This course develops the core mathematical tools used across computer science: matrices and vectors (linear algebra), and differentiation and integration (single- and multi-variable calculus). Emphasis is both theoretical (definitions, theorems, proofs when appropriate) and practical — students will learn to apply these tools to real computing problems such as linear systems, data transformations, optimization for machine learning, graphics transforms, and numerical methods.

Learning outcomes

By the end of the course students will be able to:

1. Perform and interpret matrix and vector operations (addition, multiplication, transpose, dot/cross product, norms, projections).

2. Solve linear systems using Gaussian elimination and understand the role of matrix rank, inverse, and determinants.

3. Compute eigenvalues/eigenvectors and apply diagonalization and singular value decomposition (SVD) for dimensionality reduction (e.g., PCA). Compute derivatives. Evaluate integrals