# Basic Mathematical Language

##### The course is divided into three sections:
1. Module on Algebra and Probability (3 CFC)
2. Module on Elements of Mathematical Analysis (Functions, Graphs, Relations) (3 CFC)
3. Module on Euclidean Geometry, Analytic geometry, Trigonometry (3CFC)

### Module on Algebra and Probability (3 CFC)

#### Learning outcomes:

Students will be able to manage numerical and algebraic expressions, solve equalities and inequalities of the first and second order and problems, solve both combinatronics and probability related problems.

#### Prerequisites

Numerical and algebraic calculus

#### Teaching methods

• Lectures are carried out using a blackboard.
• Exercises are carried out in the classroom: students will practice the exercises, even in groups, under the supervision of the lecturer.
• Interaction with the teacher is done through interviews (on fixed office hours or by appointment) and by e-mail.

#### Syllabus

1. Powers, radicals, logarithms, exponentials and their properties.
2. Linear equalities, linear inequalities and linear systems.
3. Second order equalities and inequalities.
4. Ruffini’s rule and resolution of higher order equalities and inequalities.
5. Combinatorial  calculus and probability

#### Bibliography

• Israel M. Gelfand, Alexander Shen-Algebra (1993)
• Larson R., Boswell L., Kanold T., Stiff L. – Algebra 1_ Concepts and Skills
• Zanichelli: Test your skills, online resources: [a],[b]
• High School Math Contests: online resources.
• Sheldon Ross, A First Course in Probability, A (5th edition) – Prentice Hall college (1997)

#### Assessment methods

Written test consisting of a few problems to be solved in three hours.

### Module on Euclidean Geometry, Analytic geometry, Trigonometry (3 CFC)

#### 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.
• 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. Analytic geometry in the plane and in the space.
4. Trigonometric functions and relations.

#### Bibliography

• Online mathematics school
http://onlinemschool.com/math/library/vector/
• Online mathematics school http://onlinemschool.com/math/library/analytic_geometry/

#### Assessment methods

Written test consisting of a few problems to be solved in three hours.

### Module on Elements of Mathematical Analysis (Functions, Graphs, Relations) (3CFC)

#### Learning outcomes:

The students will learn the principal concepts of sets, functions and relations, the elementary functions of real variable and their graphs. Students will also learn  to solve problems related to the study of simple functions of real variable and draw graphs of these functions.

#### Prerequisites

Numerical and algebraic calculus.

#### Teaching methods

• Lectures are carried out using a blackboard.
• 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 done through meetings (on fixed office hours or by appointment) and by e-mail.

#### Syllabus

1. Basic language of sets, functions and relations.
2. Elementary  functions of a real variable and their properties.
3. Study of the graphs of the simple functions of a real variable. Resolving problems involving the functions of a real variable.

#### Bibliography

• M. Bramanti, C.D. Pagani, S. Salsa. Analisi Matematica I, Zanichelli, 2008.
• N.S. Piskunov. Differential and Integral calculus, vol. I, chapter I, Mir, 1969.

#### Assessment methods

Written test, consisiting of a few problems to be solved in three hours.