BASIC MATHEMATICS

The "Basic mathematics" course is designed for students with gaps in their secondary school–level mathematical knowledge. It covers a core topic of mathematics — the concept of functions — breaking it down into five chapters: rational functions; irrational functions; exponential and logarithmic functions; trigonometric functions.
The course provides students with the tools they need to successfully tackle the logical-mathematical subjects of the first year and offers support in meeting additional educational requirements (OFA).

By the end of the "Basic mathematics" course, students will have a firm grasp of the concept of function and how it is applied in various areas of mathematics. They will be able to identify and define rational and irrational functions involving modulus and fractions, as well as logarithmic, trigonometric and exponential functions. They will have completed exercises to consolidate their understanding of calculation procedures and techniques in preparation for the first-year logic and mathematics exams. They will also have practised linking the definitions and properties of functions to their graphical representation.
To consolidate their study methods for mathematics and problem solving, a number of specific metacognitive activities are planned.

No prerequisites are required. Only needed the qualification required to access the Computer Science degree programme.

1. Rational functions (5 hours)
Knowledge
- Definition of real function of real variable
- Methods for solving polynomial, rational equations and inequalities, with e without modules
Ability to solve basic problems
- Plot the graph of first-, second- and third-degree polynomial functions, with and without modules
Problems for developing mathematical skills
- Study the domain and sign of rational functions with fractions and modules. Draw the areas of the plane in which their graph lies
Problems for developing personal, study and updating skills
- Build and adapt formula sheets and summaries for learning and training purposes.

2. Irrational functions (5 hours)
Knowledge
- Schemes for solving irrational equations and inequalities
- Definition of composite function
Ability to solve basic problems
- Solve systems of inequalities and solve irrational inequalities
- Study the domain and sign of irrational functions
Problems for developing mathematical skills
- Study the domain and sign of fractional or irrational functions, with and without modules. Draw the areas of the plane where their graph lies
Problems for developing personal, study and updating skills
- Build and adapt formula sheets and summaries for learning and training purposes.

3. Exponential functions (5 hours)
Knowledge
- Definition of the power of a number
- Properties of powers
- Definition of exponential function and its invertibility
Ability to solve basic problems
- Plot the graph of exponential functions
- Apply definitions to study equations and inequalities containing exponential functions
Problems for developing mathematical skills
- Study the domain and sign of exponential functions and defining the areas of the plane in which their graph lies
- Draw the graph of composite functions related to exponential functions
Problems for developing personal, study and updating skills
- Build and adapt formula sheets and summaries for learning and training purposes.

4. Logarithmic functions (5 hours)
Knowledge
- Definition of logarithm and logarithmic function
- Properties of logarithms
Ability to solve basic problems
- Plot the graph of logarithmic functions
- Apply the definitions and properties of logarithms to the study of logarithmic equations and inequalities
Problems for developing mathematical skills
- Study the domain and sign of logarithmic functions and defining the areas of the plane in which their graph lies
- Draw the graph of composite functions related to logarithmic functions
Problems to develop personal, study and updating skills
- Build and adapting formula sheets and summaries for learning to use logarithms. Use them for studying and training purposes.

5. Basic trigonometry (5 hours)
Knowledge
- Measuring angles: degrees and radians.
- The operational definition of sine, cosine and tangent of an angle in the first quadrant.
- Extending trigonometric functions by symmetrys and periodicity
Ability for solving basic problems
- Measure angles using degrees and radians
- Plot the graph of trigonometric functions
- Determine the period and amplitude of a trigonometric function
- Solve trigonometric equations and identities
Problems for developing mathematical skills
- Draw graphs of composite functions related to basic trigonometric functions
- Manipulate trigonometric formulas
Problems for developing personal, study and updating skills
- Build a trigonometric formula sheet based on its use in solving trigonometric problems
- Use trigonometric formula sheet to solve trigonometric identities, equations and inequalities

Any textbook on mathematics for secondary school that covers the course topics.

The course does not include a final assessment, but offers the possibility of completing the OFA by passing a test. There are five exam sessions throughout the academic year: one at the end of the course and one at the beginning of each subsequent exam period.
The test consists of a 60-minute written exam containing six open-ended questions : one for each of sections 1–4, and two for section 6. Credit is awarded for achieving 70% of the total score.

The training requirement is fulfilled or not fulfilled after passing the verification test.

Lectures and classroom exercises.