Me and my friend, doctor in computer science, have applied mathematics to many problems in the past. We've done lot of work separately.

Hi [MENTION=988]UnitOfPopulation[/MENTION], this seems very cool. Thanks for the prompt response. I really dig this. Btw, as of today I've changed my college major from electronics technology (boring!!!) to applied math, with an interest in operations research.

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.

Can you recommend a book or online reference on this subject? Thanks.

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.

Interesting.

I used to read a lot. Dr. Art Benjamin did a course called, The Joy Of Mathematics, by The Great Courses. It was my first exposure to combinatorics. After, I bought both of Art's mental math publications. Two years ago, when I lived in Southern CA, I was delivery driving for a paint company. When I was dispatched to the city of Montclair I instantly knew it's where Art had a math professorship at Harvey Mudd College. Zip! There I was, hopped out the truck, and loitered the campus. Meandered up the steps to his 2nd story office but, I got cold feet. Instead I walked the entire campus - very small but quaint.

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.

I see.

Related to set theory. I started off watching lectures by a Dr. Jason J Campbell's numerous Youtube logic series. This dendritic surge of interest made me veer into a used book store in the Riverside CA mall. I scanned the book shelves, spotted this below book, then tested myself. It was cool what I'd learned and didn't know...

Afterward I wasn't sure where to go next so I picked up an introductory mathematical logic text. Feeling a big intimidated I decided to learn some set theory. That got me interested in abstract algebra. But I've since stopped my wondering and now plugging away my prerequisites to transfer to university. I wish the community college/university level would accept MOOC credits. But so far it's a no go. :sad:

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.

This is of interest to me.

Yeah, I'd no idea what discrete mathematics was until I took a computer science class for programming in Java. My mind exploded. What I recall is what my community college instructor lacked in pedagogy he made up for in funny code monkey stories from his employment in Bay Area CA - it helped reverse track ideas I was puzzled by i.e. industry culture etc. I keep signing up for coding classes online but get half way through and stop because there's no interesting application.

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.

Cool, while a member of intpcomplex I used to correspond with this Australian math teacher who introduced me to cryptoanalysis. I then pirated some books on it. I mostly just learned the history of it and that set me on a pathway to research number theory. I got great advice from a guy named Limes, who suggested my personality type (barring the ASD etc issues) might favor the theoretical vs the hands-on technology focus. And might check out information security. I'm an odd specimen and couldn't grasp interesting applications so I shifted from the subject.

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.

Hm.

Would you please provide a reference? Thanks!

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.

I see.

I'm interested in the big picture view of calculus and its applications. Physics came up, during a google search, related to engineering. Perhaps you could enlighten me with a quick reference?

If I can grasps the end goal of the material I can sometimes modify how I learn it and shorten the time learn the material, kinda thing.

Yeah I think maths are a ton of fun. Exciting stuff!

No

it's double rainbow exciting!

(Btw, I've taken the liberty to google the topics you've mentioned but, again feel free to respond with examples as you desire. Thanks for taking the time to read this message.)