I chose math instead of physics. Was it a mistake?

[engmathengphys]

Long story short, my career goals are to work as a researcher/research scientist in machine learning or to develop models/algorithms for forecasting such as in financial markets or otherwise. Fundamentally, I find think this is quite similar to physics as a science, but that is for another discussion. I don't explicitly plan on becoming a physicist even though I think I would enjoy it, just not to the extent of machine learning which is still a relatively new and fast moving area of research.

In my country, there are basically only two real options: engineering physics or, more recently, engineering mathematics. These programs consist of a three year bachelor's and a two year master's. As the choices of master's are quite similar, I will only focus on the first three years.

Engineering physics is an applied math & physics program that has for many years been the flagship program and feeder for graduate studies in mathematics and physics. Naturally, this program has a very good reputation nationally and every year some of it's alumni go to top US institutions for their graduate studies. Yearly there are about 150-200 admits here.

A year ago, the engineering mathematics program was started which is a spin-off/sibling-program of engineering physics. The main difference is that instead of studying applied math & physics, you study more math and some CS. Having said this, both programs study identical courses in single- and multi-variable calculus, real analysis and a decently advanced course in linear algebra. The difference is still significant though as one can fit in measure theory, additional course in statistics, complex analysis, groups & rings, optimization and more during the bachelor's portion of the degree. Yearly there are about 60-70 admits here.

From a pragmatic point of view, the choice is pretty obvious; engineering mathematics will allow me to study significantly more relevant math for my goals before the master's even begins. This will in turn allow me to go deeper and reach the cutting edge sooner during my master's studies.

Despite this, my heart is with engineering physics.
First of all, I believe I have a stronger natural talent for physics as opposed to mathematics. I find most physics I've studied so far to be intuitive and easy to pick up. It's relatively easy to build a mental model of physical laws and understand or further derive other relationships from them. While I think mathematical proofs can be as intuitive as physics, I find the actual use of math in an applied sense to be less intuitive and require some level of abstraction/acceptance that certain properties have been proved. Even if I know the proof, it's sometimes difficult to see the whole line of reasoning from from the fundamental proof to the actual application you're doing. With physics I can to a much larger extent rely on a complete mental model without abstracting away things.

Secondly, my interest for physics has been bigger than my interest for mathematics for a few years now. I still enjoy mathematics, but it's more of a means to an end (ML/CS).

Thirdly, I'm a little concerned about reputation and how well known engineering mathematics is internationally. While the quality of students at engineering mathematics is probably very similar to engineering physics (entrance exam cut off was actually higher for engineering mathematics), it's still a very new program with no alumni as of yet. To make things worse, class size is significantly smaller for engineering mathematics so marketing through alumni will remain small for a long time. Engineering physics on the other hand already has some alumni that have broken through the door. Granted, none of these are well known internationally so it might not matter that much.

Lastly, there is something very attractive with the duality of having studied both math and physics to reasonable levels. Having the ability to engage in both subjects and/or change career paths. "Polymath".

Am I being unwise for favoring engineering physics? Are there some factors I'm not considering or overestimating the value of?
Any input is helpful appreciated.

I got admitted to engineering mathematics a week ago.

 

[Zap]

Physics doesn't have much to do with machine learning. I think some of the business people think physics is like a type of philosophical study. Idk. Maybe people just don't want to give me any credit LOL.

Obviously statistics and computer science is more related to machine learning.

I really don't think physics is directly related to AI and machine learning. After a physics degree, you'll have the mathematical background to be able to start learning AI and ML, but that's pretty much it.

At my school, the electrical engineering, computer science and statistics departments had classes in AI and ML. The physics department did not.

Outside of applying math, I can't think of anything you study in physics that is relevant to machine learning. There was one class called computational physics that went over numerical methods and even the central limit theorem, but not all physics degree programs offer computational physics.

 

[engmathengphys]

Physics doesn't have much to do with machine learning. I think some of the business people think physics is like a type of philosophical study. Idk. Maybe people just don't want to give me any credit LOL.

Obviously statistics and computer science is more related to machine learning.

I really don't think physics is directly related to AI and machine learning. After a physics degree, you'll have the mathematical background to be able to start learning AI and ML, but that's pretty much it.

At my school, the electrical engineering, computer science and statistics departments had classes in AI and ML. The physics department did not.

Outside of applying math, I can't think of anything you study in physics that is relevant to machine learning. There was one class called computational physics that went over numerical methods and even the central limit theorem, but not all physics degree programs offer computational physics.

Thanks for responding!
I agree that physics isn't very relatable to machine learning and that the domain-specific knowledge isn't really transferable. Both engineering mathematics and physics offer master's/specializations in pure math, applied & computational math, CS, and machine learning. My thinking is more like: can I get away with studying physics without significantly compromising my goals in ML? Is it even wise?

It's too late for me to update my post unfortunately.

 

[sysprog]

Does multivariant linear regression analysis application to market fluctuationalities have appeal for you?

 

[engmathengphys]

Does multivariant linear regression analysis application to market fluctuationalities have appeal for you?

What parameters are you measuring for the regression? My hunch is that many of the direct applications of machine learning and/or statistics are already priced in.

I don't understand what you're getting at with your question? I can assure you I find predictions in financial markets or otherwise to be very interesting.

 

[gwnorth]

Does your program's degree structure allow you to take Physics courses as electives?

 

[sysprog]

What parameters are you measuring for the regression? My hunch is that many of the direct applications of machine learning and/or statistics are already priced in.

I don't understand what you're getting at with your question? I can assure you I find predictions in financial markets or otherwise to be very interesting.

I think that the 'predictive value' of a system of analysis clearly is important. I do not suppose that machine-aided analyses mendations are, as you said was your hunch, "already priced in". I was asking my question in an attempt to learn something about what you thought about the utility of multivariant linear regression analysis . . .

 

[Delta2]

The math you ll do at engineering mathematics will probably be a superset of the math at engineering physics, so if later you wish to switch to physics (to become a theoretical physicist for example) you ll have a solid and extensive mathematical background to support it. But from what I know machine learning seems to be an exciting new technology, I think you will find promising jobs easier than if you become a physicist.

 

[atyy]

It used to be thought that gradient descent in machine learning got stuck in local minima. Nowadays we realize that in deep neural networks with many parameters, there are probably few local minima, and many saddle points, which explains why gradient descent work well for deep learning. This insight came from Surya Ganguli (who did a string theory PhD) and colleagues: https://arxiv.org/abs/1406.2572. They mention statistical physics in their abstract.

Some older methods in machine learning, like variational methods, are inspired by the variational methods of statistical physics and quantum mechanics.
https://people.eecs.berkeley.edu/~jordan/papers/variational-intro.pdf

Alex Graves, a machine learning researcher, did his undergraduate work in physics.
https://en.wikipedia.org/wiki/Alex_Graves_(computer_scientist)

 

[pbuk]

Long story short, my career goals are to work as a researcher/research scientist in machine learning or to develop models/algorithms for forecasting such as in financial markets or otherwise.

If engineering mathematics in your country is anything like it is in the UK I think it is an ideal match for these interests. Enjoy it!