Mathematics
A.Y. 2025/2026
Learning objectives
The aim of the course is to provide students with a basic understanding of mathematics, an indispensable tool for dealing with the more quantitative aspects of the course of study.
Expected learning outcomes
By the end of the course the student will acquire a sound knowledge of basic mathematics, the tools to handle the concepts learned in a formally correct language, and the ability to apply them to simple problems motivated by the biotechnological sciences. This knowledge is preparatory to the study of the other subjects in the degree course and an essential tool in the training of a scientist.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
The course begins with a reflection on numerical sets and measurable quantities in biology: from the natural numbers, through generalisation of elementary operations, we progressively arrive at studying the field of real numbers. The next leap is the complex numbers: a bridge between algebra and geometry, they allow any algebraic equation to be solved.
After a detailed introduction to the concept of a function, a rigorous but intuitive study of the notions of a neighbourhood and a limit continues. Limits of elementary functions and techniques for calculating limits of any functions are then dealt with. Finally, the concepts of continuity and derivability are addressed, as well as extremal points and local/global minima and maxima of a real variable function.
The course continues with the study of the Riemann integral: from the calculation of the primitives of a function (indefinite integral), we move on to the notion of measuring the area subtended by the graph of a real function with a real variable (definite integral) and its relation to the primitives of that function (fundamental theorem of calculus). Improper integrals and the concept of convergence are then addressed. The course ends with an introduction to ordinary differential equations with constant coefficients of the first and second order.
After a detailed introduction to the concept of a function, a rigorous but intuitive study of the notions of a neighbourhood and a limit continues. Limits of elementary functions and techniques for calculating limits of any functions are then dealt with. Finally, the concepts of continuity and derivability are addressed, as well as extremal points and local/global minima and maxima of a real variable function.
The course continues with the study of the Riemann integral: from the calculation of the primitives of a function (indefinite integral), we move on to the notion of measuring the area subtended by the graph of a real function with a real variable (definite integral) and its relation to the primitives of that function (fundamental theorem of calculus). Improper integrals and the concept of convergence are then addressed. The course ends with an introduction to ordinary differential equations with constant coefficients of the first and second order.
Prerequisites for admission
Basic skills acquired in high school are required for successful completion of the course: solving linear, quadratic and fractional equations and inequalities, elementary equations and inequalities with radicals, exponentials, logarithms and trigonometric functions. The ability to graph elementary functions is also very important.
Teaching methods
The course, lasting 56 hours, is organised in face-to-face lectures on the blackboard, divided into lectures (40 hours) and exercises (16 hours), which include both a theory part and exercises and examples. Attendance is compulsory.
Teaching Resources
M Bramanti, F. Confortola, S. Salsa, "Mathematics for the sciences with fundamentals of probability and statistics", Zanichelli
Please also note the availability, on the University's MyAriel portal, of "Mathematics with assistance" handouts (theory + exercises with solutions).
Please also note the availability, on the University's MyAriel portal, of "Mathematics with assistance" handouts (theory + exercises with solutions).
Assessment methods and Criteria
The exam for the Mathematics course is written only and will also include a theory part. It is not permitted to consult notes, books or anything else during the test or to make use of electronic equipment. The grade for the written test is in thirtieths. For students attending the course, there are two partial tests, the cumulative result of which is considered equivalent to the written test.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Practicals: 16 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Capoferri Matteo
Professor(s)