AR100503 BASIC METHODS II

General university college entrance requirements

The course shall provide knowledge in mathematics relevant for problems which may be encountered in the study of management, business and economy.

The course shall provide basic knowledge in probability and statistics. By solving problems the students are expected to gain insight and training in the use of statistical methods.

The course shall provide training in logical thinking.

Mathematics:
- Elementary algebra.
- Functions of one variable. Definition of function; polynomial and rational functions; asymptotes.
- Differentiation and analysis of functions. Limits, continuity, methods for differentiation, simple and composite functions, the chain rule, computation of elasticities.
- Application of differentiation: Problems related to maximum and minimum.
- Exponential and logarithmic functions: The number e, natural logarithms, continuous interest, differentiation and discussion of exponential- and logarithmic functions.
- Mathematics of finance: Series, annuity, current value, effective interest.
- Functions of several variables: Partial differentiation, stationary points. Problems of maximum and minimum for two variables. Problems of maximum and minimum under biconditions (Lagrange’s method).
- Simple computation with integrals as the opposite of differentiation, definite integrals and areas. The treatment is adjusted to be relevant for the application in business and social economic topics.

Probability and Statistics:
- Descriptive statistics: Inference for typical value and spread, frequency distribution, graphical presentations.
- Combinatorics and probability: The definition of probability, probability models, calculation of probabilities, conditional probabilities.
- Discrete random variables. Calculation of expected value and variance. Binomial, hypergeometric, Poisson distributions…
- Continuous random variables: normal distribution, normal approximation, Students t distribution….
- Several random variables. Simultaneous random distributions: Calculation of expected values, variance and covariance.
- Estimation: Point and interval estimates.
- Test of hypotheses: Hypotheses, level of significance, test methods, strength function.
- Chi squared tests , hypothesis tests in binomal model, …
- Simple correlation- and regression analysis: Estimation and tests for the regression coefficients.

Lectures. A collection of problems specified during the teaching period are to be solved and the solutions are to be collected to be at hand during the written examination.

Admission to the exam may require approval of compulsory exercises.

A three hour individual written examination.

The solution of a collection of problems specified during the teaching period are to be brought to the written examination. It will be necessary to have these solutions at hand to be able to solve some of the problems given at the examination. Photo copies are not allowed in the collection during the examination.