I am from Hong Kong and have just finished all the public exams. In my high school life, I've learned some topics on mathematics which are fundamental, yet I think are not in-depth enough.
The topics I've studied:
- Mathematical induction
- Binomial Theorem
- Trigonometry-- Basically CPD Angle Formula, Sum-to-angle/Angle-to-Sum Conversions
- Calculus-- First Principle/ Differentiation (up to 2 variables)/ Integration (1 variables)(by part)(substitution)
- Matrices and Determinants (up to 3x3)/ Systems of Linear Equations (up to 3 variables)
- 2-D/3-D Vectors/ Manipulation of Scalar products & Vector Products
1) Which of these topics should be studied in broader field? Is there any advanced subtopics that I am strongly recommended to study?
2) I know there're many fields in math that should also be explored, say Set Theory, Topology, Number Theory, etc. Is there any priority in studying these fields?
P.S. I'm quite intrigued by ALGEBRA.