Topology
General topology: topological spaces, continuous functions, metric spaces, compactness, separation axioms. Introduction to algebraic topology: fundamental group and covering spaces, classification of surfaces. Introduction to differentiable topology: regular values, Sard's theorem, degree theory, notions of Morse theory. Notions of computational geometry and geometric mechanics.
Mandatory:
- Lima, Elon Lages. Metric Spaces - IMPA;
- Rudim, Walter. Principles of mathematical analysis;
- Introduction to Differential Topology.
Complementary:
- DI PRISCO, C. A. (1997) An introduction to set theory;
- Lima, Elon Lages. Fundamental Group and Covering Spaces. Euclides Project Collection - IMPA;
- Yukio Matsumoto. An Introduction to Morse Theory (Translations of Mathematical Monographs, Vol. 208) (9780821810224);
- Lima, Elon Lages. Differential Varieties;
- Milnor, John. Topology from the differentable.