The teaching is organized as follows:

Learning outcomes

Module: Mathematics - teacher dott. Simone Ugolini
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This course aims at providing the students with the mathematical tools (set-theoretic and algebraic
structures, differential and integral calculus in one or several real variables, ordinary differential
equations) whose knowledge is indispensable for the achievement of the degree. A particular
attention is paid to the concrete application of the learned notions.

Module: Statistics - teacher dott. Roberto Chignola
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The aim of the course is to make the students acquainted with basic statistical ideas and methods and their applications in the correct planning of experiments, data sampling and analysis, and data presentation. The course intends to conjugate concepts of basic statistics and probability theory with real situations as they emerge in a generic biotechnology laboratory. The lessons will integrate the topics presented and discussed in the reference textbook.

Program

Module: Mathematics
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1) Some notions of set theory.
2) The complete ordered field of the real numbers.
3) Euclidean distance and induced topology on the real line. Absolute value of a real number.
4) Cartesian plane.
5) Real functions of one real variable.
6) Polynomials and polynomial functions. Power, exponential and logarithmic functions. Trigonometric functions.
7) Limit of a function of one real variable.
8) Continuity of a function of one real variable at one point. Fundamental theorems on continuos functions.
9) Derivative of a function. Derivation rules. Fundamental theorems on differentiable functions.
10) Monotonicity of a function. Local and global minima and maxima of a function.
11) Convex functions.
12) Riemann integral. Integration rules. Improper integrals.
13) Ordinary differential equations.
14) Linear algebra. Matrices and operations on them. Determinant of a square matrix.
15) Distance between two points in the plane and geometrical loci. Conics.
16) Functions of more variables. Level curves and level sets.
17) Topology in R^2. Continuity of a function of 2 variables.
18) Differentiable functions of 2 variables. Partial derivatives.
19) Local and global minima and maxima of a function of more variables.

Module: Statistics.
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The program will essentially follow the topics listed in the textbook up to chapter 17 with the following extras: key aspects in probability theory, probability distributions in the biotechnology lab (practical examples), error propagation theory

Bibliography

Examination Methods

Module: Mathematics
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Written exam.

Module: Statistics
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Written exam.