Me and my friend, doctor in computer science, have applied mathematics to many problems in the past. We've done lot of work separately.
We've applied probability and sampling theorems to improve 3d graphics results with path tracing. Probability can be used to find out the distribution of results of some processes for which we have a description. Probability theory can be applied for testing whether some explanations or findings are true.
We've applied combinatorics to find out what kind of moves are available in a game, to improve the game AI. Combinatorics can be used to find out how many and which kind of variations there are for some configuration of parameters, and how much they overlap with some other configuration of parameters and permutations thereof.
Set theory is readily applied to data structures which describe the breakdown of some complex structures. Similar to combinatorics, it can be used to count to overlap of some sets of parameters. It can also be used to establish a hierarchy for a sets of sets of parameters. These kinds of structures can assist in the data handling part of some miscellaneous AI operations, or they can be used for AI in some applications.
Discrete mathematics can be applied to discrete optimization problems. There we have parameters which obey some strict rules within the system where the values may only obtain certain values. This could be a card game, or the delivery of packages, or the logistics of people or cargo.
I've done some cryptanalysis to find out the complexity of decrypting some cryptosystems without having the keys. It can also be applied to finding out how much of the original information is available after it has been scrambled with some method.
Multidimensional analysis applies to situations where we have multiple parameters describing some object, and we have a set of those objects. This can be used to things like classifying parts of a video, or it can and has been used to classify loan applicants.
Differential equations come up in simulating some physics-based systems, and in in the design and implementation of finite element analysis to simulate those systems.
Yeah I think maths are a ton of fun. Exciting stuff!
