Mathematics: My system and foundation learning journey [Day 1-3]
Tags: mathematics, system, optimisation, career
Published: 2022-01-30 15:28:07

This week, my year 2.2 has finally started. The 2 modules that started this week are: 

1. Basic Mathematical Optimsation (2 lessons)

2. Mathematical foundations for data science (1 lesson) 

Prior to the start of the lessons, we are given access to our notes and assignments. Having only the knowledge of O-level Additional Mathematics, mathematics modules are the ones that I fear most for the whole of my university life, at least for the modules that I have taken so far. 

Looking through the notes, I'm not sure if they are full of cryptic wording or it's just me, I couldn't quite grasp the concepts simply by reading it. Still, the assignments seem pretty straight forward, the type of questions in which there are definitive ways of solving. It's straight forward on the premise that one has already grasp the methods of application. 

Honestly, I am looking forward to a module that will teach us the concepts of proofing and deriving solutions. Though I appreciate the applicability of how these courses are structured. 

Both the foundations and optimisation course starts off with linear algebra. The foundations course seem to also venture more into the programming side of thing. 

I'm glad that I've taken the foundations with the optimisation course as it does help me to fill up the gap that the optimisation course assumes knowledge on. 

We start off nice and easy, with the following topics:
- Vectors and matrix
- Various operations on vectors and matrix
- Programmatic way of dealing with vectors and matrix 

These are the overlapping topics covered by both of the courses. Almost at the end of the last 2 of the 3 lessons, I am attacked by the z monster. I wonder if it is my brain working hard to absorb the concept or if it is just a tired day for me. Anyway, side note for me to drink more caffeine when I have to attend these classes. 

While the foundations course take 1 lesson to cover the above, albeit in greater detail, the optimisation course squeezes in more concept for the past 2 lessons. 

In the first session, the additional topics are being covered: 
- Gauss Elimination method
- LU decomposition 
- Matrix iterative method 

We are only taught how the methods work. While novel to me, I'm pretty sure these just take a few practices to get the gist of it. The good thing about SUSS is that all of our modules come with accompanying textbook, be it e-textbook or physical textbook. It could be interesting to delve into more details to understand the why/proofs of these methods. 

To be honest, it is not until the second lecture of optimisation course and the first lecture of foundations course that I see a good reason to learn these concepts. I have a vague idea that these concepts are applicable in machine learning and also in solving linear programming problems. Though, there is nothing too concrete in my mind yet. 

In the second session, we are given a glimpse of the application of linear algebra via linear programming. It touches briefly on
- Linear programming model
- Expressing the model in canonical and standard form 
- Solving the model graphically 
- Various terminology related to linear programming

The main motivation of taking a data science minor and taking up mathematics elective is that I want to trade better. I want to be able to understand the derivatives analytics book that is full of mathematics and python. The python portion is easy to understand, but for the mathematics portion, I'm pretty much stuck to googling each symbol that I come across.  

According to my notes, this optimisation process can be model a range of problems from airline scheduling, to least-cost manufacturing to distribution of goods. Perhaps, as a starter, I could formulate a risk-reward problem. Or most probably, I should read more into linear models and finish these modules first.