RECOVERY COURSE OF MATHEMATICS
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Delivery method
- Teaching methods
- Contacts/Info
Possess the basic knowledge of mathematics common to all secondary education pathways.
No final examination is foreseen; instead, several intermediate self-assessment quizzes are offered to monitor and consolidate students’ learning progress throughout the course.
The course aims to provide students with a basic preparation that facilitates the recovery of any knowledge gaps in mathematics. The course is aimed at facilitating the passing of the verifca test of initial preparation to fulfill the additional educational obligation (OFA) and the passing of the exam of the ordinary course in Mathematics through the consolidation of what was covered during that course.
At the end of the course, the student will be able to:
• master the essential terminology of mathematical logic, set theory and functions;
• perform basic algebraic calculations for solving equations, inequalities and simple systems;
• employ the concepts of power, root, exponential and logarithmic functions, together with their fundamental properties;
• analyze real functions of one variable, identifying their domain, sign and main qualitative features;
• apply the techniques of analytic geometry in the plane, with particular reference to the line and the parabola.
• Elements of mathematical logic, set theory and functions
• The real numbers — integers, rationals and decimals
• Powers and roots; exponential and logarithmic functions
• Basic combinatorial calculus
• Polynomials and fundamental algebraic operations
• Equations, inequalities and simple systems (polynomial and non-polynomial)
• Real functions of one variable: basic notions
• Lines and parabolas in the Cartesian plane
• Elements of mathematical logic, set theory and functions | Propositions, logical connectives and quantifiers; sets and main set operations; domain and range of a function; injective, surjective and bijective functions; composition and inverse function.
• The real numbers — integers, rationals and decimals | Review and further study of the different numerical classes (integers, rationals, irrationals and reals); algebraic and ordering properties; representation on the real line.
• Powers and roots; exponential and logarithmic functions | Definitions, fundamental properties and calculation rules; functional relationships and analytical meaning; basic applications and graphical representations.
• Basic combinatorial calculus | Factorial, binomial coefficients and the binomial theorem.
• Polynomials and fundamental algebraic operations | Sum, product and factorization; remarks on polynomial equations of degree higher than two.
• Equations, inequalities and simple systems (polynomial and non-polynomial) | Solution of first- and second-degree equations and inequalities, linear and non-linear; graphical analysis and interpretation of solutions; simple systems of equations and inequalities.
• Real functions of one variable: basic notions | General concepts, domain and range; graphical representation and main transformations; qualitative analysis of sign, monotonicity, parity and boundedness.
• Lines and parabolas in the Cartesian plane | Equations, representation and study of lines and parabolas; applications to the main problems of intersection and tangency.
The course is entirely video recorded and available online in asynchronous mode. The lectures, combining theoretical explanations and practical exercises, are organised progressively to support students in reviewing and consolidating their basic knowledge, thereby promoting autonomous and informed learning.
The University has adopted the Leganto system for managing course bibliographies; therefore, the bibliography for this course must be compiled through the Leganto portal, available at the following URL: https://www.uninsubria.it/leganto-testi (access requires authentication with University credentials).
For further information, please refer to the page dedicated to the Leganto service on the SiBA – Digital Library portal (https://uninsubria.libguides.com).
Student office hours are held exclusively online and by appointment, to be arranged via e-mail at marco.tarsia@uninsubria.it.