Jan 20, 2023
(Points at the function I'm doing my thesis on) this is my son who has every disease
seen from Türkiye
seen from China
seen from Malaysia
seen from Türkiye
seen from United States
seen from China
seen from United States
seen from China
seen from Mexico
seen from T1
seen from China
seen from China
seen from Yemen
seen from Malaysia
seen from Russia
seen from Japan
seen from Russia
seen from United States
seen from United States
seen from Canada
(Points at the function I'm doing my thesis on) this is my son who has every disease
I have polls now what's your favourite set
Z (integers)
Q (rationals)
R (reals)
C (complex numbers)
L^1 (integrable functions)
L^2 (square-integrable functions)
GL_2(R) (real invertible 2x2 matrices)
Set of all sets that do not contain themselves (paradoxical)
Mandelbröt set
I've been thinking about math lately (as usual) and specifically about what I do and do not like within the field. There is a deep dark approaching (bachelor thesis) and if I want to make it through unscathed (graduate by summer 2023) I feel like I should differentiate between the things I would like to study and the things I would prefer to stay away from.
Doing different courses over the past 4+ years gave me some insights. For example, applied math in the form of probability/measure theory is cool, actually. Abstract algebra is really hard, but when I studied finite Galois theory I had the time of my life. Analysis can be fun at times, but also super infuriating and tedious. Statistics is not for me.
A lot of these feel contradictory to me. For example, why are some parts of analysis cool and some super wack to me? I enjoyed my courses in both Fourier Analysis (FAVE ANALYSIS COURSE SO FAR) and ODEs, but studying Differentiable Dynamical Systems makes me consider dropping the course (I can't, though). Then again, I find Random Dynamical Systems/Ergodic Theory/Fractals to be fascinating (surprising, I know)... so what about DDS makes it so bad for me?
My feelings about Probability vs Statistics is also hard to explain, especially to non-mathematicians, but somehow despite wanting to know all about probability, random walks, random matrices, or any other advanced probability topic, statistics just is not able to live inside my head. You can talk to me about the MLE or datasets all you want, but I Will Not Understand Nor Do I Desire To. Even though those fields are lumped together for most of the time.
And algebra... oh, algebra. I followed three abstract algebra courses, including two electives, but somehow everthing just... feels too advanced for me. I never did anything in algebra again after Finite Galois Theory, and all of the topics I could choose from in algebra seemed impossible to follow for different reasons. I really want to get back into algebra, but how?
Sigh. Study math, they said, it'll be fun, they said.