I need general advice on how I should learn math, while working.
A litte background: I work full time as a data scientist and am studying for a masters degree in financial engineering.
The good news is: The degree is extended and planned to be a part-time degree, so I don't have the usual workload, but I still cover a tone of financial mathematics topics. My question is: what is the best way to study math, when you have "just" a couple of hours every day. Still try to solve a lot of exercises or maybe reduce the exercises, so I can cover more material ? If somebody has a crude example study plan for me, that would be great. My current strategy is as follows: I read the script and try to understand the definitions and proofs. Then I try to do the exercises and if I can't, I look at the solutions. In general, I don't try to reproduce the proofs. If I have questions, I ask my professor. Is that a good way to study math or should I change something ?
Thanks !
I'm in a similar boat, where I work full-time while doing my masters to make up the costs my scholarship doesn't. Here is a (non-exhaustive) list of advice:
Take things in stride, and don't cram everything at once. Balancing learning and work is a delicate balance that's easily susceptible to burnout. If you experience burnout, not only do you risk forgetting what you were recently studying, but it will be even more difficult to recover and get back into studying. If at any point you start to get that heavy internal feeling like things are too much, it's genuinely okay to step back and take a break. In actuality, take it as a time to test yourself on your own knowledge of the subjects you are studying, from memory, when you're away from pen and paper. Think of as if you were tutoring a student, friend, or a class about the topic you just learned, how would you explain it to them, what would be first thing you should talk about to help them better learn about it, and what real-world examples could you provide? Doing this in balance will not only improve and protect your mental health, but it will prolong the longevity of your overall study time and retention.
Do the proofs, even if they look trivial, because this is where the core logic and rigor lives. Exercises are great and all, but they are usually used to show you where you can apply the end results of the theorems you are given, and that is susceptible to the plug-and-chug phenomena that most intro students do. Proving these theorems for yourself not only gives you a better understanding of where those theorems came from and originated, but it also gives you the opportunity to amalgamate them in the future to help you solve different, but similar, problems. In other words, use the building blocks of the materials required to make those theorems to build other theorems of your own.
Since your degree is in Financial Engineering, and you want to study on your own time more than what your part-time degree provides, it certainly would not hurt to reach out to professors of higher courses you'll have to take in the future and ask them what books they're using and get, and start, reading those and doing exercises from them. With that, not only are you buying yourself more time to fully understand future topics you'll encounter, but you'll be saving yourself future time when you officially enroll in those courses.
Nevertheless, there does exist better advice out there that only people who personally know you could provide. Thus, it would be extremely beneficial to setup an appointment with your college advisor on ways you can supplement your free time such that it would boost your degree path in the mathematical aspect. In addition, extend this idea to your past math professors and ask them for advice too, as I genuinely bet they'd be willing to give you more personalized tips that could help guide you even further.