MATHEMATICS

The course is offered to the students an additional learning requirement in mathematics.
In particular, the course is aimed at recovering the basic skills necessary to attend the courses of Mathematics - 1 and Mathematics - 2.
In addition to the students with additional learning requirements, also the students who need to refresh their basic knowledge in mathematics are invited to attend.

1. Knowledge and understanding
1.1. understanding the terminology and the methodology of mathematics;
1.2. understanding the properties of powers and logarithms;
1.3. recognizing the different types of function;
1.4. understanding the solution techniques for equations and inequalities.
2. Ability to apply knowledge and understanding:
2.1. understanding a textbook of mathematics;
2.2. formalizing mathematical statements and problems;
2.3. identifying the goal of a given problem;
2.4. making the necessary calculations to solve a given problem.
3. Judgement skill:
3.1. interpreting simple mathematical models;
3.2. analyzing problems formalized in mathematical terms.

The course is compulsory for students recommended by the School. No special prerequisites are required

Terms and forms of mathematical language: logical connectives; implication; quantifiers; definition; axiom; theorem.
Elements and sets. Subsets and operations between sets.
Natural and integer numbers. Rational and real numbers. Properties of powers. Logarithms and their properties. Algebraic expressions and polynomials. Percentages.
Equations and inequalities: rational; irrational; with absolute value; exponential; logarithmic.
Coordinate systems in the plane and in the space. Distance in the plane. Line, circumference, ellipse, hyperbole and parabola.
Functions. Composite and inverse functions. Real functions of real variables: monotone; periodic; even; odd . Graph of a function. Transformations of function graphs. Linear, quadratic, exponential and logarithmic functions.
Basics of Trigonometry

Teacher's slides in the Moodle platform https://moodle.unive.it

For functions and basics of Trigonometry
David Lippman and Melonie Rasmussen (2020)
Precalculus - An Investigation of Functions
http://www.opentextbookstore.com/precalc/
section indicated by the teacher

For basics of algebra et al.
https://www.khanacademy.org/math/
section indicated by the teacher

This exam assigns 12 CFU university credits.
The final evaluation is composed as follows.
-10% for participation in online activities.
-80% for on-going tests.
-10% for the outgoing test.
The on-going tests will be 5, one for each section and will take the form of quizzes.
They will have different weights, depending on the content of each section.
-Terms and forms of mathematical language 5%
-Natural, integer, rational, real number. Operations. Equations and inequalities 35%
-Coordinate systems in the plane 20%
-Functions 35%
-Basics of Trigonometry 5%

The course is articulated into:
a) lectures dual mode;
b) exercises carried out during the lectures;
c) individual study.
Students are strongly encouraged to actively attend classes.
The exercises to be done partially individually, partially in groups. The correction will be immediate, when possible.

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