Teaching code

4S02690

Credits

12

Coordinatore

Margherita Zorzi

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

Moodle Seminars

The teaching is organized as follows:

Learning objectives

Mathematics: 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. At the end of the course students should be able to use appropriately the mathematical language and the notions of the syllabus and furnish valid arguments in support of the solution of the proposed problems. Statistics: The aim of the course is to make the students acquainted with basic statistical ideas and mathematical methods and their applications in the correct planning of experiments, data sampling, analysis, and presentation. The course conjugates concepts of basic statistics and probability theory as well as applied mathematics with real situations as they emerge in a standard biotechnology laboratory. The students acquire appropriate skills to understand how biological systems work and more generally to cope with real-life problems in different applied scientific fields. At the end of the course the students are able to: - analyse experimental observations and prepare professional reports - appropriately plan experiments - autonomously acquire new skills in specific fields of applied statistics and mathematics.

Prerequisites and basic notions

Basic mathematical skills (high school level)

Program

MATHEMATICS ZORZI
Part I: basics
- introduction to sets, basic set operations
- Numeric sets N, Z, R, C;
- operations on complex numbers
Part II: functions and study of functions
- definitions, graph of a function, examples
- classes of interesting functions: exponential, logarithmic, polynomial, trigonometric functions
- limits: definition, properties, left and right continuity, asymptotes
- derivative of a function, rules of derivation.
Part III: Integrals
- Definitions
- definite integrals
- indefinite integrals
- integrations by parts
Part IV: elements of differential equations
- first order differential equations
- some hints about higher-order differential equations
STATISTICS CHIGNOLA
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

Didactic methods

classroom-taught lesson

Learning assessment procedures

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UL: Matematica Mod. 1
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Written test with open questions. Neither midterm tests nor oral exams will take place. The minimum mark for the exam to be considered passed for the Mathematics module is 18.
There are no differences between attending and non-attending people.
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UL: Matematica Mod. 2
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Written test that will be carried out in parallel with the Statistics test following the rules described therein. Specifically, the students will have to solve one exercise concerning aspects of interest for biology, biomedicine or biotechnology through mathematical reasoning.

The test will be carried out remotely.
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UL: Statistica
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Written test. Students will have to solve 4 problems (3 concerning statistics and 1 probability theory) within a maximum time of 2 hours, and they will be allowed to consult the reference textbook and other didactic material (e.g. slides, handouts,...). Personal computers or other electronic devices used to access the internet are not allowed.
The problems will be inspired by the analysis of data from real biological and biomedical experiments.
The assessment methods could change according to the academic rules.

Evaluation criteria

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UL: Matematica Mod. 1
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The teacher evaluates the mastery and understanding of the concepts by proposing the resolution of exercises. There are possible theory questions regarding the first part of the course.
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UL: Matematica Mod. 2
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Accuracy in carrying out the written exercise.
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UL: Statistica
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Eight points are assigned to the solution of each exercise and all points are then summed up. To pass their test students must reach a minimum score of 18 points.

Criteria for the composition of the final grade

Arithmetic average of the two modules. To get honors the student take thirty in both modules.

Exam language

------------------------ UL: Matematica Mod. 1 ------------------------ Italiano ------------------------ UL: Matematica Mod. 2 ------------------------ Italiano o, su richiesta, Inglese ------------------------ UL: Statistica ------------------------ Italiano o, su richiesta, Inglese