In order to pass the course (grade 3) the student should
be able to give an account of important concepts and definitions for numbers and polynomials;
master the rules for powers and logarithms, and be able to compute with polynomials and complex numbers;
know how to solve simple combinatorial problems;
be able to carry out simple proofs by induction;
know the definitions of the trigonometric functions and some important trigonometric formulas, and know how to solve simple trigonometric equations;
be able to do computations with coordinates, and know how to use the equations of the line and the circle;
be able to formulate important results and theorems in the area of the course.
Arithmetic for rational and real numbers, inequalities, absolute value. Permutations and combinations. Induction. Polynomials: factorisation and division, completing squares, simple algebraic equations. The binomial theorem. Complex numbers: real and imaginary part, polar form, the complex plane, second degree equations and binomial equations.
Elementary functions: the exponential function, logarithms (in different bases), logarithmic rules, and trigonometric functions. Trigonometric formulas. Simple exponential, logarithmic and trigonometric equations.
Coordinate systems in the plane. The distance formula. Equations for the line and the circle. Equations for the ellipse, hyperbola and parabola in standard form.
Lectures and problem solving sessions.
Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.