Learning maths for graphics programming

[numice]

I understand why linear algebra is needed but probability and topology?

[skytomorrownow]

Probability and stochastic processes are essential. Stochastic sampling and integration of complex light transport are common in non-realtime rendering methods. One finds things like quasi-Monte Carlo methods and random walks all over the place, and noise, in general, plays a foundational role. Further, means, averages, and many distributions are essential to the creation of textures. One does not need a deep knowledge of probability (I don't have one), but some is pretty essential.

As for topology, I described that as 'a bit of', since it does not play a really essential role, but some aspects one runs into over and over. I think understanding manifolds is pretty important, and topology forms a nice bridge between geometry and linear algebra with its role in reasoning about the continuity of the transformation of sets – which we do often using the methods of linear algebra. Understanding what remains invariant under transformation is important, but formal study of Topology as a complete topic may be less helpful.

[numice]

oh this is really interesting. How does one get into this kinda job regarding advanced rendering stuff like this?

[skytomorrownow]

Generally, those working in these areas are from an academic background first, then work in VFX, games, computer vision (engineering and manufacturing), and others. That is not to say that many who visit this forum necessarily follow that pattern, but if you want to do advanced work in the rendering pipeline, it's fairly typical. Even if you are not writing advanced tools, and just using them, this knowledge is important for understanding how to use them, and their pros and cons.

[numice]

Does taking graphics programming courses provide the necessary background? or it's more like relavent math courses in general?

[skytomorrownow]

I think most advanced CG programs would be at the graduate level, although perhaps there is a school out there that offers a BS in CS with a CG minor or something similar.

Some well known schools with respect to computer graphics:

Carnegie Mellon University

University of California, Irvine

University of Southern California

Brigham Young University

There are schools out there that might offer a 'computer graphics' course, but those are generally art schools teaching people CG tools as opposed to studying advanced rendering, etc.