I'd like to learn mathematics at a (semi-?)professional level.
I'm studying Undergrad Medicine in South Asia. I'm looking to build up on my understanding of mathematics from scratch. This is to help me better comprehend the Physics and Chemistry that makes up much of Medicine (besides, I've taken a liking to pure Mathematics anyways).
To this end, I wish to follow (more or less) the curriculum prescribed for Undergrad Math courses in my spare time. To elaborate: I feel the best way for me to grow as a student of mathematics would be to adopt a typical Undergrad Math course's curriculum, and work on it in my spare time.
However, I have absolutely no idea how an actual Undergrad math course is structured to begin with.
I did try to look up university brochures/handbooks for the course, but as someone with no exposure to mathematics-education outside of high school, I'm not able to make much sense of it.
So if it isn't too much to ask, I'd greatly appreciate it if the Community at Math.SE can offer me guidance in this regard. So, I suppose my question ultimately boils down to:
What's the pedagogic hierarchy of various sub-disciplines in Undergraduate Mathematics?
(Should I start with Algebra? If so, what kind of Algebra? Should I follow up with Geometry? Or should I read them side-by-side?) Hopefully, you get what I'm on about.
1) I'm not requesting book recommendations here (I'm aware there's a separate, dedicated post for that on Math.SE). However, I'd still appreciate recommendations, should you have any :-)
2) I'm aware of "capsule"-books like Mathematical Methods for Physics and Engineering, however, I wish to acquire a far more rigorous understanding of the subject. This, I feel, can only be accomplished by actually following the curriculum prescribed for a generic Undergrad Math course.