30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE

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 15 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.
• First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

Classroom part:

• Real functions of one real variable: general concepts and examples. Composite and inverse functions. Graph of a function. Graphs of elementary functions: linear, power, exponential, and logarithmic functions. Piecewise-defined functions and their graphs. Transformations of elementary functions.

• Exponential equations and inequalities. Properties of logarithms. Logarithmic equations and inequalities.

• More on functions: increasing/decreasing, concave/convex, and bounded functions. Global and local extrema of a function.

• Behavior of elementary functions at the boundaries of the domain. Hierarchy of infinite functions.

• Graph of a function: domain, behavior at the boundaries, zeros (or x-intercepts), y-intercept, sign, monotonicity, points of maximum and minimum, concavity and convexity.

• Summation symbol and remarkable sums. Summation properties. 

• Limits: an intuitive idea.

• Basic language and examples of differential and integral calculus.

• Face-to-face lectures
• Online lectures

Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platfor

 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.