My first year of undergrad maths - experience

Hi everybody,

I am about to complete my first year of undergraduate mathematics course. I am doing an undergrad with mathematical finance in view. I wished to pen down my some learnings here.

I took courses on calculus, linear algebra, abstract algebra and analytic geometry.

Calculus : I solved plenty of calculus problems from this book - A collection of problems in mathematical analysis by GN Berman. To further my study of integral calculus and gain confidence, I am studying this text, A treatise on Integral Calculus which is very well organized.

Linear Algebra : Linear algebra has helped me build more mathematical maturity - e.g. work with objects like vector spaces, inner product spaces. It's all very intuitive. Proving some results (like a corollary), or a theorem's intermediate steps helped me gain more confidence. I created a small notebook of how cubic splines work - using elementary calculus and some numerical algebra. PCA is also a very useful tool.

Objects like a measurable space, a measurable function, sigma algebras, the probability triple - the typical setup in quant finance don't sound arcane to me, unlike before. I feel I am better equipped.

General reading habits: I have decided to educate myself a little more about the people who matter in modern mathematics beginning 1700 onwards. As a student of mathematics, I feel it is beautiful, to know about the work and life of a few key figures.

Taking notes: I have made it a practice to take detailed notes, important results and problems verbatim. Perhaps, not the best way to learn mathematics.

Courses in second year: The courses I am taking in my second year are advanced calculus, real analysis, ODEs, basic probability. I will be using Apostol's book for advanced calculus and Bartle and Shebert for real analysis.

I will be refreshing my C++ this year. To break in to a quant/semi-quant role, I think theory and the ability to solve problems numerically are equally important.

- Quasar.