AI Researcher

20/02 -

• Finally understand how the Taylor series works, although just refining last bit of understanding
• Started learning about brownian motion with the notation to dive into stochastic calculus
  • made a connection to topology since they both require continuitiy! made me think about whether you can transition from continuous to discrete and back to continuous with topology.
• Learned about the fractal dimension and how there are rational number dimensions instead of natural numbers!
  • Also learned about fractal topology
• Been reading Topology Without Tears and refining my understanding of the axioms of topologies and solved some questions!
• Kind of fomoed into doing derivatives again because i wanted to solve a PDE that contained every rule and possible derivative type you could do (not trig functions though) to test my skills. Realised i needed to prove log derivatives and power of x derivatives. Was learning about Eulers number too and the intuition behind it all.
• I think topology has been the best thing in my math journey so far bc it made me really excited for set theory (bijection, etc) and now abstract algebra. it was my gateway drug into pure math and now im really enjoying it and seeing how powerful it is. i highly rec anyone to do this path too!
• I was burned out but i bounced back yesterday and now im all good! taking time away from talknig to people to come back to equilibrium was important to not falling into weeks long burn out. PROGRESS from last burn out!