**General Mindforming**

**Solving Problems** - One fundamental method of math, independent of the area, is transofrming an unknown problem into a known one. Even if you don't have the same problems, you need the same skill. In math, as in programming, virtually everything has different representations. Understanding the equivalence between algorithms, problems or solutions that are completely different on the surface helps you avoid the hard parts.

(A similar thing happens in physics: to solve a kinematic problem, choice of the coordinate system is often the difference between one and ten pages full of formulas, even though problem and solution are identical.)

**Precision of Language / Logical reasoning** - Math has a very terse yet precise language. Learning to deal with that will prepare you for computers doing what you say, not what you meant. Also, the same precision is required to analyse if a specification is sufficient, to check a piece of code if it covers all possible cases, etc.

**Beauty and elegance** - This may be the argument that's hardest to grasp. I found the notion of "beauty" in code is very close to the one found in math. A *beautiful* proof is one whose idea is immediately convincing, and the proof itself is merely executing a sequence of executing the next obvious step.

The same goes for an elegant implementation.

(Most mathematicians I've encountered have a faible for putting the "Aha!" - effect at the end rather than at the beginning. As have most elite geeks).

You can learn these skills without one lesson of math, of course. But math ahs perfected this for centuries.

**Applied Skills**

Examples:
- Not having to run calc.exe for a quick estimation of memory requirements
- Some basic statistics to tell a valid performance measurement from a shot in the dark
- deducing a formula for a sequence of values, rather than hardcoding them
- Getting a feeling for what c*O(N log N) means.
- Recursion is the same as proof by inductance

(that list would probably go on if I'd actively watch myself for items for a day. This part is admittedly harder than I thought. Further suggestions welcome ;))

**Where I use it**

The company I work for does a lot of data acquisition, and our claim to fame (comapred to our competition) is the brain muscle that goes into extracting something useful out of the data. While I'm mostly unconcerned with that, I get enough math thrown my way. Before that, I've implemented and validated random number generators for statistical applications, implemented a differential equation solver, wrote simulations for selected laws of physics. And probably more.