30400 - MATHEMATICS AND STATISTICS - MODULE 1 (MATHEMATICS)

This course covers the fundamentals of Real Mathematical Analysis (univariate and multivariate calculus) and Linear Algebra .

• Mathematical Logic.
• Set theory.
• Topology.
• Fundamentals of Calculus:
  • Univariate Calculus: Continuity, Differentiability, Riemann Integral.
  • Multivariate Calculus
  • Linear Algebra: Vector Spaces, Matrices, Determinant, Rank.

• 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 (ordinary and partial) and antiderivatives, series expansions, integrals, matrix theory tools).
• Formulate definitions, theorems and their proofs as presented in the course.
• Use the theorems, definitions and techniques learnt in class to analyze the correctness of new statements.
• Perform corresponding calculations and solve problems posed in the form of exercises.

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

• Exercises: the course material includes a collection of exercises, some of them taken from past exam papers, that help students improve their performances.
• Every week the class is assigned a homework consisting of some selected exercises, some theorems/statements to be proved and additional "multiple choice" and "true or false" questions. Homework assignments is not graded but they are possibly discussed in class in the following week.

• Assignments and general exams consist of open ended questions. All types of questions contribute to the assessment of the students' acquired knowledge. Questions are aimed at verifying the knowledge of specific facts and properties about mathematical objects in order to assess students' ability to correctly apply theorems and other mathematical statements in solving dedicated problems.

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