30400 - MATHEMATICS AND STATISTICS - MODULE 1 (MATHEMATICS)

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

• Mathematical Logic.
• Set theory.
• Topology.
• Fundamental ideas and theorems on:
  • Calculus: Continuity, Differentiability, Riemann Integral.
  • Linear Algebra: Vector Spaces, Matrices, Determinant, Rank.
  • Discrete structures: Sequences, Series, Recurrences, Mathematical Induction.

• Explain the theoretical foundations of mathematics: axioms, definitions, theorems, proofs.
• Explain in detail, through definitions, theorems and proofs, some selected topics of Real Analysis, Linear Algebra and Discrete Mathematics.
• 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, sequences, series, recurrences, algorithms).
• 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.)

• 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.

• Partial tests and general exams consist of multiple choice questions, true/false questions and open ended questions. All types of questions contribute to the assessment of the students' acquired knowledge. In particular, multiple choice questions focus on verifying the knowledge of specific facts and properties about mathematical objects, while open ended questions allow for the assessment of the students' ability to correctly state and prove theorems and various other statements.
• 4 partial tests are scheduled. The first and the third contribute each for 1/6 of the final grade. The second and the fourth contribute each for 1/3 of the final grade.
• Grading is relative to the class.
• The general exam is graded with respect to the partial relative grading scale.

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