MATHEMATICS

Academic year
2025/2026 Syllabus of previous years
Official course title
MATHEMATICS
Course code
FOY02 (AF:600929 AR:338344)
Teaching language
English
Modality
On campus classes
ECTS credits
12
Subdivision
C
Degree level
Corso di Formazione (DM270)
Academic Discipline
NN
Period
1st Semester
Course year
1
Where
VENEZIA
Moodle
Go to Moodle page
This course is designed to complement students’ prior mathematical knowledge, with the primary objective of reinforcing the foundational skills required for successful completion of Mathematics 1 and Mathematics 2. While particularly intended for students who need to strengthen specific areas of their mathematical background, the course also provides valuable consolidation for those who wish to reinforce their existing competencies.
1. Knowledge and Understanding
1.1. Understanding of mathematical terminology and methodology.
1.2. Understanding of the properties of powers and logarithms.
1.3. Ability to recognize different types of functions and their properties.
1.4. Understanding of problem-solving techniques related to equations and inequalities.

2. Applying Knowledge and Understanding
2.1. Ability to comprehend a mathematical text.
2.2. Ability to formalize statements and problems in mathematical language.
2.3. Ability to identify appropriate problem-solving strategies.
2.4. Ability to carry out the computations required for problem solving.

3. Making Judgements
3.1. Ability to interpret simple mathematical models.
3.2. Ability to analyze problems formalized in mathematical terms.
The course is compulsory for registered students. There are no special prerequisites.
- 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. Percentages. Properties of powers. Logarithms and their properties. Algebraic expressions, polynomials and algebraic fractions.
- Equations and inequalities: rational, irrational, with absolute value;
- Equations and inequalities: exponential; logarithmic.
- Coordinate systems in the plane and in the space. Distance in the plane. Line and parabola.
- Circumference, ellipse, hyperbole.
- Functions. Composite and inverse functions. Real functions of real variables: monotone; periodic; even; odd.
- Graph of a function. Linear, quadratic, polynomial functions. Transformations of function graphs.
- Exponential and logarithmic functions.
- Basics of Trigonometry.
Teacher's materials:
slides and PDF materials (available on the course platform).

For functions and basics of Trigonometry
Textbook:
Lippman, David and Rasmussen, Melonie (2020). Precalculus - An Investigation of Functions.
Available at: http://www.opentextbookstore.com/precalc/
Students must refer to the sections specified by the instructor.

For basic algebra:
Khan Academy (website): https://www.khanacademy.org/math/
Students must refer to the sections specified by the instructor.
Assessment Methods:
10% for participation.
60% for in-progress/midterm tests.
30% for the final examination.
written
Grades are expressed on a thirty-point scale (out of 30).
A minimum score of 18/30 is required to pass the examination.
Dual mode lectures (In-person and online/remote)
Exercises (completed during class time)
Individual study

Students are strongly encouraged to participate actively in all lectures and discussions.
Exercises will be completed both individually and in groups.
Immediate correction will be provided whenever possible.
Definitive programme.
Last update of the programme: 29/09/2025