30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE
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For the instruction language of the course see class group/s below
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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 deals with different topics with respect to the online 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.
- 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.
Introduction to propositional logic. Basic logical connectives, truth tables. Tautology and contradiction. De Morgan’s laws. Conditional and biconditional statements. Contrapositive and converse statements. Predicates. Universal quantifiers. Negating quantified statements.
- Sets. Operations on sets and logical connectives. Properties. Power set. Set of natural, integer, rational and irrational numbers. Factorial of a number. Binomial coefficient. Sum and product of numbers.
- Meaning of the following terms: definition, theorem, proposition, lemma, corollary, and proof. Direct and contrapositive proofs. Proofs by contradiction. Special forms of the premise or of the conclusion. Proof by induction.
- Order structure of R. Intervals. Lower and upper bounds. Bounded sets. Maxima and minima. Supremum and infimum. Least upper bound principle. The extended real line. Short review of powers and logarithms.
- Notion of real function of one real variable. Domain, codomain, and image of a function. Surjective, injective, and bijective functions. Bounded functions. Elementary functions. Geometric notion of derivative of a function at a point. Derivatives of elementary functions. Algebra of derivatives. Introduction to the calculation of partial derivatives.
- Face-to-face lectures
- Online lectures
Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.
|Continuous assessment||Partial exams||General exam|
Assessment is included in the first year, first semester mathematics course, with the methods used for that course.
- Online part: all teaching materials are available on the Bboard platform.
- Classroom part: teaching materials prepared by the instructor.