Foundations of Algebra 1. Sets and maps 2. Arithmetic spaces and linear equations 3. Determinants 4. Matrices 5. Complex numbers 6. Polynomials Linear Algebra and Geometry 7. Vector spaces 8. Bilinear and quadratic functions 9. Linear operators 10. Metric vector spaces 11. Tensors 12. Affine, Euclidean, and projective geometry Basic Algebraic Structures 13. Groups 14. Rings 15. Elements of representation theory
