PS: At least they dominate the curriculum for CS studies in Germany.

I won't start to elaborate further why, since it's off topic.

Probability, maybe? Probability and statistics have enough non-intuitive surprises that understanding them affords things from reporting to security. I haven’t done calculus (manually) in 20 years and never formally had to multiply matrices or such. I haven’t found that to hinder my particular path through dev-world. I think image/graphics programming is where heavier, smarter math is necessary. When I have to do that or other math-centric stuff like encryption, I rely on pre-done algorithms and libraries and forums far more than my own knowledge.

From Wikipedia:

Computer science is considered by some to have a much closer relationship with mathematics than many scientific disciplines, with some observers saying that computing is a mathematical science. Early computer science was strongly influenced by the work of mathematicians such as Kurt Gödel and Alan Turing, and there continues to be a useful interchange of ideas between the two fields in areas such as mathematical logic, category theory, domain theory, and algebra.

I've found that my interest in the science of computing has motivated me to become more proficient with mathematics. They really go hand in hand.

The public education system where I live recently made a subtle shift in high school graduation requirements. Previously, a student could take a CS elective and apply it toward his or her math requirements. Now that CS elective can be applied either toward a math requirement, or toward a science requirement. It might be seen by some that this is a step toward supporting that CS is a science. But the reality is that the change was made to encourage CS students to take more math (the implication being that if this CS elective is used to fill a science credit, there will still be a need to fill another math credit). Sort of a round-about "social engineering" approach to encouraging more math. I guess I would have preferred to see some other requirement relaxed in order to support kids who want to focus more on science, math, engineering, etc. But everyone has their own agendas, and somehow a curriculum is arrived at. ;)

I've used multiplication quite a lot, and found it very helpful.

The reason for this question was this: I found a tretris game online written in perl. I read through the code, and it was very interesting how they used transformations. It was quite clever...check out this link: http://docstore.mik.ua/orelly/perl2/advprog/examples/GUI/tetris.pl.

In light of the consideration: "Is that a link to pirated content?"

The code (tetris.pl) is part of the content of the book Advanced Perl Programming (Chapter 15: GUI Example: Tetris).

O'Reilly freely provides example code from the book in both .tar.gz and .zip formats. This specific script is in examples/GUI/tetris.pl.

Be aware this book was published in 1997. While I couldn't find a reference to a specific Perl version used for the code examples, it must be earlier than Perl v5.5 which was released in 1998 (see perlhist).

-- Ken

carlriz:

For me, the most useful math has been algebra and trigonometry. Generally for rearranging problems into a form that I can express as a program. I use it often enough that I don't normally have to look up algebra and simple trigonometry equations. In previous jobs, I've found calculus and linear algebra handy, but those were in jobs requiring modelling (milk production) and robotics. I seem to have an obsession with graphs, and frequently read articles on them, and many of my hobby projects use graph structures a good deal.

However, that's just the practical day-to-day stuff. I wish I was better at math. I think that learning math is a lot like learning LISP--you won't necessarily use it in your programming, but it helps you think about better ways to do things. I frequently wonder how often I could solve programming problems more quickly if I were familiar with more math.

While I don't use probability and statistics much, I think it's valuable to be conversant with it. It's not uncommon to get questions or tasks based on incorrect assumptions of how probabilities and statistics work--leading to wasted time and money. (Unfortunately, I can't think of any specific examples at the moment.)

...roboticus

When your only tool is a hammer, all problems look like your thumb.

I understand exactly where you are coming from. I am no expert in math but I understand concepts in calculus, discrete math, basic trigonometry, and whatever else I have learned in school. I do not use (high level) math on a daily basis at all. But, I will say all of the math learned in school really helped me program more creatively.

Propositional calculus / boolean algebra (De Morgan's laws and all that jazz), and set theory.

I suspect that we all find use for the skills we have. We often do not have a clue that some other branch of math could help us.

I have used vector and matrix algebra more than anything else.

I was often required to write probability code that I knew made little or no sense. Perhaps if I had had the skill to explain what was wrong...

Differential equations and calculus don't help much other than conceptually; for example, if you're writing a computer simulation that models partial differential equations, then you're not going to solve it the way they teach in general diff eq as an undergrad.

Finite automata and cellular automata are also very useful to know.

While not often related to computer work, everyone should have a good understanding of compound interest.

What math skills should you know that extremely useful/set you apart from other programmers

The ability to skip read through the goals, methodologies, philosophies, proofs, formulaic notation and bibliographies and other similar BS in 'formal' papers in order to extract the 5% of content that actually useful.

Its taken me 30+ years to get half good at it; and I still wish I was better, but I'm getting there. (I'll just have got really good and I'll kick the bucket; but that's ... er ... maybe not :)

Yes, CS is definitely part of math (a small part of math, though). After all, remember that Dijkstra was a professor of applied mathematics at the University of Texas (Austin).

The theory of generating functions (known in the math world as Formal Power Series) is just insanely useful.

Galois theory (field extensions, finite fields) comes up in coding theory and cryptography.

If you learn about p-adic numbers and p-adic analysis then you'll understand why 2s-complement arithmetic works (and then kvetch about the lack of a proper 2-adic division instruction in hardware :-)

If you're doing graphics programming then linear algebra and trigonometry matter matter a lot. Spherical trigonometry matters if you're doing anything with cartography, or GPS/navigation. Hyperbolic trigonometry would be more brain-stretching. Projective geometry (if you want to understand why those 2x3 matrices come up all over the place when talking about scaling/rotating/translating)

Calculus, on the other hand, comes up surprisingly non-often unless you're doing work in physics or statistics. (I always thought the high school math curriculum should go straight into group theory and number theory from plane geometry rather than the comparative dead-end of calculus, but hell will probably freeze over first)

Basic statistics and number theory come up sometimes.

Recursion -- lots of definitions involve recursion, or are more simply stated recursively. Functional programming fits in here, though most languages have some form of recursion available.

There are many nuggets in TAOCP, but it seems you have to know where to look, or guess that your topic has been mentioned. I often find pointers there from other searches.