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MATHEMATICAL METHODS AND TOOLS
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MATHEMATICAL METHODS AND TOOLS
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Academic year 2023/2024
- Course ID
- BIO0230B
- Teacher
- Maria Teresa Giraudo (Lecturer)
- Year
- 1st year
- Teaching period
- First semester
- Type
- Related or integrative
- Credits/Recognition
- 3
- Course disciplinary sector (SSD)
- MAT/04 - mathematics education and history of mathematics
- Delivery
- Formal authority
- Language
- English
- Attendance
- Obligatory
- Type of examination
- Written
- Type of learning unit
- modulo
- Modular course
- MATHEMATICAL AND PHYSICAL METHODS AND TOOLS (BIO0230)
- Prerequisites
- ● 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 calculus - Propedeutic for
- Bioanalytical Chemistry
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Sommario del corso
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Course objectives
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.
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Results of learning outcomes
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.
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Program
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
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Course delivery
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
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.
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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
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