Álgebra I
March-June 2018, IMPA
Instructor: Reimundo Heluani
Office: 432
Tuesdays and Thursdays 15:30-17:00 Sala 347
Bibliography
- Algebra. Michael Artin. Prentice Hall
- Algebra. Serge Lang. Graduate Texts in Mathematics. Springer
- Categories for the working mathematician. Sauders Mac Lane. Graduate Texts in Mathematics. Springer
Evaluation
- 30% weekly homework
- 30% First test: 10/4
- 40% Second test: 28/6
Homework
Tentative Schedule
Lecture 1 13/3
Examples of Categories: sets, groups, topological spaces, etc. Functors. Natural transformations.
Lecture notes
Lecture 2 15/3
Limits and colimits. Products and coproducts. Examples with Sets and groups.
Lecture notes
Lecture 3 20/3
Groups: definitions, examples, homomorphisms, isomorphisms, actions of groups.
Lecture notes
Lecture 4 22/3
Groups: More on group actions, centralizers and normalizers. Torsors. Cosets. Counting formulas.
For lecture notes see Lecture 3.
Lecture 5 27/3
Rings: definitions, homomorphisms, ideals, quotients.
Lecture 6 29/3
Rings: integral domains and fraction fields. Maximal ideals.