Entry requirements

Mathematics D

Learning outcomes

In order to pass the course (grade 3) the student should

• be able to give an account of elementary concepts and definitions of numbers and polynomials;
• master powers and logarithms as well as be able to calculate with polynomials and complex numbers;
• be able to solve simple combinatorial problems;
• be able to present simple induction proofs;
• be familiar with the properties of exponential, logarithmic and trigonometric functions and be able to solve simple equations with such functions;
• be able to solve systems of linear equations with Gauss elimination and be able to describe solvability properties in terms of the rank;
• be able to use matrices and to compute matrix inverses and determinants;

• be able to give an account of the vector concept;
• be able to use scalar products and to interpret them geometrically;
• be familiar with the equations of lines and planes and be able to use them for calculating intersections and distances;
• be able to use the theories, methods and techniques taught in the course to solve mathematical problems.

Content

Arithmetics for rational and real numbers, inequalities, absolute value. Permutations and combinations. Induction. Polynomials: factorising and polynomial division, completing squares, elementary algebraic equations. The binomial theorem. Complex numbers: basic and polar form, the complex plane, second degree equations and binomial equations.

Elementary functions: the exponential function, the logarithm (in different bases) and trigonometric functions. Trigonometric formulas. Simple exponential, logarithmic and trigonometric equations.

Coordinate systems in the plane. The distance formula. Equations for lines and circles. The normal equation of ellipses, hyperbolas and parabolas.

Systems of linear equation systems: Gauss elimination, rank, solvability. Matrix algebra. Determinants. Vector algebra. Scalar products. Equations for lines and planes in space. Distance, area and volume.

Instruction

Lectures, lessons and problem solving sessions.

Assessment

Written examination at the end of the course possibly combined with written assignments during the course according to instructions provided at course start.

Other directives

The course may not be included in exam with the courses Algebra and Vector Geometry, the Basic Course in Mathematics and Linear Algebra and Geometry.