Groups, rings and modules, bodies, polynomials, Galois Theory. Gröbner bases, Buchberger algorithm. Applications: automatic demonstration of theorems, integration of rational functions, graphs, robotics.
• Coutinho, S.C. - Polynomials and Algebraic Computation
• Gonçalves, A. - Introduction to Algebra
• Hefez, A - Algebra Course
• Abstract Algebra: An Introduction Thomas W. Hungerford;
• Algebra, Thomas W. Hungerford;
• Contemporary Abstract Algebra Joseph Gallian;
• Modern Computer Algebra Joachim von zur Gathen, Jürgen Gerhard;
• Computer Algebra Recipes: A Gourmet's Guide to the Mathematical Models of Science (Undergraduate Texts in Contemporary Physics) Richard Enns, George C. McGuire.