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How much math you need for programming (2014)

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Re: How much math you need for programming (2014)

#71

Post by susam »

pc86 wrote: post #54

> You want to learn computer programming, then learn computer programming. Do not flip through Math books, read whatever is written on a particular newsgroup (comp.lang.c, comp.lang.lisp for example). I'm sorry but how long has it been since newsgroups were relevant? I loved them back in the day but it's absolutely not where a programmer noob should go in order to learn programming.

I have found Reddit r/lisp and Freenode #lisp to have great communities these days. They serve as good alternatives to comp.lang.lisp. It wasn't always so but both communities have evolved over the last decade to become more friendly to beginners.

Also some of us here from this forum also hang out at a Freenode channel named #spxy (also accessible via https://app.element.io/#/room/#spxy:matrix.org on Matrix). This is a small computer science and mathematics literature club, so quite relevant to those who are curious about or who work in the intersection of mathematics and programming. Incidentally, many members of this channel are also Lisp programmers.

Re: How much math you need for programming (2014)

#72

Post by username90 »

mkl wrote: post #60
enriquto wrote: post #48

Earlier quoted context omitted.

> I would argue that this is wrong. That's what physicists do, not mathematicians. Notice that many mathematicians would not agree with you, here (but probably, a majority would). As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". So, yes, in the minds of lots of mathematicians, what they do is precisely to study and understand nature.

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "disc…

You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are a part of our universe and not a fundamental logical truth.

Re: How much math you need for programming (2014)

#73

Post by mkl »

coldtea wrote: post #67
mkl wrote: post #60

Earlier quoted context omitted.

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "disc…

> I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. It's not about actual nature (the universe etc) being into consideration. It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process. So, they come to see mathematics as a kind of physics in this regard, no in the sense that…

Yes, that's what my comment says (but maybe you read it before I edited it to be clearer):

>> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.

Re: How much math you need for programming (2014)

#74

Post by ccortes »

js8 wrote: post #47
ccortes wrote: post #42

Earlier quoted context omitted.

>Traditional math (which came mostly out of physics and geometry) studies primarily infinite but countable structures (functions on countable sets, infinite series). The finite structures are often considered trivial, and the uncountable structures are considered to be too large to have practical importance. I don't think this is the case at all. Basically all of calculus theory in based on uncountable structures and…

I understand what you're saying, but disagree. In calculus, uncountable sets are just the theater, the real actors are sequences. As long as the theater is a complete metric space, we don't really care about its structure. Hence the name, it signifies that we are unconcerned with cardinality above aleph 0. The finite/countable/uncountable distinction IMHO shows where the focus is. Analogically, in CS, you use infinit…

> As long as the theater is a complete metric space, we don't really care about its structure.

I agree with that, but I fail to see how that means that traditional math studies primarily infinite countable structures.

Re: How much math you need for programming (2014)

#75

Post by mkl »

username90 wrote: post #72
mkl wrote: post #60

Earlier quoted context omitted.

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "disc…

You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are…

> I'd argue it is impossible to imagine a world where 1 + 1 is not 2.

Actually, you've probably done that yourself, in a programming setting: integers modulo 2, where 1+1 = 0. It's useful in places and the consequences aren't too ridiculous in this case.

Following through figuring out the consequences of rule changes is a key thing mathematicians do. E.g. do we need this rule? What if this was weaker? What if this was reversed? What if we had this extra restriction?

Re: How much math you need for programming (2014)

#76

Post by ddxxdd »

username90 wrote: post #72
mkl wrote: post #60

Earlier quoted context omitted.

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "disc…

You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are…

A universe where 1 + 1 != 2 is a universe filled with self-contradictions and so cannot exist.

It's like imagining a universe where True == False. It's not a hypothetical, it's a logical impossibility.

Re: How much math you need for programming (2014)

#77

Post by refactor_master »

alkonaut wrote: post #66
MeinBlutIstBlau wrote: post #62

Earlier quoted context omitted.

I still fail to see how calculus relates to programming for what most people do. Web or not.

I mean things like knowing simple polynomials, which ties into things like asymptotic complexity. Which has the word “asymptotic” in it. That basic.

With that weak of a definition of math, you might as well say any first year high school subject is a prerequisite. If you didn’t pass any of those, chances are you’re not a great programmer either.

Re: How much math you need for programming (2014)

#78

Post by z3t4 »

When working with CSS/design I used subtraction, multiplication and division. When working with e-commerce/finance I used algebra. When making a 2d game I used geometry. When making a 3d engine I needed to learn about vector, matrices, etc. When working with weather forecasting there where formulas involving sin,cos,atan etc. So while you do not need math to get started in programming/development, you will definitely stumble on it. And you don't really know your math until you put the wrong formula into programs/production used by thousands of people.

Re: How much math you need for programming (2014)

#79

Post by coldtea »

mkl wrote: post #73
coldtea wrote: post #67

Earlier quoted context omitted.

> I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. It's not about actual nature (the universe etc) being into consideration. It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process. So, they come to see mathematics as a kind of physics in this regard, no in the sense that…

Yes, that's what my comment says (but maybe you read it before I edited it to be clearer): >> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.

Yes, that.

Though I wouldn't necessarily consider it "muddying the waters", but taking another criterium as important in the distinction of physics-like or not.

Namely, not whether it concerns the study of the material universe, but whether it involves experimentation/discovery of in place structures, and other such physics-like processes (which they think it does).

Re: How much math you need for programming (2014)

#80

Post by username90 »

mkl wrote: post #75
username90 wrote: post #72

Earlier quoted context omitted.

You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are…

> I'd argue it is impossible to imagine a world where 1 + 1 is not 2. Actually, you've probably done that yourself, in a programming setting: integers modulo 2, where 1+1 = 0. It's useful in places and the consequences aren't too ridiculous in this case. Following through figuring out the consequences of rule changes is a key thing mathematicians do. E.g. do we need this rule? What if this was weaker? What if this wa…

That is a number system where 1 + 1 isn't 2, not a universe. At least I can't imagine a universe where the concept of 1 + 1 equals 2 doesn't exist.
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