Im nearing the end of my bachelor in mathematics and am looking at some more applied fields for a masters as I do not...

Im nearing the end of my bachelor in mathematics and am looking at some more applied fields for a masters as I do not want to end up in research. I have some questions regarding different fields.

Ive always had an interest in artificial intelligence, and I love topology. I once picked up on somebody saying some applied topology is used in ai, can anyone tell me more about this?

Another course I liked was in mathematical finance (stochastic calculus, Black-Scholes-Merton) but I fucking hate statistics. Could financial mathematics or financial engineering be contenders for my choice in msc?

Last, I like theoretical computer science but I dont want to end up as a code monkey. From what I can tell a lot of comp sci msc programmes are about programming, programming and functional programming. Is this worth looking at?

Or, do you have any other options I could look into?

Thanks holmes

How much statistics have you done? Time series analysis, regression analysis, and probability theory are all very intense mathematical fields that fall under the umbrella of "statistics". You get a lot of stuff in these fields like measure theory, functional analysis, linear algebra, numerical analysis, and analysis in general. Basic statistics sucks but I've grown an appreciation for statistics.

With that in mind, there're fields like machine learning and image processing, both of which use heavy amounts of time series analysis which actually boils down to linear algebra and analysis. Not even the mundane stuff like doing matrix computations but like thinking about transformations, finding bounds, working in with Fourier transformations etc.

I'm doing a research project in image processing. As an additional example, the whitening transform is used to suppress periodic noise within an image in the frequency domain (Fourier domain). Creating the transform actually boils down to taking a symmetric matrix, diagonalizing it, and solving it so that the covariance of the matrix becomes independent (I don't remember the details as it wasn't useful to me at the time). When you implement the method in Matlab or whatever, it involves finding the eigenvalues of the matrix describing the image and dividing by the mean or something like that. I think you should give statistics a better chance.

I know probability theory and statistics as seperate fields, probably because I havent gone deep enough into them. I know they are both derived from measure theory so it makes sense. Ive heard that functional analysis is basically an extension of linear algebra to infinte dimensional spaces, but past that I dont know much about it. It did sound interesting and I may take a course in it before I finish up, granted that I find the space in my curriculum. Most I know is basic statistics like hypothesis testing and linear regression.

It was my understanding machine learning would fall under either computer science or artificial intelligence, but its not a masters in its own right. Was I mistaken? I have read something about it before, but it may be too specific for my liking. Im really fumbling in the dark about what I want to be doing for the rest of my life.

Sounds very computationally heavy. Is that correct? It does show a side of statistics I hadnt seen before.

if you go the computer route, your knowledge could be very valuable assuming you put the time in to learn various coding languages and programming.

Finance is another great option, though like you said it probably involves a lot of statistical analysis and a lot of time breaking into the field. finance is a social science, not an analytical one. you use a bunch of math to make predictions to the best of your ability, but in the end changes are made based on social trends. Im going to assume you would be working in a department where mathematics is more your flavor though, so maybe you wouldnt have to bother with all that other baggage.

ultmately, you are right. you cannot get stuck in a pure mathematics field if you are expecting a good job. applied in some field is the way to go.
>financial engineering
is that even a thing? it sounds like a meme degree dude.

>if you go the computer route, your knowledge could be very valuable assuming you put the time in to learn various coding languages and programming.

I have a minor in computer science and took some courses about using computers as a support in mathematics, I know some basic languages like C# and Python. I think those are a good basis to expand upon.

>Finance is another great option

Im afraid this is something that people caught wind of and are now flocking to in the form of econometrics because of the promise of good pay. Im no expert but if that (to me) perceived trend continues it could be a questionable choice. Though I liked the finmath course this, in combination with statistics component, makes me doubt this track. Im leaving it open as a possibility, still need to get a good overview of this field as it is potentially very interesting.

>is that even a thing? it sounds like a meme degree dude.

Could be, its a track in an applied mathematics program. From what I can tell it focuses on modeling, measure theory, game theory and I see something about time series. I dont know much about time series, though. Ive read that financial engineering is not a "real" engineering discipline like for instance electrical engineering is. Another alternative would be simply a financial/probability/statistics oriented track in a mathematics program but... yeah. Statistics and research.

> once picked up on somebody saying some applied topology is used in ai, can anyone tell me more about this?

Google "persistent homology".

> Could financial mathematics or financial engineering be contenders for my choice in msc?

If you really like finance, then yes.

> I like theoretical computer science but I dont want to end up as a code monkey.

There's no escaping this unfortunately.

>Persistent homology is a mathematical tool from topological data analysis. It performs multi-scale analysis on a set of points and identifies clusters, holes, and voids therein. These latter topological structures complement standard feature representations, making persistent homology an attractive feature extractor for artificial intelligence. Research on persistent homology for AI is in its infancy, and is currently hindered by two issues: the lack of an accessible introduction to AI researchers, and the paucity of applications. In response, the first part of this paper presents a tutorial on persistent homology specifically aimed at a broader audience without sacrificing mathematical rigor. The second part contains one of the first applications of persistent homology to natural language processing. Specifically, our Similarity Filtration with Time Skeleton (SIFTS) algorithm identifies holes that can be interpreted as semantic "tie-backs" in a text document, providing a new document structure representation. We illustrate our algorithm on documents ranging from nursery rhymes to novels, and on a corpus with child and adolescent writings.

>Research on persistent homology for AI is in its infancy, and is currently hindered by two issues: the lack of an accessible introduction to AI researchers, and the paucity of applications.

Am I correct in assuming this is gold for me?

>If you really like finance, then yes.

Thats a problem Im struggling with besides what I described here I liked one course, but it may be I start to dread it after one more course. Its up to me to decide this, I know. But I mostly wanted to add it to my story cause I came here to ask advice and wanted to be complete.

>There's no escaping this unfortunately.
Is this set? Its hard to get a good understanding of what kind of opportunities this would grant me as the field is overhyped on the internet and the universities themselves are somewhat glorifying the prospects.

Going to bed now, open to any and all advice. Bump.

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