Education

(1) – 30 Years Later: Re-learning Calculus and Linear Algebra in One Week

Olivier Krieger
24.12.2025 · 3 min read

A recap of the vectors, derivatives, and YouTube tutorials that saved my life during Week 1 of my Professional Certificate.

I just kicked off my Professional Certificate journey about a week ago, and let me tell you: they didn’t waste any time. We dove straight into the heavy mathematics that forms the foundation of the course. I’m not going to lie—it has been a tough week!

Since I don’t come from a strong math background, a lot of these concepts felt like completely new territory. It has been a steep learning curve, requiring me to double down on my study time to absorb the new content. I’ve practically lived on YouTube this past week, hunting down explanations to make sense of it all.

I’m writing this post as a way to process everything I’ve just crammed into my brain. Think of this as a recap of what I’ve learned, but also a collection of the specific resources and videos that saved my life this week. Hopefully, they can help you too.

Tackling the Beast: My Deep Dive into Linear Algebra

I used to have a pretty fuzzy idea of what Linear Algebra actually was. Turns out, getting a clear picture required a lot of time, Tea (I don’t drink coffee), and commitment. Here is a look at what I’ve been working on.

The Fun Stuff: Vectors & Python We kicked things off with vectors. Basic addition and scalar multiplication were a breeze, while dot-products and cross-products added a nice layer of complexity. The best part? Using NumPy and Matplotlib to visualize everything in 2D and 3D. It’s amazing how these libraries simplify rendering; you can create complex visualizations with just a snippet of code.

The “Aha!” Moments: Matrices & Eigenvalues Moving on to Matrices, the arithmetic (addition, subtraction, multiplication) felt straightforward once the logic clicked. I’ll be honest—Eigenvalues and Eigenvectors sounded terrifying at first. But once I got into the weeds, I realized they aren’t so bad. You just have to be rigorous with your equations.

The Challenge: Transformations & Decomposition After covering the “Big 4” Linear Transformations (Scaling, Rotation, Projection, and Reflection), things got real. Matrix Decomposition—specifically SVD and LU Decomposition—was where I really had to sweat. The multi-step processes are a minefield for potential errors (and yes, I stepped on a few), but resolving them felt like a major victory.

Facing the Final Boss: Calculus

I’ll be honest: this was the topic I feared the most.

Conquering the Ghosts of Math Past: Derivatives We started with Derivatives and Partial Derivatives. I last studied these about 30 years ago, and let’s just say they left me with some dark memories. Re-learning this required a serious amount of hard work and mental gymnastics. But, after wrestling with the concepts, I think I’ve finally made peace with them. I’m feeling somehow confident in my understanding now.

The Alphabet Soup: Chain Rule & Norms Next up, we tackled the Chain Rule and Vector Norms (specifically Manhattan, Euclidean, and Maximum). Sure, there were a lot of equations, variables, and moving parts flying around. However, despite the visual complexity, the logic actually clicked. It turns out that once you get past the notation, it’s not as intimidating as it looks.

Next week, I will continue with Probability & Statistics, as well as with the Optimisation essentials.

Resources used during that week: