ID:
SCV0700
Duration (hours):
108
CFU:
12
Year:
2025
Overview
Date/time interval
Annuale (23/09/2025 - 20/06/2026)
Syllabus
Course Objectives
The Course of Mathematics, Computer Science and Statistics is structured in two segments, over two consecutive semesters. The first segment (Mathematics and Computer Science) teaches the necessary basis for the analytic comprehension of scientific phenomena in Biology through the acquisition of mathematical methods and how to acquire an essential, rigorous language. In particular, students will learn the basis of linear algebra and differential and integral calculus, which are the starting points for the analysis of biological events. In the second segment (Principles of Statistics and Biostatistics), students will learn the theoretical basis of inferential statistics and the statistical tests commonly used in Biology. Particular emphasis will be given to how to correctly apply the tests.
The main goal of this course is to develop the students’ ability to critically apply the mathematical concepts exposed in the course and to stimulate their ability to utilize mathematical models and tools in a variety of cases. The basis of linear algebra and differential and integral calculus learned in the first segment will provide students with the quantitative tools needed to develop and interpret indexes for the analysis of data and characters obtained from biological and clinical experiments. In the second segment the same objectives will be analyzed from a statistical point of view; the laws of probability, how to perform correct sampling and the construction of a formal hypothesis to be tested will be learnt in order to improve the ability of analyzing experimental data, by means of the most common statistical tests. At the end of the course, therefore, students will possess the necessary knowledge to correctly analyze and interpret experimental data in Biology.
The main goal of this course is to develop the students’ ability to critically apply the mathematical concepts exposed in the course and to stimulate their ability to utilize mathematical models and tools in a variety of cases. The basis of linear algebra and differential and integral calculus learned in the first segment will provide students with the quantitative tools needed to develop and interpret indexes for the analysis of data and characters obtained from biological and clinical experiments. In the second segment the same objectives will be analyzed from a statistical point of view; the laws of probability, how to perform correct sampling and the construction of a formal hypothesis to be tested will be learnt in order to improve the ability of analyzing experimental data, by means of the most common statistical tests. At the end of the course, therefore, students will possess the necessary knowledge to correctly analyze and interpret experimental data in Biology.
Course Prerequisites
The following basic knowledge is necessary to fully understand the Mathematics segment: natural, integer, rational and real numbers. Basic elements of logic and set theory. Elementary algebra. Powers, logarithmic and exponential functions. Equations and inequalities (polynomial, fractional, irrational, logarithmic and exponential). Systems of equations and inequalities. Plane analytical geometry. Basic notions of trigonometry. All these topics are however explained during the course. Before attending the Biostatistics Segment, the Mathematics segment needs to be covered.
Teaching Methods
For both segments, traditional classes will be held. In the first segment, exercitations will also be held. In the second segment, some exercises will be taught under the teacher’s guidance.
Assessment Methods
Segment of Mathematics: at the end of the course a written exam must be passed, made up of two parts. The first part will present seven multiple choice questions. Each correct answer will yield two points, the threshold being four correct answers (eight points). In the second part three open exercises are proposed, for a total of 17 points if all of those are correctly done. The aim of this part is to verify whether the student has a critical knowledge of the mathematical issues presented and can apply, in different situations, the appropriate mathematical methods, models and tools. The allotted time is two hours. Unless there are particular situations (BES, DSA, etc.), which must be certified by the competent office, it will not be possible to use notes, books, calculators or other similar tools (smart watches, tablets, etc.) during the test.
According to the grade obtained, the following rules apply:
Score up to 7/30 (points which are obtained exclusively in the multiple choice part of the exam): the minimum threshold has not been reached in the multiple choice part of the exam; the second part (open-ended) is not corrected; the test is insufficient
Mark between 8/30 and 17/30: exam failed. Mark equal to or higher than 18/30: exam passed.
NB: to be able to access the General Mathematics sessions it is necessary to have fulfilled any additional training obligations; the fulfillment of this obligation consists in passing the "OFA test".
Segment of Biostatistics: at the end of the module, the student will undergo a written examination. S/he will be presented with two numerical exercises aimed at verifying the knowledge of the logic and methodological tools required for a correct evaluation of experimental data, plus three simpler exercises aimed at testing the knowledge in the field of probability laws, normal distribution and confidence interval. The allotted time for the exam is 2.5 hours and the exam will be considered passed equal or over the 18/30 mark. During the exam, the use of pocket calculators and PCs is allowed.
N.B: To access the Statistics and Biostatistics sessions you must also have passed the OFA test.
