Lilly Tech Systems
Math & Linear Algebra Coding
Math coding problems are the backbone of ML interviews. This course covers 27 hands-on problems spanning matrix operations, eigenvalues, SVD, calculus and gradients, optimization algorithms, and probability — all implemented from scratch in Python with complete solutions and complexity analysis.
Your Learning Path
Follow these lessons in order to build math coding mastery for ML interviews, or jump to any topic you need to practice.
1. Math Coding in ML Interviews
What level of math is expected, how it is tested in code, the difference between theory and implementation, and a roadmap for this course.
2. Matrix Operations
Six problems from scratch: matrix multiply, transpose, inverse, rank, trace, and Hadamard product. No NumPy — pure Python implementations with full explanations.
3. Eigenvalues & SVD
Five problems: power iteration, QR algorithm, SVD computation, low-rank approximation, and PCA from scratch. The linear algebra that powers ML.
4. Calculus & Gradients
Six problems: numerical gradient, automatic differentiation, chain rule implementation, Jacobian matrix, Hessian matrix, and gradient checking.
5. Optimization Algorithms
Five problems: gradient descent variants, Newton's method, Adam optimizer, L-BFGS, and constrained optimization with Lagrange multipliers.
6. Probability in Code
Five problems: Monte Carlo estimation, rejection and importance sampling, Bayesian inference, Markov chains, and random number generation from scratch.
7. Math Coding Tips
Numerical stability, floating-point precision, common pitfalls, performance tricks, and a comprehensive FAQ for math-heavy ML interviews.
What You Will Learn
By the end of this course, you will be able to:
Implement Core Linear Algebra
Write matrix multiplication, decomposition, and eigenvalue algorithms from scratch without relying on NumPy — demonstrating deep understanding to interviewers.
Code Gradient Computations
Build numerical and automatic differentiation systems, compute Jacobians and Hessians, and verify gradients — the math behind every neural network.
Build Optimizers from Scratch
Implement gradient descent, Adam, Newton's method, and L-BFGS. Understand why each optimizer exists and when to use it in practice.
Ace ML Math Interviews
Solve 27+ math coding problems covering all major topics that appear in ML engineer, data scientist, and research engineer interviews at top companies.