PRINCIPLES OF COMPUTER SCIENCE MATHEMATICS AND PHYSICS APPLIED TO BIOTECHNOLOGY 3Module PRINCIPLES OF COMPUTER SCIENCE AND MATHEMATICS APPLIED TO BIOTECHNOLOGY
Academic Year 2025/2026 - Teacher: LORENZO FEDERICO SIGNORINIExpected Learning Outcomes
By the end of the course, students will be able to:
Mathematical and digital competencies
Apply fundamental concepts of mathematics (functions, derivatives, integrals, probability, and statistics) to describe and analyze biological phenomena.
Use digital tools and spreadsheets for the management and processing of experimental data.
(SDG 4 – Target 4.4: increase technical and scientific skills for employment and innovation)
Data analysis and scientific method
Process real biological datasets through descriptive and inferential statistical methods.
Critically interpret numerical and statistical results to draw reliable conclusions.
(SDG 9 – Target 9.5: enhance scientific research and technological capacity)
Modeling of biological systems
Apply mathematical models (differential equations, regressions, growth models) to biological and biotechnological processes.
Assess scenarios and predictions relevant to biotechnological research and the management of biological resources.
(SDG 3 – Target 3.b: support research and development of biotechnological solutions for health; SDG 15 – Target 15.5: reduce biodiversity loss)
Transversal skills and sustainability
Use quantitative tools to contribute to innovative solutions in biotechnology with an emphasis on environmental and economic sustainability.
Promote a critical approach to the use of data and digital technologies, fostering responsible and inclusive practices.
(SDG 12 – Target 12.2: sustainable use of natural resources; SDG 4 – Target 4.7: ensure knowledge and skills needed to promote sustainable development)
Course Structure
In-person lectures
Lectures will be conducted in person, in accordance with current regulations.
Information for students with disabilities and/or learning disorders (DSA)
To
ensure equal opportunities and compliance with current legislation,
students with disabilities or DSA may request an individual meeting to
plan any compensatory and/or dispensatory measures, in line with the
learning objectives and their specific needs.
It is also possible to contact the CInAP faculty representative for further information and support.
Required Prerequisites
Students are expected to have:
Basic mathematical skills
Elementary arithmetic: operations with integers, fractions, and decimals.
Elementary algebra: first- and second-degree equations and inequalities, simple linear systems.
Basic plane and solid geometry: lines, planes, geometric figures and their essential properties.
Elementary functions: concept of function, graphs of linear, quadratic, power, exponential, and logarithmic functions.
Basic trigonometry (sine, cosine, tangent).
General logical and scientific skills
Ability for logical and abstract reasoning.
Basic knowledge of natural sciences (high-school level biology and chemistry) to understand examples and applications.
Basic computer skills
Essential use of a computer: file and folder management, word processing, internet navigation.
Basic familiarity with spreadsheets (data entry, simple arithmetic operations).
Attendance of Lessons
Detailed Course Content
1 – Mathematical Foundations
Sets, elementary logic, and basic operations.
Real numbers, absolute value, and the triangle inequality.
Powers, roots, and logarithms.
Percentages, proportions, and growth rates (applications to biological data).
Summations, binomial coefficients, arithmetic and weighted means.
Elementary equations, inequalities, and systems.
2 – Functions and Graphs
Cartesian plane and graphical representation of experimental data.
Concept of function and main families of functions (power, exponential, logarithmic, trigonometric).
Sequences and limits.
Continuity and asymptotic behavior of functions.
Applications to biological growth and decay models.
3 – Differential and Integral Calculus
Concept of derivative: geometric and physical interpretations.
Derivatives of elementary functions and calculation rules.
Maxima and minima: applications to optimization problems in biology (e.g., population growth, optimal dosages).
Definite and indefinite integrals: basic concepts and applications to cumulative biological quantities (e.g., concentration over time).
Introduction to differential equations with applications to dynamic models in biotechnology.
4 – Linear Algebra and Models
Vectors and matrices, fundamental operations.
Linear systems and methods of solution.
Eigenvalues, eigenvectors, and population dynamics (introduction to the Perron-Frobenius theorem).
5 – Probability and Statistics
Concept of probability, events, and equiprobable models.
Conditional probability, independence, and Bayes’ theorem.
