
Ask HN: High-level math, useful? - mlxer
I really enjoy solving mathematical puzzles and riddles in general. 
But is there any use for higher mathematica if you are going into electrical engineering? Or is the standard classes of linear algebra, one and multidimensional analysis and statistics, discrete math, complex analysis and maybe some optimization course enough?<p>Things like topology and abstract algebra, does it teach you anything that is actually applicable in electrical engineering?
Does it evolve your abstract thinking skills which could make you a better engineer?
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mathgladiator
I think studying higher maths make for a good problem solver, but you are
missing out on practicality and people skills.

For instance, in my life, I went all the way up to PhD level courses in
mathematics. This translated into me being able to go into my start-up and
solve all sorts of problems. I was also solving problems that were already
solved because I was ignorant of what was considered good programming
practice.

Like source control. Because I could, I wrote my own source control. Like an
IDE. Because I could, I wrote my own.

I attribute my fantastic problem solving skills to my mathematics back-ground.
After all, when dealing with proofs in abstract algebra and the creative
process of making up strange sets that exhibit strange behaviors... Most
things seem trivial at some level.

The fundamental problem of mathematics is that you spend a lot of time solving
fake or stupid problems to build up the ability to solve real problems. If you
are going to go into the cutting edge of research, then you will need those
skills. Otherwise, you will be very good at solving artificial problems.

I want to say that it will make you a better engineer, but I'm very biased. I
feel like it has helped me compared to my peers in terms of raw engineering
power.

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RiderOfGiraffes
Studying higher math does not automtically mean you miss out on practicality
and people skills. Perhaps in your case it did, but a good engineer will be
dealing with some of that.

It's important to have a balance - there are infinitely many things that you
could advise would be useful, and time is limited. When solving problems it's
important not to dive in immediately, but also to ask "What of this has
already been done?"

But even then, solving some of the problem first gives an appreciation of what
has been done, and often makes you better understand the strengths and
limitations of existing solutions. Your example of an IDE is one where re-
doing it from scratch is unlikely to give a better result, but Linus re-did
the source control idea, and did it better.

~~~
mathgladiator
That's very true.

Part of the culture of learning higher math however rewards/tolerates esoteric
behavior where practicality is just not valued.

I think it is all about related rates. If you are studying abstract algebra
now hard-core, then you are missing out on doing some cool Kinect hacks now.
Or, you are missing out on chatting up the girls over at the pub.

I found math very ... addicting, and I wish I had learned balance sooner.
Instead, I thought it was a lot of fun to sit down every evening and grind on
problems from "Berkeley Problems in Mathematics"

~~~
dfox
In most mathematicians and theoretical physicist I know this tolerance for
"esoteric behavior" probably caused exactly opposite effect: they are probably
too much sociable and cool.

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RiderOfGiraffes
My feeling is that topology can help your abstract thinking as it's likely to
be in engineering, but abstract algebra less so. Having said that, if you're
not actually inclined to take these subjects, you'll probably end up
struggling and not caring.

Topology, and the insights it brings, can make some of the analysis and linear
algebra make more sense - there are unifying concepts and structures. Abstract
algebra is more about symmetries and actions, and while also useful, possibly
don't give the same sorts of insights.

Just my $0.02.

~~~
sz
Doesn't topology past a certain basic level rely on algebra pretty heavily?

~~~
RiderOfGiraffes
There are two flavors of tolopogy: Point/Set and Algebraic. Point/Set topology
is really useful in understanding how things can go wrong, and what's true for
sure in analysis. Algebraic topology is less obviously useful for things like
engineering.

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npp
Some higher-level math will be important, other parts will not be. The parts
that will be more useful are more on the analysis side (real analysis, complex
analysis, functional analysis, convex analysis, Fourier analysis, probability
theory). These are higher math and are very applicable, or are prerequisites
to understanding the applied stuff (convex optimization, dynamical systems,
control, ...).

It helps to know what a topology is, but not much more, and you would learn
enough "on the way" in learning analysis properly. It helps to know what
groups are, because they do show up in practical things, but you don't really
need to know full-up "group theory". (They show up because they capture the
idea of symmetries, and it is useful in certain practical situations to talk
about something being symmetric with respect to various transformations, e.g.
under permutations or rotations or whatever. But in this case you don't tend
to do much analysis actually using group theory beyond this.) A whole course
on abstract algebra is not necessary unless you're interested. It may help in
some indirect way of "helping you think better", it may not.

See, say, <http://junction.stanford.edu/~lall/engr207c/> as an example of an
EE course that does a fair amount of math.

(Also, above, I don't mean 'applicable' in the very indirect sense of "helping
you think better" -- I mean people use it to do real stuff. Whether you want
to do that stuff is another story -- there are certainly good things in EE/CS
that don't require this kind of math.)

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sz
I don't have as much experience as others here (~2 years) but I can tell you
that it definitely changes the way you think, not just about engineering
problems but life situations too, and the change is not something you might
predict from the sub-topic you're learning about. Math is really just the art
of thinking precisely (lots of inventing beautiful abstractions and
interesting examples).

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drallison
Mathematics and Statistics are fundamental tools of Science and Engineering,
tools you need in your kit. Linear algebra, analysis, statistics, discrete
math, complex analysis and optimization are about the minimum. Abstract
algebra, topology, differential geometry, combinatorics, number theory, and so
forth all may prove useful and enriching. The problem is that you never know
what will be useful.

Years ago, abstract number theory was seen as pure mathematics unsullied by
practical applications. And then along came cryptography.

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tkok
As an EE student nearing a bachelor's, I haven't seen all that much use for
more abstract mathematical topics in my classes. I would say it is much more
important to be very comfortable with the more basic, concrete topics that
will show up all the time: algebra, ODEs and PDEs, (vector) calculus,
Fourier/Laplace transforms, linear algebra, probability. An EE specializing in
the physics side of things may wind up using abstract algebra or other higher
math, but that is a pretty small percentage of engineers.

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BTBurke
It depends on what particular field within electrical engineering you're going
to pursue. My specialty is signal processing and the general feeling in our
field is that more math is always better. I haven't used topology or abstract
algebra on the job. A solid understanding of the basics will take you pretty
far. I'd choose depth in those fields before I worried about breadth.

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JonnieCache
If you want to learn it, learn it. There is no other justification required.
If you enjoy learning it, then it _will_ benefit you.

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JCThoughtscream
I'm only guessing here, not being an engineer or a mathematician, but...
wouldn't that be rather dependent on what kind of engineering you're getting
into?

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mlxer
Yes, poorly defined question. I guess electrical engineering and CS has a lot
more math and then your specialization matters obv.

