30400 - MATHEMATICS AND STATISTICS - MODULE 1 (MATHEMATICS)
Course taught in English
Go to class group/s: 25
- Mathematical logic.
- Elements of topology of the real line.
- Functions. Real functions of a real variable. Injective, surjective functions. Inverse functions. Maxima, minima. Concave and convex functions.
- Limits of real functions. Theorems about limits. Fundamental limits. Continuity.
- Derivative, differential. Theorems of differential calculus. Taylor's theorem. Extrema of functions.
- Riemann definite integral. Properties. Integrable functions.
- Antiderivatives & indefinite integrals. Integration techniques. The FToC.
- Generalized integrals.
- Relations. Cardinality of sets. Counting and discrete probability.
- Sequences, recursive Sequences and difference equations.
- Numerical Series. Series of functions.
- Matrices. Operations with matrices.
- Inverse matrix. Rank of a matrix. Determinant. Simultaneous equations.
- Numerical linear algebra with Matlab.
Grading percentages is:
- 20% on completion of problem sets.
- 10% on completion of Matlab problem sets.
- 70% on two written exams.
For non attending students
Grading is based on a written examination with a mix of open ended and multiple choice questions. The exam is closed book. Students are required to solve numerical and theoretical exercises, give definitions and prove theorems.
- S. Cerreia Vioglio, M. Marinacci, E. Vigna, Principles of Mathematics for Economics.
- Other materials provided online.