A.Y. 2020/2021
Overall hours
Learning objectives
This course is an introduction to some basic facts about real functions, real analysis and linear algebra with applications to finding solutions to linear systems.
Expected learning outcomes
The course is devoted to provide a basic knowledge of the main mathematical tools with specific attention to the concept of mathematical function, of limit, and of differential and integral calculus. Part of the course gives the students the main techniques to solve linear systems in many variables.
Course syllabus and organization

Single session

Lesson period
First semester
The educational activity of the course will be provided as frontal teaching and distance teaching (in synchronous modality). The presence in the classroom will be possible in shifts in compliance with anti-covid regulations.
The methods and criteria for participating in the lessons in attendance, which require a reservation with a special app, will be published on the Ariel pages of the teaching and/or by the teaching secretary of the course.
In case of a new suspension of frontal lessons, all students will be asked to switch to synchronous distance learning. Each hour of the lesson will be divided into 45" formal teaching followed by 15" discussion / interaction / question time.
All lectures will be recorded and available to students on dedicated platforms (e.g. Ariel, TEAMS, etc.).
Any notice regarding updates or also related to the evolution of the regulations imposed by Covid-19 will be published on the degree course Ariel website and on Ariel website of the individual courses as well as communicated by the teaching secretariat.

The program and reference material will not be changed. The latter will be made available on dedicated platforms (e.g. Ariel, TEAMS, etc.)

Unless otherwise specified, the exams will be organized in the classroom and according to the reported learning methods. If the student will not be able to reach the exam center due to problems with COVID, other modalities may be considered (this applies only to exams scheduled until 31 December - 2020)
Course syllabus
The course starts with a short recall of some basic facts about set theory, functions and logic. After this the first part of the course, the one which deals with real function with one variable and which covers about three quarters of the lessons, begins.
We define the classical notion of domain and limit of a function. We talk about continuity, differentiability and higher regularity of a function. The main theorems related to the study of the graph of a function and those which gives useful techniques for the computations of limits are stated. Finally, we explain the theory of integration according to Riemann and some techniques to compute the primitive function of a given one.
In the second part of the course we deal with matrices and vector (products between matrices, determinant and rank). Then we apply these techniques to the study of linear systems in any number (but finite) of variables. Theorems which tell whether a linear system has solutions or not and which tell how many solutions there are, are stated. Other results which enable the students to simplify a linear system and to arrive to its solution are the last topic presented.
Prerequisites for admission
Prior knowledge of some important basic mathematics concept such as: basic equations and inequalities with radicals, exponentials, logarithms and trigonometric functions, graphs of elementary functions.
Teaching methods
The course (which is composed of 48 hours) is organised in classes (with both theory and exercises).
During class a lot of attention is given to examples. Lessons are always followed by exercises although is not planned an explicit division between theoretical lessons and practical ones.
Attendance in mandatory. A student can undergo the exam only if he has participated 70% of the lessons. Nevertheless, attendance to all the lessons is recommended.
Teaching Resources
Matematica per le scienze, A. Guerraggio, Pearson
Matematica e Statistica, M. Abate, McGraw Hill.
On the online platform Ariel of the University there are the notes "Matematica Assistita" which covers basically the whole program of the course (with some extra).
Assessment methods and Criteria
Exam is a single written test. It consists of practical exercises (in general, one about the qualitative study of the graph of a function, one about integration and one about the study of a linear system, possibily with parameters) and of some questions related to the study of the theory.
No partial tests are planned. During the exam it is forbidden to use notes, books, formulary and electronic devices.
In addition to the ability to correctly solve the given exercises it will be evaluated also the ability of being able to use theoretical tools and the proficiency with the mathematical language.
The mark is given by a number between zero and thirty. A mark of eighteen is the minimum value for passing the exam.
The outcome of the exams is announced on the website of the professor and is thereafter recorded online giving to the student the possibility to refuse a mark (for a given time, according to the regulations of the University).
MAT/03 - GEOMETRY - University credits: 6
Lessons: 48 hours
Educational website(s)