Mathematics (1-15 cr)

Aim

After completing the course, students will be able to- Read and interpret mathematical texts in arithmetic, algebra, geometry, and initial function theory- Formulate and explain basic concepts, laws and theorems in arithmetic, algebra, geometry and function theory- Solve problems in arithmetic, algebra, geometry, and function learning by applying key concepts, theorems and methods- Perform standard calculations- Check the results to verify that these are correct, or reasonable- Describe the didactic aspects of the school's central concepts, operations, theorems and methods in arithmetic, algebra, geometry and function theory.- Use of laboratory and technical facilities in Mathematics, including computer software in geometry.

Content

The course covers general numeracy, basic mathematical concepts, properties of elementary functions and classical geometry, specifically: Calculation with numeric and algebraic expressions, inequalities, absolute value, and complex numbers. Solving equations, algebraic equations, functions and graphs. Definition and basic properties of, the elementary functions. Basic principles of logical reasoning and evidence. Coordinate systems in the plane, polar coordinates, equations of straight lines and circles. Complex plane, complex numbers in Cartesian and polar form, Euler and de Moivre formulas. Geometric and arithmetic sum. Binomial theorem. Number systems: natural, whole, rational, real and complex numbers, the positioning system. Polynomials: divisibility, zeros and factor theorem, real polynomials, methods for solving equations.Euclidean geometry based on axioms: congruence and similarity, basic geometric theorems as the Pythagorean theorem, sine and cosines, the peripheral angle theorem, the intersecting chords theorem, the angle bisector theorem. Elements of tesselations.Beginning with basic definitions and axioms, and using logical reasoning and evidence, as well as skills training in the form of both exercises and theoretical reasoning, the students work on solving tasks, choose the appropriate solution once, examine and explain mathematical relationships, as well as illustrate and present solutions.Students also work with computer labs, which highlights the geometric properties.Students will also didactic analyzes included in the course school relevant mathematical concepts and methods, focusing on multiple representations and explanations.