30448 - MATHEMATICS - MODULE 1 (THEORY AND METHODS)
Course taught in English
Go to class group/s: 13
Class 13: FABRIZIO IOZZI
This course covers the fundamentals of Real Mathematical Analysis. Emphasis is given to the methodological approach, with focus on theorems, proofs, and reasoning.
- Topology on the real line.
- Convergence of sequences and series.
- 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.)
- 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 are not graded but they are possibly discussed in class in the following week.
|Continuous assessment||Partial exams||General exam|
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.
- 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. MARINUCCI, E. VIGNA, Principles of Mathematics for Economics.
- Homeworks and exercises, available online.