Mathematics (31-45)

Aim

After completing the course, students will be able to - Formulate and explain basic concepts, laws and theorems in linear algebra, probability and statistics - Demonstrate basic skills in calculus, problem solving and applications of linear algebra, probability and statistics through the application of its central concepts, theorems and methods - With good safety perform standard calculations in linear algebra, probability and statistics - Use statistical software - Describe the historical development of mathematics and discuss its role in society from an international perspective and a gender perspective, and give examples of how this can be addressed in the teaching of mathematics in schools

Content

The course covers basic linear algebra and statistics, namely: Vector geometry, scalar and vector products, lines and planes in different representations, quadratic curves, quadratic surfaces. Matrices and linear transformations. Determinants, area and volume change. Simultaneous equations, least-squares method. Bases and base changes. Eigenvalues and eigenvectors, spectral theorem, diagonalization, recursive effects, quadratic forms. Basic probability theory with sample space, events and the probability concept. Random variables and their properties in the form of probability distributions, expected value, variance, covariance and correlation. Special treatment of normal distribution and binomial distribution. Descriptive statistics and index calculations are discussed. Uncertainty of parameter estimation is illustrated via confidence intervals. Approximate linear relationships is studied in regression analysis. Statistical surveys and statistics in school. Use of statistical software. Beginning with basic definitions and theorems by reasoning, evidence and skills training as well as theoretical reasoning exercises, students work on solving tasks, choose the appropriate solution once, examine and explain mathematical relationships, as well illustrate and present solutions. Additionally, the course covers the history of mathematics with a focus on the development of key mathematical ideas, concepts and methods. The course also highlights the role of mathematics in society from different perspectives and how it and the historical development can be treated in school education.