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Mathematicians are chronically lost and confused (2014)

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Re: Mathematicians are chronically lost and confused (2014)

#141

Post by nitwit005 »

pathsjs wrote: post #135
nitwit005 wrote: post #96

Earlier quoted context omitted.

I've seen some examples that don't seem to agree with that. Programmers often don't need advanced math, but the ones that do, such as video game engine developers, seem to get fantastically good at it. You need a lot of time to master any skill, and few jobs provide that for mathematics. At least, not with any diversity in problems. The degree provides some years of dedicated effort.

Videogame engine developers do not need advanced mathematics

What sort of standard are you asserting? The games with fluid dynamics simulations to simulate water aren't using fancy enough models?

Re: Mathematicians are chronically lost and confused (2014)

#142

Post by keyboardwarrior »

naasking wrote: post #121
jondubois wrote: post #43

My favourite quote about Mathematics is from John von Neumann: "In mathematics you don't understand things. You just get used to them." - This quote highlights precisely why I ended up choosing software engineering over maths. I'm just not very good at applying processes/methodologies which I don't fully understand. For example, I wasn't very good with linear algebra until I was able to visualize the equations in my…

> "In mathematics you don't understand things. You just get used to them." - This quote highlights precisely why I ended up choosing software engineering over maths. Haha probably the most unintentionally funny and ironic comment I've read in awhile. Given more than 50% of software projects fail, which is worse than chance, I think it's safe to say the no one really understands software engineering either. Like math,…

Programming and math start at opposite ends but will eventually meet in the middle,

they both deal with computation (modification through time).

Only math as a language originates from past assertions to model a determinant factor,

while programming deals with future assertions as to produce determinant factors.

Its alot easier to make arbitrary mistakes in the latter then the former.

Re: Mathematicians are chronically lost and confused (2014)

#143

Post by jwdunne »

goldenkey wrote: post #131
agentultra wrote: post #112

Earlier quoted context omitted.

No, not completely unaware. I'm glad I've reminded you of something you find entertaining. I hope you discourage more people from learning something awesome.

Hes just being real. Ive been self learning group theory, and cardinality/ordinals, surreal numbers, VN universe, shit is hard. Foundation is key. In order to be profound one needs tools. Unlike programming, dedication to tightening ones toolbelt first, helps immensely later. Order in math progression is way more significant than programming by trial and error.

It'd be interesting to know what the optimal order of progression would be.

It'd be simple to grab a curriculum and start from point A (as in, the method is simple - not the content), taking that as the order.

More thoughts and discussion on this would be extremely interesting.

Re: Mathematicians are chronically lost and confused (2014)

#144

Post by goldenkey »

jwdunne wrote: post #143
goldenkey wrote: post #131

Earlier quoted context omitted.

Hes just being real. Ive been self learning group theory, and cardinality/ordinals, surreal numbers, VN universe, shit is hard. Foundation is key. In order to be profound one needs tools. Unlike programming, dedication to tightening ones toolbelt first, helps immensely later. Order in math progression is way more significant than programming by trial and error.

It'd be interesting to know what the optimal order of progression would be. It'd be simple to grab a curriculum and start from point A (as in, the method is simple - not the content), taking that as the order. More thoughts and discussion on this would be extremely interesting.

I'd say it really depends on what one wants to specialize in. You could do a ton of calculus and it wouldn't help all that much in some other areas of math. Yet, calculus is a pillar for some things. Ramanujan used integrals everywhere in his work on infinite series. I don't think there's a very straight forward path. Math is a very diverse subject.

Re: Mathematicians are chronically lost and confused (2014)

#145

Post by jwdunne »

goldenkey wrote: post #144
jwdunne wrote: post #143

Earlier quoted context omitted.

It'd be interesting to know what the optimal order of progression would be. It'd be simple to grab a curriculum and start from point A (as in, the method is simple - not the content), taking that as the order. More thoughts and discussion on this would be extremely interesting.

I'd say it really depends on what one wants to specialize in. You could do a ton of calculus and it wouldn't help all that much in some other areas of math. Yet, calculus is a pillar for some things. Ramanujan used integrals everywhere in his work on infinite series. I don't think there's a very straight forward path. Math is a very diverse subject.

I was intrigued because there is some indication of a rough but important ordering to the topics in formal maybe antics education. I was interested in seeing what that order was.

I've seen others say that linear algebra is a prerequisite of any kind of maths maturity goal.

I think, personally, maths is an incredibly important field and there's a feeling that some degree of comfort with it will help me in more ways than I can imagine. That is, however, an opinion formulate after some self study based on a great interest in the field.

It fascinates me that even things we take for granted, such as addition and multiplication, has entire subfields that have generalised the structure of those operations over those types of sets (in what's taken for granted: addition and multiplication over the set of integers). What's even more fascinating is that this work has had an impact on other areas of deep interest e.g category theory and Haskell.

Re: Mathematicians are chronically lost and confused (2014)

#146

Post by goldenkey »

jwdunne wrote: post #145
goldenkey wrote: post #144

Earlier quoted context omitted.

I'd say it really depends on what one wants to specialize in. You could do a ton of calculus and it wouldn't help all that much in some other areas of math. Yet, calculus is a pillar for some things. Ramanujan used integrals everywhere in his work on infinite series. I don't think there's a very straight forward path. Math is a very diverse subject.

I was intrigued because there is some indication of a rough but important ordering to the topics in formal maybe antics education. I was interested in seeing what that order was. I've seen others say that linear algebra is a prerequisite of any kind of maths maturity goal. I think, personally, maths is an incredibly important field and there's a feeling that some degree of comfort with it will help me in more ways th…

Right, in fact the interaction between multiplication and addition is one of the most fundamental forms of chaos due to combining recursive operations. One could say, addition is repeated counting. Multiplication is repeated addition. And the interaction between the two points a finger at the relationship between space and time.

And yes I agree. It is glorious that the binary operations that seemed so natural to us formed the basis for groups, rings, and fields. Associativity, commutativity, distributivity of two related operations are quite the pearls :-) Its also interesting as a programmer and from a "properties of functions" perspective to study magmas and semigroups and groupoids..etc..

Knowing more about abstract algebra in terms of special properties of functions has led me to believe that most programmers are missing out on some of the beauty of functions by merely implementing them and not so much understanding the common properties and classifications of them.

Re: Mathematicians are chronically lost and confused (2014)

#147

Post by vinchuco »

vinchuco wrote: post #24
kinai wrote: post #2

Does anybody know a good guide on where to begin? Resources are not the issue here, but usually the overwhelming amount of information regarding all those topics and areas of mathematics. I was always very interested but got discouraged rather quickly, even after a semester at university. So far my favorite access to math was through philosophy.

I made a 3-page overview of calculus as an extra section of some notes for a class I'm teaching. Mostly to see if it could be done. Here it is. https://www.dropbox.com/s/yp8ijkzir4h8rz9/Calculus%20in%20e%... I'm REALLY sorry for the picture quality. I'll use a proper scanner later. My phone's camera and app are terrible.

In case you check back on this, I made a better resolution copy. Hopefully it's useful to someone :) https://drive.google.com/open?id=0B2FKX2JZ061dTzRNTjl6SFJVaV...
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