Can You Self-Study Advanced Mathematics and Physics While Working Full-Time?

[yenchin]

Hi. I am a mathematics major and will graduate soon in a few months time. I came into the university 4 years ago with a dream of obtaining a good degree and pursue a PhD afterwards. Unfortunately things did not go smoothly, and I basically screw my grades up because of emotional problems and all that, with a D+ in my Ordinary Differential Equations and subsequently another D in my second course in Algebra (I have average of B in most mathematics courses, with a few A) In my third year I took Differential Geometry and realized that my main interest lies in geometry and geometrical aspects of physics, but unfortunately my department does not have much courses in these areas.

I will be graduating soon with at best, only a Second Lower Honours, and as expected I had been rejected by the graduate school in my own university.

Anyway I am better off getting a job first because I have accumulated lots of debts from my undergraduate study loan which does not allow me to defer even if I get into graduate school. However I have a strong interest in geometry and mathematical physics which refuses to die ... so I figure that I should continue to study anyway and perhaps do some research on my own when I am ready, whether or not I go into graduate school. I will still be able to consult my professors whenever necessary, but I am not sure how feasible self-study is when I have a job to do

Also, I am not sure what subjects should I master. I should probably re-learn algebra first since I barely passed the second course. My main interests are in black holes and cosmology, but I have not done any physics courses except Relativity and basic astronomy. How much should I master, say, Classical Mechanics, Quantum Mechanics, Thermodynamics, Electrodynamics, Quantum Field Theory etc.? As for mathematics, I have background in Functional Analysis, Differential Manifolds, Complex Analysis and the standard undergraduate courses, and I did my Honours Project on Riemannian Geometry. I am thinking of learning Hyperbolic Geometry and Lie Groups. In what order should I learn all these? For example, should I learn Lie Group and Lie Algebra before Quantum Mechanics? And is there any other subject that I should definitely learn?

I would appreciate any suggestion. Maybe after I clear my debt in a few years time I will try applying to graduate schools again... though I am not sure whether I can go anywhere with my lousy transcript.

 

[Emieno]

How about this http://www.a-star.edu.sg/ ?

it looks good, only some pictures that might be ugly in your eyes. It's just an explicable fact that there are not enough diversity in the area. I am too myself an Asian though,...

 

[piercas]

Hi there,

I understand your frustration and disappointment with your grades and the rejection from graduate school. However, it's important to remember that setbacks and challenges are a natural part of any academic journey. It's commendable that you have identified your interests in geometry and mathematical physics and are determined to continue studying and pursuing research in these areas.

Self-study is definitely a feasible option, especially with the support of your professors. It's important to create a structured and realistic study plan that takes into account your job responsibilities and financial obligations. Start by identifying the areas you need to improve on, such as algebra, and then gradually build on that foundation by studying more advanced topics like Lie groups and quantum mechanics. You can also look into online courses or textbooks that can supplement your self-study.

In terms of the order in which you should learn these subjects, it's best to consult with your professors and seek their advice. They can provide valuable insights on the connections between different topics and the most effective way to approach them. Additionally, don't be afraid to reach out to other experts in your field for guidance and advice.

As for your transcript, it's important to remember that it's not the only factor that graduate schools consider. Your passion and determination, as well as any research or projects you have undertaken, can also make a strong impression. So don't let your grades discourage you from applying in the future.

Overall, I would advise you to create a realistic and structured self-study plan, seek guidance from your professors and other experts, and continue pursuing your interests and passion for geometry and mathematical physics. Best of luck to you!