ID:
500300
Duration (hours):
56
CFU:
6
SSD:
ANALISI MATEMATICA
Year:
2025
Overview
Date/time interval
Primo Semestre (29/09/2025 - 23/01/2026)
Syllabus
Course Objectives
This section deals with the "intended learning outcomes", i.e. the learning outcomes that are expected from students who will attend the course of Calculus and topics in Statistics.
At the end of the course students are expected to have acquired the ability to both identify the mathematical relationships between the quantities of interest in the typical application context of the degree course and cope with the typical problems of a chemical and biological nature. More precisely, students will have to be able to apply the abstraction and calculation tools that mathematics provides to solve problems typical of the chemical-pharmaceutical and biological context. To achieve this macro-objective, the student must:
- know and be able to describe the different functional forms illustrated in class;
- have the skill to apply the elementary operations of derivation and integration;
- be able to to identify the most appropriate functional model for the description of simple growth/decrease phenomena in the biological and/or chemical fields;
- know and understand the concept of probability and the basic tools of probability calculation;
- be familiar with the application of conditional probability and know how to use the concept in the study of diagnostic tests;
- know the definition of hypothesis tests and know how to carry out an appropriate test given a set of samples.
Achieving the learning outcomes outlined above will allow the student to acquire a grounded problem solving attitude and to cope efficiently with the typical problems of CTF degree course.
At the end of the course students are expected to have acquired the ability to both identify the mathematical relationships between the quantities of interest in the typical application context of the degree course and cope with the typical problems of a chemical and biological nature. More precisely, students will have to be able to apply the abstraction and calculation tools that mathematics provides to solve problems typical of the chemical-pharmaceutical and biological context. To achieve this macro-objective, the student must:
- know and be able to describe the different functional forms illustrated in class;
- have the skill to apply the elementary operations of derivation and integration;
- be able to to identify the most appropriate functional model for the description of simple growth/decrease phenomena in the biological and/or chemical fields;
- know and understand the concept of probability and the basic tools of probability calculation;
- be familiar with the application of conditional probability and know how to use the concept in the study of diagnostic tests;
- know the definition of hypothesis tests and know how to carry out an appropriate test given a set of samples.
Achieving the learning outcomes outlined above will allow the student to acquire a grounded problem solving attitude and to cope efficiently with the typical problems of CTF degree course.
Course Prerequisites
Basic concepts in mathematics and logic are requested.
More precisely, students must possess the following skills and competences:
- deep know-how in arithmetic and algebraic calculation;
- expertise with operations with integer and rational numbers, with irrational numbers and have an intuitive knowledge of real numbers;
- knowledge of polynomials and ability to execute operations between them;
- skills in handling literal expressions;
- to be able to solve first and second degree equations and inequalities, linear systems with two unknowns, systems of inequalities (at least linear and second degree ones).
As far as geometry is concerned, knowledge of the concept of the Cartesian plane, the ability to apply Pitagora's theorem, and knowledge of geometric transformations and the properties of the circumference are required.
Finally, it is desirable that students have curiosity in mathematcal applications to life sciences.
More precisely, students must possess the following skills and competences:
- deep know-how in arithmetic and algebraic calculation;
- expertise with operations with integer and rational numbers, with irrational numbers and have an intuitive knowledge of real numbers;
- knowledge of polynomials and ability to execute operations between them;
- skills in handling literal expressions;
- to be able to solve first and second degree equations and inequalities, linear systems with two unknowns, systems of inequalities (at least linear and second degree ones).
As far as geometry is concerned, knowledge of the concept of the Cartesian plane, the ability to apply Pitagora's theorem, and knowledge of geometric transformations and the properties of the circumference are required.
Finally, it is desirable that students have curiosity in mathematcal applications to life sciences.
Teaching Methods
Lectures, exercises and tutoring.
