The course is divided in two modules:
- Euclidean Geometry, Analytic geometry, Trigonometry (3CFC)
- Algebra and Probability (3 CFC)
Academic year: 2025-26
Course: Euclidean Geometry, Analytic geometry, Trigonometry
Credits: 3
Period: first semester
Number of hours: 24
Teacher: Eugene Stepanov (stepanov.eugene.sns@gmail.com)
Language of instruction: English
Learning outcomes
The students will learn the principal concepts of euclidean geometry in the plane and of trigonometry, and will be able to solve geometry problems in the plane and in the space using Euclidean geometry and analytic geometric methods, to calculate lengths, areas and volumes of geometric sets.
Prerequisites
Numerical and algebraic calculus. Basic concepts of Eulidean geometry (points, lines, line segments, angles, measures of length, area and volume, measures of angles)
Teaching methods
• Lectures are carried out using a blackboard (maybe online).
• Exercises are carried out in the classroom: students will practice the exercises, even in groups, under the supervision of the lecturer.
• Interaction with the lecturer is done through meetings (during fixed office hours or by appointment) and by e-mail.
Syllabus
1. Principal plane figures and their elementary properties. Euclidean geometry in the plane.
2. Vectors and operations with vectors.
3. Basic analytic geometry in the plane.
4. Basic analytic geometry in the space (optional).
5. Trigonometric functions and relations.
Bibliography
• Online mathematics school
http://onlinemschool.com/math/library/vector/
• Online mathematics school http://onlinemschool.com/math/library/analytic_geometry/
• Csaba Vincze, Laszlo Kozma. College Geometry. http://www.freebookcentre.net/maths-books -download/College-Geometry.html
Assessment methods
Written tests consisting of a series of problems.
Academic year: 2025-26
Course: Algebra and probability
Credits: 3
Period: Second semester
Number of hours: 24
Language of instruction: English
Language of instruction: English
Learning outcomes/ Knowledge
Ruffini’s Theorem. And consequences. Sturm’s Theorem and consequences.
Assessment criteria of knowledge
Periodical discussions on the described topics. In the written exam the students must demonstrate their knowledge of the course topics through answers to specific questions and the solution of problems.
Skills
Students will be able to compute the number of zeroes of a polynomial real function. Using Sturm’s Theorem the will lear how to determine intervals where the zeroes are located.
Assessment criteria of skills
Periodical exercises on the described topics. In the written exam the students must demonstrate their skills through answers to specific questions and the solution of problems.
Behaviors
The student will be encouraged to partecipate to oral discussions and to try to solve problem and exercises under the supervision of the teacher.
Prerequisites
Basic numerical and algebraic calculus. Properties of powers, operations with fractions, operations with polynomials.
Syllabus
- Polynomials, algebraic calculus, factorisation.
2 Computing exact polynomial roots with Ruffini’s method.
3 Computing the number of zeroes of a polynomial real function.
4 Isolating roots via the interval method.
Bibliography
- Mathematics for the international student 10E MYP (Extended), Hease M., Hease R., Hease S., Kemp, Vollmar.
- Mathematics for the international student 6 MYP 1, Vollmar, Hease M., Hease R., Hease S., Humphries.
- High School Math Contests: online resources.
- Zanichelli: Test your skills, online resources.
- Assessment methods
Written test. The test must be passed with a score the same or higher than 18.