Entry requirements

Mathematics E

Learning outcomes

The course is a basis for further studies in Mathematics. On completion of the course, the student should be able to

• use the computer systems that are required for the introductory courses within the Bachelor Programme in Mathematics and be able to use the IT-systems of the university in accordance with the rules laid down;
• communicate, search and find information via Internet;
• give an account of basic concepts and definitions for numbers (also complex) and polynomials, and be able to perform calculations with these;
• give an account of the exponential and logarithm functions, master the power and logarithm laws and be able to solve elementary equations containing these;
• solve simple combinatorial problems and use the binomial theorem;
• carry out inductive proofs in simple cases;
• give an account of the definitions of the trigonometric functions and explain and use some important trigonometric formulae, and be able to solve trigonometric equations;
• use the coordinate concept and the equations of the line and the circle.

Content

The course consists of the following three subparts.

Computer introduction (1 credit): Basic operations and everyday situations that include the local UNIX systems, UpUnet-S and e-mail. Information retrieval and communication on Internet, e.g. using web pages that are important for the studies. Ethical rules and safety for the use of computer networks and databases. File management. Applications. Knowledge of the possibility to work externally, e.g. from home.

Seminars (1 credit): Information about some of the subareas of mathematics and their different application fields and about the labour market for mathematicians.

Basic Mathematics (3 credits): Arithmetic for rational and real numbers, differences, absolute values. Permutations and combinations. The binomial theorem. Induction. Polynomial: factorisation, long division and completion of the square, simple algebraic equations. Complex numbers: normal and polar form, the complex plane, second order equations and binomial equations. The function concept. Elementary functions: the exponential function, the logarithm (in different bases) with logarithm laws and trigonometric functions. Trigonometric formulae. Simple exponential, logarithmic and trigonometric equations. Coordinate systems in the plane. The distance formula. Equations for the line and the circle in the plane. The equations of the ellipse, the hyperbola and the parabola on normal form.

Instruction

Seminars, lectures and teaching sessions.

Assessment

A passing grade in the entire course requires passed presentations on prescribed assignments within the part Computer introduction (1 credit), active participation in seminars and lectures within the part Seminars (1 credit), and approved examination within the part Basic Mathematics (3 credits). When all parts are passed, the course grade is decided by the examination result on the part Basic Mathematics.

Other directives

The course can not be included in higher education qualification together with Basic Course in Mathematics.