Course contents: Part A, Mathematical Analysis: Basic topology concepts, Real numbers, Sequences, Series, Functions of one variable (limit, continuity etc), Derivatives, Definite and indefinite integral, Power series, Taylor expansions.
Part B, Algebra and Linear Algebra: vectors, matrices, characteristic polynomials, linear system solving, vector spaces, bases, inner product, orthogonal spaces, eigenvectors. Algebraic structures, polynomials, finite fields and extensions, irreducible and primitive polynomials, polynomial factorization, trace and norm functions.

At the end of the course the student will be able to:

• describe the basic topological concepts and use them to solve problems
• describe the basic principles of calculus of single variable functions and use them to solve problems
• describe the concepts of continuity, sequences and series, differentiation and integration of functions, be able to present the related mathematical proofs and use these concepts to solve problems
• describe the basic concepts of vector spaces and matrices and use them to solve linear systems and other problems
• describe the basic concepts of polynomials and use them to solve problems

Assessment: Written exams at the end of the semester. It is possible that home assignments will be given, which will contribute to the final grade with a percentage ranging between 25% and 30%.