Fudamentals of Algebra (1st course, 1st semester); Linear Algebra (1st course, 1st semester)

1. Basic counting techniques: combinatorics a) Basic counting rules; b) Permutations and combinations; binomial coefficients and identities; c) Permutations and combinations with repetition. 2. Recursion a) Recursively defined sets and functions; dependence tree; b) Linear difference equations; c) Time complexity of `divide-and-conquer' algorithms; 3. Binary relations a) Relations and their basic properties; b) Order relations; c) Equivalence relations; 4. Graph theory and applications a) Graphs: basic definitions and concepts; undirected graphs; b) Euler and Hamilton paths; c) Directed graphs; d) Weighted graphs; e) Trees.

THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.76 ECTS] Knowledge and concepts students must acquire. Student receive course notes and will have basic reference texts to facilitate following the classes and carrying out follow up work. Students partake in exercises to resolve practical problems and participate in workshops and evaluation tests, all geared towards acquiring the necessary capabilities. TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.16 ECTS] Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher. STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.92 ECTS] FINAL EXAM. [4 hours with 100% on site, 0.16 ECTS] Global assessment of knowledge, skills and capacities acquired throughout the course. METHODOLOGIES THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the subject`s main concepts are developed, while providing material and bibliography to complement student learning. PRACTICAL CLASS. Resolution of practical cases and problems, posed by the teacher, and carried out individually or in a group. TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with a teacher as tutor.