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# Advanced Mathematics for Computer Science

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#1
Members - Reputation: **834**

Posted 17 March 2012 - 04:46 AM

For example:

Abstract algebra? Number theory? Chaos theory/nonlinear dynamics? Combitorics? Graph Theory? Optimization?

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#4
Crossbones+ - Reputation: **7022**

Posted 17 March 2012 - 08:19 AM

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#6
Crossbones+ - Reputation: **19965**

Posted 17 March 2012 - 02:51 PM

I only know a little bit about Chaos Theory, but my understanding is that it's pretty useless. It's just one of these things that have a sexy name and produce pretty pictures, but I don't think you can really do a whole lot with it.

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#8
Members - Reputation: **2143**

Posted 17 March 2012 - 06:26 PM

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#12
Members - Reputation: **604**

Posted 19 March 2012 - 05:41 PM

Discrete math covers such a potporrui of stuff you will see in CS that any decent CS program will require it.

More Statistics than covered in Discrete.

Linear Algebra for graphics and matrix work you will see popup

and

if you can

2nd course in logic preferablly covering HOL(higher order logic) you will see if you ever mess with Lisp, Haskell, and theorem proving.

Abstract algebra if you plan on doing any crypto stuff since a lot of advance number theory is used.

Public key cryptography draws on many areas of mathematics, including number theory, abstract algebra, probability, and information theory.

numerical analysis if you plan on doing any scientific programming or otherwise work with very large or small numbers, etc where results have to be very precise.

Actually, chaos theory comes into play in numerical analysis:

In numerical analysis, the Newton-Raphson method of approximating the roots of a function can lead to chaotic iterations if the function has no real roots

bottom line is that you can never take/have enough mathematics as someone once said I'm sure

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#16
Crossbones+ - Reputation: **19965**

Posted 20 March 2012 - 06:57 AM

[/sarcasm]

Computer Scientists should learn Differential Geometry? Really? Why? If you are a physicist, sure... but for CS?

Of course, the more Math you learn, the easier it will be for you to think mathematically, and that can be very useful for a computer scientist, but I don't think every CS student should get a Ph.D. in Math to do his job.

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#17
Members - Reputation: **194**

Posted 20 March 2012 - 07:26 AM

I am comIng at this from the perspective of a graphics/computational-geometry phd with an undergrad math major. I don't think that this math is something that everyone would benefit from directly, but i definitely believe that it would be beneficial for anyone who works in computer graphics at a reasonably sophisticated level - not necessaily because they will use it every day, but because it helps to see the bigger picture (except computational geomety - that you really may use every day :-) ).

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#18
Members - Reputation: **510**

Posted 20 March 2012 - 12:45 PM

These subjects can be taught at a low or high level in a class, but the subjects themselves run quite deep. Linear algebra becomes functional analysis, operator algebras, etc - fields of current research. Discrete math branches into combinatorics, graph theory, etc. You don't have to look far in discrete mathematics to stumble on unsolved problems.

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#20
Members - Reputation: **510**

Posted 20 March 2012 - 10:44 PM

http://www.extension...bstract-algebra

For (convex) optimization, there are two great video lecture series by Steven Boyd at stanford:

http://academicearth...-optimization-i

http://academicearth...optimization-ii

For numerical analysis and more advanced numerical linear algebra, I really liked Gilbert Strang's (MIT) computational engineering videos,

http://academicearth...d-engineering-i

http://academicearth...or-engineers-ii

For a lot of the topics mentioned (topology, differential geometry, nonlinear dynamics, etc), basically anything where there is a continuum instead of just finite structures, it will be difficult to make much progress without a solid grounding in real analysis. There's a great set of video lectures by Francis Su from Harvey Mudd where I did my undergrad,

http://beta.learnstream.org/course/6/

(or http:/ /www.youtube.com/watch?v=sqEyWLGvvdw and click through to the other videos)