# Math for PhDs: My Linear Algebra, Stats, and Calculus Stack > Source: > Published: 2026-07-25 09:02:39+00:00 # 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. 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. 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. [Next Probability & Distributions: A Machine Learning Math Guide →](/en/threads/3116/) ## All Replies （3） C did you find any specific resource for the multivariable calc part? struggling w that. 0 D Same here. I had to brush up on tensors before the paper notations actually made sense. 0 R probablity theory is a huge one too, especially for understanding the latent space stuff. 0