The exams of the two modules can be taken in any order. The passed exam of a module and the related evaluation will be considered valid for the duration of two years (e.g. January 2026 to January 2028), after which both tests will have to be repeated. The final mark will be the weighted average of the marks from the two segments.
According to the grade obtained, the following rules apply:
Score up to 7/30 (points which are obtained exclusively in the multiple choice part of the exam): the minimum threshold has not been reached in the multiple choice part of the exam; the second part (open-ended) is not corrected; the test is insufficient
Mark between 8/30 and 17/30: exam failed. Mark equal to or higher than 18/30: exam passed.
NB: to be able to access the General Mathematics sessions it is necessary to have fulfilled any additional training obligations; the fulfillment of this obligation consists in passing the "OFA test".
Segment of Biostatistics: at the end of the module, the student will undergo a written examination. S/he will be presented with two numerical exercises aimed at verifying the knowledge of the logic and methodological tools required for a correct evaluation of experimental data, plus three simpler exercises aimed at testing the knowledge in the field of probability laws, normal distribution and confidence interval. The allotted time for the exam is 2.5 hours and the exam will be considered passed equal or over the 18/30 mark. During the exam, the use of pocket calculators and PCs is allowed.
N.B: To access the Statistics and Biostatistics sessions you must also have passed the OFA test.
The exams of the two modules can be taken in any order. The passed exam of a module and the related evaluation will be considered valid for the duration of two years (e.g. January 2026 to January 2028), after which both tests will have to be repeated. The final mark will be the weighted average of the marks from the two segments.
Contents
SEGMENT OF MATHEMATICS AND COMPUTER SCIENCE (9 CFU):
Real functions of a real variable – 4.5 CFU
Introductory concepts: The set of real numbers R. Elements of topology in R. Domain. Maximum, minimum, upper bound and lower bound. Limited functions, monotonic functions, composite functions, invertible functions. Concave and convex functions, elementary functions and plane transformations
• Limits and continuity: Limits and relative theorems. Operations on limits and forms of indecision. Continuous functions and relative theorems. Horizontal, vertical and oblique asymptotes. Remarkable limits and indeterminate shapes. Classification of points of discontinuity. Landau symbols (asymptotic and "small o").
• Differential calculus: Incremental ratio and derivative. Differentiable functions. Operations on derivatives. Derivative of composite functions. Theorems of differential calculus. Absolute and relative maximum and minimum points. Inflection points. Necessary and/or sufficient conditions for the existence of relative maximum/minimum points. Concavity/convexity. Function study. Properties of a function from its graph. Applications of theorems on differentiable functions: de l'Hopital theorem; Taylor - Mc Laurin formulas.
Integral calculus – 3 CFU
• Primitives and indefinite integral.
• Integrals of elementary functions
• Generalized integrals
• Riemann integral in a limited interval [a,b] and relative theorems.
• Integration methods: by substitution, by parts.
• Differential equations with separable variables; first order differential equations
Linear Algebra – 1.5 CFU
• Vectors in Rn, matrices, operations between matrices, matrix inverse
• Determinant and rank of a matrix
• Systems of linear equations (Gaussian elimination method; notes on Rouché-Capelli)
SEGMENT OF PRINCIPLES OF STATISTICS AND BIOSTATISTICS (3 CFU):
Introduction – 0.5 CFU
- Populations and samples. Basics of the laws of probability. Random variables.
- Frequency distributions. The meaning and purpose of the statistical test.
- Power and protection of the test, type I and type II errors.
- Parameter estimation; the standard error of the mean; the confidence interval.
Cathegorical variables – 0.5 CFU
- The χ2 test for comparing two proportions. Contingency tables.
Quantitative variables – 2 CFU
- Comparison between two or more means. Student’s t and one-way
Analysis of Variance (ANOVA).
- Randomized blocks ANOVA.
- Simple regression analysis.
Real functions of a real variable – 4.5 CFU
Introductory concepts: The set of real numbers R. Elements of topology in R. Domain. Maximum, minimum, upper bound and lower bound. Limited functions, monotonic functions, composite functions, invertible functions. Concave and convex functions, elementary functions and plane transformations
• Limits and continuity: Limits and relative theorems. Operations on limits and forms of indecision. Continuous functions and relative theorems. Horizontal, vertical and oblique asymptotes. Remarkable limits and indeterminate shapes. Classification of points of discontinuity. Landau symbols (asymptotic and "small o").
