30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE
Per la lingua del corso verificare le informazioni sulle classi/
For the instruction language of the course see class group/s below
Vai alle classi / Go to class group/s: 13
Class group/s taught in English
Lezioni della classe erogate in presenza
The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.
- Online part:
- Sets. Operations with sets. Number sets. Representation of number sets on the line.
- Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
- Polynomial algebra.
- First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
- Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
- Elements of trigonometry.
- First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.
- Classroom part:
- Mathematics as an axiomatic system: primitive notions and definitions, axioms and theorems. Set axioms, number sets.
- Elements of logics: propositions, quantifiers. Implication, equivalence. Sufficient condition, necessary condition, necessary and sufficient condition. The negation of a proposition. The contrapositive proposition.
- Basic terminology on theorems. Examples of proofs and demonstration techniques. Proofs by contradiction. The principle of mathematical induction; proofs by induction. Conjectures: proofs and counterexamples.
- Countable and uncountable sets. Combinatorics.
- Face-to-face lectures
- Online lectures
Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.
- Online part: all teaching materials are available on the Bboard platform.
- Classroom part: teaching materials prepared by the instructor.