##### The course is divided in two modules:

- Euclidean Geometry, Analytic geometry, Trigonometry (3CFC)
- Algebra and Probability (3 CFC)

**Academic year**: 2021-22**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 isntruction**: 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:** 2021-22**Course**: Algebra and probability**Credits: **3**Period**: Second semester**Number of hours**: 24**Teacher**: Anna Rita Giammetta (anna_rita_giammetta@hotmail.it)**Language of instruction**: English

**Learning outcomes**

**Knowledge**

Number sets. GCF and lcm. Numerical calculus. Percentage (simple and compound). Mean. Absolute value. Scientific notation. Radicals. Exponentials, logarithms. Polynomials. Factorisation. Linear and quadratic equations. Linear and quadratic inequalities. Higher order equations and inequalities. Liner systems. Systems of nonlinear inequalities. Domain of functions involving rational expressions, log, square roots. Sign of functions involving irrational terms and log. Counting principle. Permutations. Factorial. Combinations. Probability.

**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 manage numerical and algebraic expressions, to solve problems involving simple or compound percentages, to use properties of log function, to solve problems using exponential models, to solve equalities and inequalities of the first and second order, to solve first and second order inequalities, to solve both combinatronics and probability related problems.

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**

1. Fractions, percentage, powers, scientific notation, simple and compound interest, mean, radicals, logarithms, exponentials, models: exponential growth or decay.

2. Polynomials, algebraic calculus, factorisation

3. Linear equalities, linear inequalities, linear systems, second order equalities and inequalities., resolution of higher order equalities and inequalities.

4. Irrational inequalities, exponential inequalities, logarithmic inequalities.

5. Permutations, factorial, combinations, theoretical probability.

**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.

• Sheldon Ross, A First Course in Probability, A (5th edition) – Prentice Hall college (1997)

**Assessment methods**

Written test. The test must be passed with a score the same or higher than 18. If the student fails twice the exam, an oral exam will be scheduled.