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Knowledge and skills of Mathematics graduates

**MATHEMATICS**

Graduates in Mathematics have an excellent knowledge of the fundamentals:

- of mathematical analysis (differential and integral calculus in one and several variables, theory of ordinary differential equations);
- of algebra (linear algebra, fundamental algebraic structures);
- of Euclidean affine and projective geometry, general topology, theory of curves and surfaces;
- of Mathematical Physics.

They also know some fundamentals

- of functional analysis;
- of the theory of holomorphic functions of a complex variable;
- of differential geometry and cohomology of varieties;
- of probability and statistics.

and have an adequate knowledge of the fundamental methods of Numerical Analysis;

Furthermore,

- they know and understand the basic applications of Mathematics to Physics and Computer Science;
- they are able to read and understand even advanced texts in Mathematics, and to consult research articles in Mathematics;
- they are able to construct and develop arguments in Mathematics with a clear identification of assumptions and conclusions.

Graduates in mathematics are able to:

- produce rigorous demonstrations of mathematical results that are not identical to, but clearly related to, those already known;
- solve problems of moderate difficulty in various fields of mathematics by taking advantage of symbolic formulation;
- formalise and model problems in mathematical form, analyse them and solve them using mathematical methods;
- use computational tools both to support mathematical processes and to acquire further information.

**PHYSICS AND COMPUTERS**

Graduates in Mathematics:

- know the fundamentals of programming;
- know and understand the basic applications of Mathematics to Physics and Computer Science;
- have adequate computer skills, including programming languages and specific software;
- know the theoretical foundations of classical Physics.

Graduates in mathematics are able to:

- use computer and computational tools both to support mathematical processes and to acquire further information;
- understand possible connections between different areas and subjects in mathematics and between these and the fields of other disciplines;
- evaluate and understand the formulation of elementary physical models.