Courses and Pathways in Science
To begin with, the basic notions of set theory and equalities/inequalities properties will be reviewed; after that, the founding postulates will be given, along with first results on straight lines, segments, planes, angles and orthogonality.
In another section, polygons will be introduced and described, with a particular attention to triangles; congruence criteria and basic inequalities are then analysed.
After that, a further section on parallelism issues will introduce rhomboids and basic proportionality Thales’ theorem. Circles and regular polygons will be introduced in another section, along with main results related to those figures.
All results obtained will lead to the final two sections: the first one concerning areas, equivalence, and Euclidean and Pythagorean theorems on right-angled triangles; and the second one dealing with similarity and homothety.
This course presents the basic mathematics topics, which are necessary in order to fruitfully follow the Mathematics and Mathematical Analysis courses which are common to all scientific Bachelor courses (e.g., Mathematics, Physics, Engineering, Biological Sciences, Biotechnologies, …).
First, the basic algebraic operations on polynomials and the first notions of analytic geometry in the
plane are reviewed, including, among other things,
the equations of lines, parabolas, circumferences, ellipses, and hyperbolas.
The concept of function in the abstract is then introduced and the fundamental functions that are used in Mathematical Analysis are presented: in addition to polynomial functions, trigonometric, exponential and logarithmic functions are defined and illustrated.
Finally, the methodologies that allow solving equations and inequalities, both single and in systems, involving all the functions covered in the course are addressed.