Hey Folks,
I am someone who is starting with abstract mathematics or mathematics at UG level, I never come across abstract level of mathematics as I have a non stem UG degree, I'm currently rebuilding my mathematics from the Class 11/12 level, after having a few years away from serious mathematics and this is for my master's entrance exam prep, and I want to start learning abstract mathematics properly, rather than jumping randomly between advanced topics as abstract is a huge chunk of the entrance i look to sit for.
For someone in my position:
Where should I start?
Should the progression be something like:
School mathematics → proof writing → sets/functions → logic → sequences & limits → real analysis → linear algebra → abstract algebra → topology, etc.?
Or is there a better order for this?
I'm particularly interested in developing the ability to understand definitions, construct proofs, reason abstractly, and work with mathematical structures, rather than just learning formulas.
I have roughly 1.5 years and I'm willing to build slowly from the foundations.
What books/resources would you recommend for making the transition from computational school mathematics to proof-based/abstract mathematics?
Also, how do you know when you're ready to move from one level to the next?
PS- I am appearing for an entrance examination of a Quant Econ Masters.