Introdução à Álgebra. Adilson Gonçalves. 5ta edição, Projecto Euclides IMPA, 2017. 

Abstract Algebra: an Introductory Course. Gregory T. Lee. Springer Mathematics Undergraduate Series. 2018.

A Concrete Introduction to Higher Algebra. Lindasy N. Childs. Undergraduate Texts in Mathematics, Springer-Verlag, New York 2009.

Abstract Algebra. David S. Dummit and Richard M. Foote. John Wiyley & Sons, 2003.  

Proofs and Fundamentals: A first course in Abstract Mathematics, 2nd Ed. Ethan D Bloch. Undergraduate Texts in Mathematics, Springer-Verlag, New York, 2011.

Class of June 22nd, 2023. All topics from Chapter VI Reference 1. Section 3, Conjugacy Classes: Definition of conjugation equivalence relation, Proposition 3, Proposition 4, Theorem 2, Corollary 1. LAST CLASS OF THE SEMESTER. 

Class of June 20th, 2023. Class suspended due to city protesting activities.

Class of June 15th, 2023. All topics from Chapter VI Reference 1. Examples 11, 12 and 13 from page 132. Example 13 dives in the combinatorial approach. Proposition 2, Theorem 1, Corollary 1.

Class of June 13th, 2023. All topics from Chapter VI Reference 1. Example 13 on the Dihedral group: the geometric approach. 

Class of June 8th, 2023. All topics from Chapter VI Reference 1. Definition of Subroups Proposition 1, Examples 1, 2, 3, 4, 5, 6, 7 and 9. 

Class of June 1st, 2023. All topics from Chapter VI Reference 1. Definition of Groups and Abelian Groups. Examples 1, 2, 3, 4, 5, 6, 7 and 8. Discussion of the different nature of permutation groups vs. abstract groups. 

Class of May 30th, 2023. All topics from Chapter IV Reference 1. Proposition 3, Example 4 discussion in deep. End of Chapter IV.

Class of May 25th, 2023. All topics from Chapter IV Reference 1. Theorem 6 (Eisenstein's Criterion), Example 1, 2 and 3. In example 3, we had a discussion on combinatorics and linear algebra, also a discussion on Lagrange's Interpolation Polynomials.

Class of May 23th, 2023. All topics from Chapter IV Reference 1. Division property lemma for irreducible polynomials, analogous to division over prime numbers. Theorem 5, Proposition 2.

Class of May 18th, 2023. All topics from Chapter IV Reference 1. Definition of Irreducible Polynomials, Theorem 4, Example 1 and Example 2. Brief review of results from chapter III. 

Class of March 30th, 2023. Cancelled due to Student's strike.

Class of March 28th, 2023. All topics from Chapter IV Reference 1. Corollary 1, Corollary 2, Definition of Pincipal Ideals, Theorem 2, Theorem 3, Definition of Monic Polynomials, Counterexample proving that Z[x] is not a Principal Ideal Domain.

Class of March 23th, 2023. All topics from Chapter IV Reference 1. Comments on Polynomilas on multiple variables. Comments on the Field of Fractions for polynomial domains. Theorem 1 and Proposition 1. 

Class of March 21st, 2023. All topics from Chapter IV Reference 1. Definition of K[x] and the degree of a polynomial. The degree of a polynomial and its basic properties. Characterization of polynomials with multiplicative inverse. Understanding the difference between polynomials as formal series and as polynomial functions: Fermat's little Theorem. Proving that K[x] is an integral domain.

Class of March 16th, 2023. Topics from Chapter III, Reference 1. Review of the Quotient Field definition. Proving the operations are well-defined and that every non-zero element is invertible. Comments on Proposition 7. Introduction to Chapter IV, Reference 1, formal series definition, operations of the polynomials.  

Class of March 9th, 2023. All topics from Chapter III, Reference 1. Characterization of Automorphisms of Q, R and Z[ √ p] (for p prime). Proposition 6, Theorem 4. Definition and Motivation of the Quotient Field.

Class of March 7th, 2023. All topics from Chapter III, Reference 1. Proposition 4, Theorem 2, Theorem 3. Definition of homomorphism and isomorphism. Examples of isomorphims and Proposition 5.

Class of March 2nd, 2023. All topics from Chapter III, Reference 1. Example 2, Example 3 (ideals). Theorem 1, Definition of the equivalence relation mod J, Proposition 3. 

Class of February 28th, 2023. All topics from Chapter III, Reference 1. Definition of Subring, Proposition 1, Examples of Subrings. Proposition 2 and Corollary. Definition of Ideals, Example 1.

Class of February 23th, 2023. All topics from Chapter III, Reference 1. Examples of Rings, Integral Domains and Fields: Z[ √ 2], Q[ 2], F(R), R^2×2, and the Quaternions.

Class of February 21st, 2023. Back to Chapter II, Reference 1. Proposition 9, Proposition 10, Theorem 6, end of Chapter II. Chapter III, Reference 1, definition of ring. 

Class of February 16th, 2023. Digression from the course on Equivalence Relations, topics from Reference 5. Definition 5.1.1., Example 5.1.2., Definition 5.1.5., Example 5.1.6., Definition 5.2.1., Lemma 5.2.3., Definition 5.3.1., Example 5.3.2., Definition 5.3.3., Theorem 5.3.4., Definition 5.3.6., Lemma 5.3.9., Definition 5.3.10.

Class of February 14th, 2023. All topics from Chapter II, Reference 1. Definition of Maximal Ideal, Theorem 4. Theorem 5, Proposition 6, Proposition 7, Definition of relation "mod n" , Definition of Z_n, Proposition 8.

Class of February 9th, 2023. All topics from Chapter II, Reference 1. Definition of  Ideal in Z, Example 1, Example 2. Definition of Principal Ideal, Theorem 2, Theorem 3. Definition of Prime Number, Proposition 4, Proposition 5.

Class of February 7th, 2023. Introduction of the course, its nature, prerequisites and objectives. All topics from Chapter II, Reference 1. Proposition 1, Proposition 2, Proposition 3 and Theorem 1.