Program Mathematics

MATHEMATICS

FIRST TWO YEARS

PURPOSE

To promote the student's intuitive and logical faculties.
To educate in the processes of abstraction and concept formation.
To exercise inductive and deductive reasoning.
To develop and enhance analytical and synthesis skills.

GOALS
To stimulate expression through increasingly clear, precise and rigorous language making use of tools such as symbols and graphic representations.
To guide analysis and synthesis by educating to a progressive clarification of concepts, recognition of similarities in different situations to arrive at a unified view on some central concepts.
Guide to the ability to expand concepts and the use of models.

CLASS I

MAIN TOPICS COVERED

Algebra:
Set theory and operations with them
Numerical sets
Literal calculus
Monomials and polynomials
Operations with monomials and polynomials
Factor decomposition of polynomials
Algebraic fractions
Equations of the first degree, whole, literal and fractional
Disequations of the first degree

Geometry:
Elementary concepts
Congruences between triangles
Parallelism and perpendicularity between lines
Quadrilaterals
Parallelograms
Trapezoids
Theorem of Thales
Circumference

CLASS II

MAIN TOPICS COVERED

Algebra:
Sets: relations and functions
Disequations of the first degree
Radicals
Equations of the second degree
Equations of degree greater than two and irrationals
Systems of second degree and higher degree equations
Disequations of second degree

Geometry:
Isometric transformations
Equivalence of polygons
Ratios, measures and proportions
Homotheticals and similarities

Analytic geometry:
The Cartesian plane and the line
Parabola
Circumference
Probability, Statistics and Combinatorial Calculus (hint)

SECOND THREE YEARS

PURPOSE.

Acquire knowledge at higher levels of abstraction and formalization
To grasp the distinctive features of various languages (natural-historical, formal, artificial)
Use mathematical methods, tools and models in different situations
Critically reexamine and logically arrange knowledge as it is acquired

GOALS
To continue and expand the process of scientific and cultural preparation of young people already begun in the two-year period
To contribute, together with the other disciplines, to the development of the critical spirit and their human and intellectual advancement.
To enable the student to use all the concepts learned so far in practical applications, specific to the chosen address.

CLASS III

MAIN TOPICS COVERED

Equations of degree greater than 1° and applications
Functions
Analytic geometry (line, circumference, parabola, ellipse, hyperbola)

CLASS IV

MAIN TOPICS COVERED

Goniometry and trigonometry
Complex numbers
Exponential and logarithmic functions
Limits of continuous functions and calculation of limits
Approximate study of the graph of a function

CLASS V

MAIN TOPICS COVERED

Derivation of a function
Complete study of the graph of a function
Integrals
Differential equations
Numerical series and series of functions