To give students the necessary knowledge to understand and work with the main algebraic tools used in some of the most important applications of Algebra to Computer Graphics, Cryptography, Data Science/Machine Learning, and Differential Equations, namely:
- matrix factorizations and Jordan normal form, and its application to the solution of systems of linear equations and of systems of differential equations, the least squares method, and principal components analysis (PCA);
- basic group theory, and its applications to cryptography and computer graphics.
Mastering both the theoretical grounding and the practical applications of the topics studied, the student should be able to solve problems in these areas, not only by direct application of the algorithms and methods studied but also by their adaption to new scenarios.
To provide students a more thorough knowledge of Algebra, in order to enable them to effectively use the power of this discipline in problem solving.