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This field of mathematics is also utilized in a wide array of programming areas such as making visuals or graphs, simulations, coding-in applications, problem-solving applications, analysis and design of algorithms, and making statistic solvers.
Any kind of low level graphics or game programming will also require math, and you'll need to study it before you attempt to do any of that. Math is also necessary to understand algorithms complexity, but you are not going to invent new algorithms, at least in the first few years of programming.
The answer to that “how?” is very simple: Coding. Math and coding are deeply related, and when teaching your students how to code, you are -at the same time- delivering mathematical content, and a way of thinking that they can use, later on, while calculating something specific in their math class.
Of course you need some basic math concepts, like calculus or algebra, or logic, but the very basics if it. You don't need to know any of complex numbers, probability, equations, graphs, exponential and logarithm, limits, derivatives, integration, differential equations and so on.
Computer graphics.
It's all matrix multiplication, vector spaces, affine spaces, projection, etc. Lots and lots of algebra.
For more information, here's the Wikipedia article on projection, along with the more specific case of 3D projection, with all of its various matrices. OpenGL, a common computer graphics library, is an example of applying affine matrix operations to transform and project objects onto a computer screen.
I think that a lot of programmers use more math than they think they do. It's just that it comes so intuitively to them that they don't even think about it. For instance, every time you write an if statement are you not using your Discrete Math knowledge?
In graphic world you need a lot of transformations.
In cryptography you need geometry and number theory.
In AI, you need algebra.
And statistics in financial environments.
Computer theory needs math theory: actually almost all the founders are from Maths.
Given a list of locations with latitudes and longitudes, sort the list in order from closest to farthest from a specific position.
All applications that deal with money need math.
I can't think of a single app that I have written that didn't require math at some point.
I wrote a parser compiler a few months back, and that's full of graph-theory. This was only designed to be slightly more powerful than regular expressions (in that multiple matches were allowed, and some other features were added), but even such a simple compiler requires loop detection, finite state automata, and tons more math.
Implementing the Advanced Encryption Standard (AES) algorithm required some basic understanding of finite field math. See act 4 of my blog post on it for details (code sample included).
I've used a lot of algebra when writing business apps.
Simple Examples
BMI = weight / (height * height);
compensation = 10 * hours * ((pratio * 2.3) + tratio);
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