# Mathematics and Mathematics Teaching II

30 ECTS credits

Module 1 Linear algebra, 7.5 ECTS cr

Linear space and subspace. Linear dependence, basis and dimension. Coordinates and change of basis. Scalar product and normalization. Linear transformations, eigenvalues, eigenvectors and quadratic forms.

Module 2 Probability and statistics, 7.5 ECTS cr

Diagrams, measures of central tendency and dispersion, and relationships in descriptive statistics. Common misconceptions and misinterpretations, and misleading statistics. Statistics and probability in a teaching and learning perspective. Outcome, event, independence, conditioning and combinatorial correlation. Stochastic variables, distribution functions, some discrete and continuous distributions, expected value, standard deviation and variance. Probability distributions as integrals. Estimate, confidence interval and hypothesis testing. Illustration and investigation of statistical correlation with digital tools, and didactical aspects.

Module 3 Modelling with ordinary differential equations, 7.5 ECTS cr

Translate problems of change in technology, science, and social sciences into mathmatical problems that can be studied with the help of ordinary differential equations. Analytical methods for solving first order linear equations, separable equations, and higher order linear equations with constant coefficients. Eigenvalue-based analytical methods for linear systems with constant coefficients. Qualitative investigation with the help of phase-plane portraits. Euler's explicit method for solving differential equations. Numerical solutions of non-linear differential equations with the help of mathematical software. Modelling with differential equations in a school perspective.

Module 4 Geometry, 7.5 ECTS cr.

Classical Euclidean geometry and geometry problem solution. Axiomatic-deductive system. Definitions, theorems and proofs for triangle and circle geometry. Constructions with compasses and ruler, constructions with concrete material and constructions with dynamic geometry software. Analytical geometry. Outline of non-Euclidean geometries. The history of geometry, the role of geometry in school mathematics education and didactical aspects.

Linear space and subspace. Linear dependence, basis and dimension. Coordinates and change of basis. Scalar product and normalization. Linear transformations, eigenvalues, eigenvectors and quadratic forms.

Module 2 Probability and statistics, 7.5 ECTS cr

Diagrams, measures of central tendency and dispersion, and relationships in descriptive statistics. Common misconceptions and misinterpretations, and misleading statistics. Statistics and probability in a teaching and learning perspective. Outcome, event, independence, conditioning and combinatorial correlation. Stochastic variables, distribution functions, some discrete and continuous distributions, expected value, standard deviation and variance. Probability distributions as integrals. Estimate, confidence interval and hypothesis testing. Illustration and investigation of statistical correlation with digital tools, and didactical aspects.

Module 3 Modelling with ordinary differential equations, 7.5 ECTS cr

Translate problems of change in technology, science, and social sciences into mathmatical problems that can be studied with the help of ordinary differential equations. Analytical methods for solving first order linear equations, separable equations, and higher order linear equations with constant coefficients. Eigenvalue-based analytical methods for linear systems with constant coefficients. Qualitative investigation with the help of phase-plane portraits. Euler's explicit method for solving differential equations. Numerical solutions of non-linear differential equations with the help of mathematical software. Modelling with differential equations in a school perspective.

Module 4 Geometry, 7.5 ECTS cr.

Classical Euclidean geometry and geometry problem solution. Axiomatic-deductive system. Definitions, theorems and proofs for triangle and circle geometry. Constructions with compasses and ruler, constructions with concrete material and constructions with dynamic geometry software. Analytical geometry. Outline of non-Euclidean geometries. The history of geometry, the role of geometry in school mathematics education and didactical aspects.

Progressive specialisation:
G1N (has only upper‐secondary level entry requirements)

Education level:
Undergraduate level

Admission requirements:
MAGL11 with at least 10 ECTS cr completed, or documented equivalent knowledge acquired through courses previously part of the teacher education program

Selection:

Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.

### This course is included in the following programme

- Secondary Education Programme: Upper-Secondary School: Mathematics (studied during year 1)
- Secondary Education Programme: Upper Secondary Education Programme: Mathematics - Physics (studied during year 1)
- Secondary Education Programme: Upper Secondary Education Programme: Mathematics - Technolog (studied during year 1)
- Secondary Education Programme: Upper Secondary Education Programme: Mathematics (studied during year 1)

### More information

#### Choose occasion

Campus, 100%
Options

- Start Spring 2019
- Mode of study Campus
- Language Swedish
- Course code MAGL12
- Application code KAU-31070
- Study pace 100% (Day)
- Study period week 4–23