Math for PhDs: My Linear Algebra, Stats, and Calculus Stack

Trying to implement custom LLM layers or dive into paper architectures usually hits a wall the moment the notation shifts to heavy linear algebra or multivariate calculus. I've realized that skipping the "boring" math foundations makes prompt engineering and model fine-tuning feel like guesswork rather than science.

To stop guessing and actually understand the gradients and tensor operations happening under the hood, I've narrowed my focus down to three specific pillars:

• Linear Algebra: This is the non-negotiable core. If you can't visualize how a matrix transformation works, you're just copying code.
• Statistics: Essential for evaluating model performance and understanding the probabilistic nature of token prediction.
• Calculus: Specifically the chain rule and partial derivatives, which are the engine behind backpropagation.

I'm treating this as a deep dive to build a more robust AI workflow. Instead of just using high-level libraries, I'm going back to the textbooks to understand why the loss functions behave the way they do. It's a slow process, but it's the only way to move from being a "user" to someone who can actually optimize a deployment from scratch.