Discrete and continuous random variables; main distributions (binomial, Poisson, normal, uniform, exponential).
Law of large numbers and central limit theorem.
Descriptive statistics: frequency tables, histograms, measures of central tendency and variability, boxplots.
Bivariate statistics: correlation and linear regression.
Inferential statistics: point and interval estimation, hypothesis testing (Z-test, t-test, χ²-test, proportion tests).
6 – Computer Science and Digital Tools
Introduction to spreadsheets (Excel, LibreOffice Calc or equivalents).
Management of biological datasets: importing, cleaning, and formatting data.
Automatic calculations, formulas, and functions.
Statistical analysis with spreadsheets: mean, variance, regression, hypothesis testing.
Creating scientific charts for data visualization and communication.
Introduction to basic programming functions in spreadsheets (e.g., IF, LOOKUP, simple macros).
7 – Interdisciplinary Applications
Mathematical modeling in biotechnology: microbial growth, enzyme kinetics, molecular diffusion.
Data management: from laboratory results to statistical representation.
Case studies: analysis of real experimental datasets from biological research.
Textbook Information
M. Bramanti, F. Confortola, S. Salsa, "Matematica per le scienze con fondamenti di probabilità e statistica", Zanichelli
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Mathematical foundations | 1 |
| 2 | Functions and graphs | 1 |
| 3 | Differential and integral calculus | 1 |
| 4 | Linear algebra and models | 1 |
| 5 | Probability and statistics | 1 |
| 6 | Computer science and digital tools | 1 |
| 7 | Interdisciplinary applications | 1 |
Learning Assessment
Learning Assessment Procedures
The exam consists of a single written test, and the evaluation will be assigned according to the following criteria:
Grade 29–30 with honors
In-depth knowledge of the subject
Ability to integrate and critically analyze the situations presented
Independent resolution of complex problems
Excellent communication skills and mastery of language
Grade 26–28
Good knowledge of the subject
Ability to perform clear and critical analysis of situations
Fairly independent resolution of complex problems
Clear presentation and appropriate language
Grade 22–25
Fair knowledge, limited to the main topics
Critical analysis not always consistent
Fairly clear presentation with acceptable use of language
Grade 18–21
Minimal knowledge of the subject
Limited ability to integrate and critically analyze situations
Sufficiently clear presentation, with weak language proficiency
Grade <18: Exam failed
Lack of knowledge of the main contents
Very limited or no ability to use specific terminology
Inability to independently apply acquired knowledge
Compensatory and dispensatory measures
To ensure equal opportunities and in compliance with current regulations:
Interested students may request a personal meeting to arrange possible compensatory and/or dispensatory measures, based on the learning objectives and their specific needs.
Students may also contact the CInAP representative (Center for Active and Participatory Integration – Services for Disabilities and/or Specific Learning Disorders) of their Department.
Examples of frequently asked questions and / or exercises
Examples of Basic Mathematics Questions
Solve the following equation:
Consider the function $f(x) = e^{-0.2x}$.
Sketch the graph qualitatively.
Calculate the first derivative and discuss its sign.
Interpret the behavior of the function as a model of biological decay (e.g., the concentration of a drug in the blood).
Examples of Differential and Integral Calculus Questions
A bacterial population grows according to the logistic law:
Calculate $P(0)$ and $\lim_{t \to \infty} P(t)$.
Determine the initial growth rate (derivative at $t=0$).
Calculate the integral:
and interpret the result as the “cumulative quantity” in a biological process.
Examples of Linear Algebra Questions
Solve the following linear system:
A matrix is given by
Calculate eigenvalues and eigenvectors.
Briefly explain how these concepts apply to the study of dynamic models in biotechnology.
Examples of Probability and Statistics Questions
In a laboratory, 200 cells are analyzed. It is observed that 40 have a genetic mutation.
Calculate the sample proportion and a 95% confidence interval for the proportion.
Suppose that the degradation time of a substance follows an exponential distribution with parameter $\lambda = 0.2$.
Calculate the probability that the substance degrades in less than 5 hours.
A dataset contains the following concentration values (mg/L):
4.1, 3.8, 4.5, 4.2, 3.9, 4.0Enter the data into a spreadsheet.
Calculate the mean, variance, and standard deviation.
Represent the data using a histogram.