Furthermore, students with specific needs who cannot attend classes in presence and who have applied for the "Inclusive Teaching Methods" are kindly invited to contact the teacher so that the most suitable methods and material for a profitable independent study can be defined together. The student may request tutoring or supplementary teaching activities, and any dedicated meetings, even online, with times agreed with the teacher. The contacts are as follows: raffaella.guglielmann@unipv.it, +390382985654
Furthermore, students with specific needs who cannot attend classes in presence and who have applied for the "Inclusive Teaching Methods" are kindly invited to contact the teacher so that the most suitable methods and material for a profitable independent study can be defined together. The student may request tutoring or supplementary teaching activities, and any dedicated meetings, even online, with times agreed with the teacher. The contacts are as follows: raffaella.guglielmann@unipv.it, +390382985654
Assessment Methods
Written examination and an oral one if the professor deems an oral interview necessary.
The exam is designed to verify that students
1. know and are able to describe the different functional forms illustrated in class;
2. have the skill to apply the elementary operations of derivation and integration;
3. are able to to identify the most appropriate functional model for the description of simple growth/decrease phenomena in the biological and/or chemical fields;
4. know and understand the concept of probability and the basic tools of probability calculation;
5. are familiar with the application of conditional probability and know how to use the concept in the study of diagnostic tests;
6. know the definition of hypothesis tests and know how to carry out an appropriate test given a set of samples.
The exam is usually in person unless the student has special needs that must be certified by the student himself.
For students who fall into the categories of Specific Learning Disorders and Special Educational Needs, it is expected that a more appropriate exam method may be agreed with the teacher.
The exam is designed to verify that students
1. know and are able to describe the different functional forms illustrated in class;
2. have the skill to apply the elementary operations of derivation and integration;
3. are able to to identify the most appropriate functional model for the description of simple growth/decrease phenomena in the biological and/or chemical fields;
4. know and understand the concept of probability and the basic tools of probability calculation;
5. are familiar with the application of conditional probability and know how to use the concept in the study of diagnostic tests;
6. know the definition of hypothesis tests and know how to carry out an appropriate test given a set of samples.
The exam is usually in person unless the student has special needs that must be certified by the student himself.
For students who fall into the categories of Specific Learning Disorders and Special Educational Needs, it is expected that a more appropriate exam method may be agreed with the teacher.
Texts
Benedetto, Degli Espositi, Maffei. Matematica per le scienze della vita. (quarta edizione) Casa Editrice Ambrosiana
Contents
Calculus: sets, combinatorics, equation of a line, functions of a real variable, graph of a function, injective function, bijective functions, operations with functions, composition of functions, inverse function, elementary functions (polynomial, exponential, logarithm, sin and cos, absolute value). Model of growth (exponential growth), logarithmic scales. Monotone functions, maxima and minima of a function, limit and continuity, evaluations of basic limits, derivative of a function and tangent to a curve, derivative rules, integrals, fundamental theorem of calculus and evaluation of basic integrals.
Statistics: descriptive and inferential statistics. Univariate and multivariate analysis.
Probability: events, definition of probability, frequency, conditional probability, cumulative distribution functions, survival functions, random variable (discrete and continuous), mean, variance, binomial distribution, gaussian distribution, properties of gaussian distributions.
Law of large numbers and central limit theorem.
Confidence intervals. Statistical hypothesis testing.
Statistics: descriptive and inferential statistics. Univariate and multivariate analysis.
Probability: events, definition of probability, frequency, conditional probability, cumulative distribution functions, survival functions, random variable (discrete and continuous), mean, variance, binomial distribution, gaussian distribution, properties of gaussian distributions.
Law of large numbers and central limit theorem.
Confidence intervals. Statistical hypothesis testing.
Course Language
Italian
More information
Students are kindly invited to attend courses organized for freshmen about the basic notions of mathematics.
Degrees
Degrees
MEDICINAL CHEMISTRY AND PHARMACEUTICAL TECHNOLOGY
Single-cycle Master’s Degree
5 years
No Results Found