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## MATHEMATICAL AND PHYSICAL METHODS AND TOOLS

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## MATHEMATICAL AND PHYSICAL METHODS AND TOOLS

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### Academic year 2024/2025

- Course ID
- BIO0230
- Teachers
- Angelo Bifone

Maria Teresa Giraudo (Lecturer) - Year
- 1st year
- Teaching period
- First semester
- Type
- Related or integrative
- Credits/Recognition
- 6
- Course disciplinary sector (SSD)
- FIS/07 - applied physics (a beni culturali, ambientali, biologia e medicina)

MAT/04 - mathematics education and history of mathematics - Delivery
- Formal authority
- Language
- English
- Attendance
- Obligatory
- Type of examination
- Written
- Type of learning unit
- corso
- Prerequisites
- MATHEMATICAL METHODS AND TOOLS

● Main types of statistical graphs: line, bar, and pie graphs. Definition and identification of the parts of a line, bar and pie graphs, examination and interpretation of information from line, bar and pie graphs;

● Descriptive statistics: mean, median, mode;

● Direct and inverse proportionality, percentages;

● Elementary functions and their graphs: algebraic, integer and fractional, exponential, logarithmic, goniometric, composite and inverse functions. Geometric transformations of functions;

● Arithmetic and geometric progressions;

● Differential calculus: derivatives and linear approximations, increasing and decreasing functions over intervals, minima and maxima, convexity and concavity;

● Examination and interpretation of information from graphs of functions;

● Definite integral of a function over an interval, fundamental theorem of calculusPHYSICAL METHODS AND TOOLS

● Fundamentals of classical PHYSICS, including basics of mechanics, thermodynamics, electromagnetisms and fluid dynamics - Propedeutic for
- Bioanalytical Chemistry
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### Sommario del corso

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## Course objectives

MATHEMATICAL METHODS AND TOOLS

The module aims at providing a basic knowledge of mathematical and statistical tools that are widely used in medicine, biotechnology and chemical sciences to analyze and interpret data. The module provides students with both theoretical knowledge and practical applications.

PHYSICS METHODS AND TOOLS

The module will focus on mathematical modeling of physics phenomena, with examples from life science and applications in biology and medicine.

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## Results of learning outcomes

MATHEMATICAL METHODS AND TOOLS

**Knowledge and understanding**At the end of the module, students must know how to work with linear maps and their representation and to measure statistically the strength of relationships and associations between variables.

**Applying knowledge and understanding**At the end of the module, students must be able to apply the basic operations on linear maps and to use dedicated software for statistical analysis.

**Making judgements**At the end of the module, students must be able to evaluate to which extent variables are related or associated and how well the model fits a set of observations.

**Communication skills**At the end of the module, students must acquire a certain acquaintance with the terminology required to express mathematical and statistical concepts applied in medicine, biotechnology and chemical sciences and be able to communicate with appropriate language.

**Learning skills**At the end of the module, students must be able to read, understand, interpret and summarise the mathematical and statistical subjects appearing in the literature concerning medicine, biotechnology and chemical sciences.

PHYSICS METHODS AND TOOLS

**Knowledge and understanding**At the end of this module, the students will be familiar with the use of mathematical models to describe physical and biophysical phenomena.

**Applying knowledge and understanding**At the end of this module, the students will be able to apply the mathematical methods of linear algebra to solve basic problems in biological physics.

**Communication skills**At the end of the module, students will acquire the terminology and language to describe physical phenomena and models in the realm of biological and medical applications.

**Learning skills**At the end of the module, will able to read, understand, interpret and summarise the physical aspects of the literature concerning medicine, biotechnology and chemical sciences.

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## Program

MATHEMATICAL METHODS AND TOOLS

**Part I: Linear Algebra**- Vectors and Matrices
- Systems of linear equations
- Eigenvalues and Eigenvectors

**Part II: Regression**- Introduction to R software
- Simple Linear Regression
- Multiple Linear Regression
- Nonlinear Regression
- Use of R software for Regression analysis

**Part III: ANOVA**- One-way ANOVA
- Multiple Comparisons
- Two-way ANOVA

Use of R for ANOVA

PHYSICS METHODS AND TOOLS

1) Eigenvectors and eigenvalues in physics

2) Matrices and tensors, with applications to the description of:

- polarization of molecules and solids;
- diffusion in biological materials;
- dynamics of biofluids;
- molecular vibrations.

3) Synchronization and time in biological systems.

4) Thermodynamics of living systems.

5) Advanced physical tools for life science.

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## Course delivery

MATHEMATICAL AND PHYSICAL METHODS AND TOOLS

The module will be provided in blended mode, with a Moodle course supporting the in-presence activities, the latter ones being made up of lectures and exercise classes.

The Moodle course facility will contain multimedia and interactive resources such as videos, worksheets with an Advanced Computing Environment, and automatically assessed tests.

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## Learning assessment methods

MATHEMATICAL METHODS AND TOOLS

For the first part of the exam students will be required to produce a short report on the analysis of a given dataset employing the methods described in the course.

The second part of the exam will consist in solving a series of exercises based on the entire program of the course and administered through an IT platform and in answering some closed questions. Some exercises will require the use of the R software.

PHYSICS METHODS AND TOOLS

The students will be required to prepare and deliver a short presentation on an in-depth analysis of one of the subjects of the course.

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## Support activities

No support activity is provided.

## Suggested readings and bibliography

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- Book
- Title:
- Using R for Introductory Statistics
- Year of publication:
- 2014
- Publisher:
- Chapman & Hall
- Author:
- J. Verzani
- ISBN
- Required:
- No
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- Dalgaard, P. Introductory Statistics with R, Springer 2008, ISBN 9780387790534
- Jones, R. Maillardet, A. Robinson Introduction to Scientific Programming and Simulation Using R, Second Edition, Chapman and Hall/CRC 2014, ISBN 9781466569997
- D.J. Robinson, A course in Linear Algebra with Applications, World Scientific 1991, ISBN 9789810205683

The material for the PHYSICS METHODS AND TOOLS will be made available in the Moodle platform.

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## Teaching Modules

- Mathematical methods and tools (BIO0230B)
- Physical methods and tools (BIO0230A)

- Enroll
- Open
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