• Differential calculus: Incremental ratio and derivative. Differentiable functions. Operations on derivatives. Derivative of composite functions. Theorems of differential calculus. Absolute and relative maximum and minimum points. Inflection points. Necessary and/or sufficient conditions for the existence of relative maximum/minimum points. Concavity/convexity. Function study. Properties of a function from its graph. Applications of theorems on differentiable functions: de l'Hopital theorem; Taylor - Mc Laurin formulas.
Integral calculus – 3 CFU
• Primitives and indefinite integral.
• Integrals of elementary functions
• Generalized integrals
• Riemann integral in a limited interval [a,b] and relative theorems.
• Integration methods: by substitution, by parts.
• Differential equations with separable variables; first order differential equations
Linear Algebra – 1.5 CFU
• Vectors in Rn, matrices, operations between matrices, matrix inverse
• Determinant and rank of a matrix
• Systems of linear equations (Gaussian elimination method; notes on Rouché-Capelli)
SEGMENT OF PRINCIPLES OF STATISTICS AND BIOSTATISTICS (3 CFU):
Introduction – 0.5 CFU
- Populations and samples. Basics of the laws of probability. Random variables.
- Frequency distributions. The meaning and purpose of the statistical test.
- Power and protection of the test, type I and type II errors.
- Parameter estimation; the standard error of the mean; the confidence interval.
Cathegorical variables – 0.5 CFU
- The χ2 test for comparing two proportions. Contingency tables.
Quantitative variables – 2 CFU
- Comparison between two or more means. Student’s t and one-way
Analysis of Variance (ANOVA).
- Randomized blocks ANOVA.
- Simple regression analysis.
Course Language
Italian
More information
RECOMMENDED TEXTS
- Mathematics Segment:
• To prepare for OFA tests:
High school science textbooks (grades I to IV);
or good websites (matematika.it, youmath.it);
or good video lessons (for example, those by Elia Bombardelli on YouTube);
or Battaia, Basic Mathematics
or Messineo et al., Mathematics Notes. Preliminary Notions, Giappichelli ed.
To prepare for the section on infinitesimal calculus, differential calculus, and integral calculus:
Bramanti, Confortola, Salsa - Mathematics for the Sciences - Zanichelli ed.
Benedetto, Degli Esposti, Maffei - Mathematics for the Life Sciences - Casa Editrice Ambrosiana ed.
Paolo Marcellini, Carlo Sbordone - Elements of Mathematical Analysis (the simplified version is also fine for new degree programs) - Liguori (2002)
Battaia, General Mathematics Course
For the Linear Algebra section in addition to the texts already listed: handouts
- Biostatistics segment: the teacher will indicate, at the beginning of the course, a list of recommended texts. Other teaching material is not necessary and attendance at lessons is highly recommended.
OFA TEST
The OFA test is administered before the official exams, covers all the topics listed in the Prerequisites and consists of 5 multiple choice questions with a threshold of 3 correct answers. The test, in paper form, lasts 20 minutes.
The Teachers will answer questions regarding the topics discussed in the course, following an e-mail. Students are kindly required not to ask bureaucratic/administrative question, if not absolutely necessary and urgent.
- Mathematics Segment:
• To prepare for OFA tests:
High school science textbooks (grades I to IV);
or good websites (matematika.it, youmath.it);
or good video lessons (for example, those by Elia Bombardelli on YouTube);
or Battaia, Basic Mathematics
or Messineo et al., Mathematics Notes. Preliminary Notions, Giappichelli ed.
To prepare for the section on infinitesimal calculus, differential calculus, and integral calculus:
Bramanti, Confortola, Salsa - Mathematics for the Sciences - Zanichelli ed.
Benedetto, Degli Esposti, Maffei - Mathematics for the Life Sciences - Casa Editrice Ambrosiana ed.
Paolo Marcellini, Carlo Sbordone - Elements of Mathematical Analysis (the simplified version is also fine for new degree programs) - Liguori (2002)
Battaia, General Mathematics Course
For the Linear Algebra section in addition to the texts already listed: handouts
- Biostatistics segment: the teacher will indicate, at the beginning of the course, a list of recommended texts. Other teaching material is not necessary and attendance at lessons is highly recommended.
OFA TEST
The OFA test is administered before the official exams, covers all the topics listed in the Prerequisites and consists of 5 multiple choice questions with a threshold of 3 correct answers. The test, in paper form, lasts 20 minutes.
The Teachers will answer questions regarding the topics discussed in the course, following an e-mail. Students are kindly required not to ask bureaucratic/administrative question, if not absolutely necessary and urgent.
Degrees
Degrees
BIOLOGICAL SCIENCES
Bachelor’s Degree
3 years
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People
People (2)
Teaching staff
Docenti di ruolo di IIa fascia
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