It’s been a long time since I had my last class in my school. Let’s see how much I still remember from my Mathematics class, and why I still remember them.

Arithmetic

I need this to keep my money in my wallet, right? Let me know if you don’t need this and you can still keep a healthy cash flow for your personal account.

Geometry

I can still remember things like proofs of identical triangles, basic definitions of trigonometric functions and equations to calculate area and volumes. I need to use them occasionally to understand how daylighting and radiation in a building work. What? Identities of trigonometric functions? Let me look up the Wikipedia first……

Linear algebra

I can still remember the definition of inverse, eigenvalues and matrix decompositions because I use them at least once a month for solving uncertainty calculation. But don’t ask me to do it manually; I do all of them numerically now. Set theory? That’s logic so I am not including them here.

Vectors

I calculate dot products of vectors quite frequently for uncertainty calculation of models, but I can’t remember how to do things beyond that such as vector cross products.

Differential equations

Differential equation is a must to describe transient and dynamic systems and to study control systems, so I am looking at them everyday. Similar to linear algebra methods, I solve them numerically now and need to look up Wikipedia to solve them analytically.

Differentiation and integration

Due to failure in automating my work, I am still differentiating functions analytically instead of doing them by automatic differentiation or symbolic differentiation. Hence I still remember how to do differentiation pretty well. Integration? I really need to look up Wikipedia to ensure that I don’t integrate them incorrectly.

Inequalities

I know how to use its basic concept to set up constraints in constrained optimization problems in engineering, but don’t ask me anything beyond that.

Numerical methods

I am using them everyday for my work. I know how to use inputs and outputs and what they are capacble of. However, similar to what I did back in my school, I couldn’t write proofs about them.

Mathematical induction

This is a strange part of mathematics that I still remember how to do it off the top of my head. Prove the statement is true when k = 1, assume P(k) is true and prove that P(k+1) is also true to prove that a statement is always true for any positive integer k. Maybe that’s because it’s too mechanical to be forgotten?

Polynomials

I am solving quadatic equations at least once a month using the equation method, and I am still using cubic equations occasionally. Factorization of cubic equations? It’s not happening.

Roman numbers

I for 1, V for 5, X for 10, L for 50 and C for 100. I don’t think I can remember anything beyond that without the Wikipedia.

Other topics like prime numbers, L.C.M., H.C.F., etc.

I don’t use them often to remember them well now. I may remember what they are, but I definitely won’t say anything about them if you don’t remind me of their existence.

So how much do you still remember?