post #139
baq wrote: post #128

Earlier quoted context omitted.

> set her nose to the grindstone Worth calling out the key observation: it takes practice, and lots of it (for most people, anyway) to get good at math. Just reading about it does zilch.

It does a little more than zilch. Exercise is important. Reading is also important. If you want to learn fast, you need a balance of both that works for you. Some people will spend months grinding hard problems on their own in a single chapter to make sure they really understand. Some people will read too fast and have to go back because they don't have solid foundations, and only thought they understood. Reading is…

This is just not true. Reading is necessary but hardly about as important. If you are lucky and get a good text, the exercises guide you to "invent" the important parts of the theory. Otherwise its just definitions and theorems, and its up to you to make your own examples to gain an intuition, which to be fair is closer to life outside of a classroom.

Re: Relearning math as an adult

#175

Post by gmadsen »

aleph_minus_one wrote: post #159
Tainnor wrote: post #158

Earlier quoted context omitted.

Not every mathematician needs to understand axiomatic set theory, but probably every working mathematician needs to understand at least basic set operations, simple identites like De Morgan's laws (I don't care if you know the name or not), as well as what cartesian products, relations and functions are.

> every working mathematician needs to understand at least basic set operations, simple identites like De Morgan's laws (I don't care if you know the name or not), as well as what cartesian products, relations and functions are. This is stuff that you learn in the 5th or 6th grade in school, and is about as far removed from what mathematicians call "set theory" as basic arithmetic operations are from college math cou…

that is a little bit of hyperbole. No school in 5th or 6th grade is giving formal definitions of relations and functions. There is a reason nearly all undergrad math books in analysis, topology, algebra, all devote an entire first chapter to it.

Re: Relearning math as an adult

#176

Post by vehicles2b »

mjburgess wrote: post #117

The "math" used in ML/AI papers is usually just a sort of 'whiteboard math' which is a domain-specific mishmash of linear algebra, calculus, set theory and statistics. If you could find a book just going through the relevant bits you wouldnt really have to "learn math again", it can be translated into english straightforwardly -- very very few ML papers relevant to industry have extended proofs, etc. that require eg.…

We probably think fluently of these mathematical structures in tangible, real world terms. Still it requires some practice translating to the mathematical abstractions, and still further practice thinking in terms of the abstractions altogether. I don’t know how relevant it is that the textbook content can be covered in a single semester.

Re: Relearning math as an adult

#177

Post by tux3 »

gmadsen wrote: post #174
tux3 wrote: post #139

Earlier quoted context omitted.

It does a little more than zilch. Exercise is important. Reading is also important. If you want to learn fast, you need a balance of both that works for you. Some people will spend months grinding hard problems on their own in a single chapter to make sure they really understand. Some people will read too fast and have to go back because they don't have solid foundations, and only thought they understood. Reading is…

This is just not true. Reading is necessary but hardly about as important. If you are lucky and get a good text, the exercises guide you to "invent" the important parts of the theory. Otherwise its just definitions and theorems, and its up to you to make your own examples to gain an intuition, which to be fair is closer to life outside of a classroom.

It really depends on the text, it doesn't have to be just a list of theorems and definitions.

Some intuition can be conveyed through text, or geometry and visualization. A good explanation can make things click.

I think you may be right about your own experience, that you get most of your intuition from exercises, but I'm confident this varies. Some people get much more than zilch from a good text, in addition to doing exercises.

The real world is harder than a classroom, but we don't have to make classroom learning as hard as research. It's okay to start with help and increase the difficulty gradually. You don't have to do everything on your own!

Re: Relearning math as an adult

#178

Post by konstante »

boxfire wrote: post #3

I may be biased as I am a trained Mathematician, but I always feel when someone says "Math is Hard", that is because they had bad teachers. Math is easy if you build up from fundamentals, not like physics education where you say "but lets delete everything before because it had an oversimplifying assumption", rather if you build your knowledge entirely sequentially from things you know or assume, you build up a toolb…

What do you mean by "trained mathematician"? I ask this because I always think that mathematicians are simply people do research in mathematics, if not they aren't mathematician. So no need to add "trained", what is an "untrained mathematician" btw?

I saw some people claimed on their twitter/blog that they are "trained mathematician" but I cannot find any single published contribution of them in mathematics.

And everyone I know who do research in math seems to agree all that "math is hard".

Re: Relearning math as an adult

#179

Post by mjburgess »

gmadsen wrote: post #175
aleph_minus_one wrote: post #159

Earlier quoted context omitted.

> every working mathematician needs to understand at least basic set operations, simple identites like De Morgan's laws (I don't care if you know the name or not), as well as what cartesian products, relations and functions are. This is stuff that you learn in the 5th or 6th grade in school, and is about as far removed from what mathematicians call "set theory" as basic arithmetic operations are from college math cou…

that is a little bit of hyperbole. No school in 5th or 6th grade is giving formal definitions of relations and functions. There is a reason nearly all undergrad math books in analysis, topology, algebra, all devote an entire first chapter to it.

It would be dangerous to teach anyone in ML what a function was, since they might realise, the premise of the entire activity is false.

(ie., that in the vast majority of cases there are no empirical functions to model, no f: Pixel -> Animal)

So better continue the current practice where few could distinguish a relation and a function; and fewer still are aware that they arent approximating empirical functions.

Re: Relearning math as an adult

#180

Post by ystad »

baq wrote: post #128
hiAndrewQuinn wrote: post #119

About a year ago my wife and I made the joint decision to get her into college for a bachelor's degree in either English or computer science. Here in Finland, university admissions are based around how well you did on various end of school exams, and she fortunately did quite well on all of them a decade ago - except for math. She bombed math due to health and family problems as a teenager decimating her ability to p…

> set her nose to the grindstone Worth calling out the key observation: it takes practice, and lots of it (for most people, anyway) to get good at math. Just reading about it does zilch.

Very true.
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