30448 - MATHEMATICS - MODULE 1 (THEORY AND METHODS)

This course covers the fundamentals of Real Mathematical Analysis. Emphasis is given to the methodological approach, with focus on theorems, proofs, and reasoning.

• Topology.
• Convergence of sequences and series.
• Continuity.
• Differentiability.
• Riemann integral.
• Linear algebra.

• Explain the theoretical foundations of mathematics: axioms, definitions, theorems, proofs.
• Explain in detail, through definitions, theorems and proofs, some selected topics of Real Analysis and Linear Algebra.
• Illustrate the structure of a mathematical reasoning through the description of the steps in a proof.

• Use selected basic computational techniques (limits, derivatives and antiderivatives, series expansions, integrals, determinants, ranks).
• Formulate definitions, theorems and their proofs as presented in the course.
• Justify the correctness of new statements (that is, statements that are not part of the syllabus) using the theorems, definitions and techniques learnt in class.
• Argue about the truthfulness or fallacy of new statements, using the relevant tools in the more appropriate way.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)
• Individual assignments

• Exercises: the course material includes a collection of exercises, some of them taken from past exam papers, that help students improve their performances.
• The class is assigned some theorems/statements to be proved as a take-home problem set.

90% of the final grade is based on partial and final, 10% from the problem sets.

100% of the final grade based on the general exam.

• S. CERREIA VIOGLIO, M. MARINUCCI, E. VIGNA, Principles of Mathematics for Economics.
• Lecture notes and exercises, available online.