VU-PPMD230 .

• Linear algebra: Linear equation systems, Gauss elimination, inverse matrices, determinants, bases, eigenvalues and eigenvectors, vector spaces and subspaces, linear transformations, change of basis, inner products and inner product spaces, norm and length, orthogonality, least squares problems, orthogonal projections. If time: Selected topics among quadratic forms, singular value decomposition, principal component analysis, Tikhonov regularization.
• Mathematics Education: Review and exploration of the varied ways of thinking and working in mathematics, based on curricula, competence goals and principles for good mathematics teaching. Planning, implementation and assessment of and for learning, based on mathematics education principles for good mathematics teaching.

Adapted education will be integrated into the mathematical and mathematics education content of the course.

Knowledge:

The students should:

• be familiar with basic concepts and theorems from the theory.
• be familiar with basic methodology in linear algebra.
• have knowledge of mathematics education principles and theories that together provide a varied repertoire of learning strategies and work and assessment methods in mathematics.
• have knowledge of curricula and competence goals in mathematics aimed at grades 8-13.

Skills

The students should:

• be familiar with basic methods for solving equation systems, also numerically.
• be able to use the theory to solve problems within linear algebra.
• be able to plan, implement and assess teaching based on research and experience-based knowledge and the school's governing documents.
• be able to lead and facilitate teaching sequences that lead to good academic and social learning processes.
• be able to use varied working methods, adapt the teaching, and create a motivating and inclusive learning environment.
• be able to use forms of assessment that contribute to promoting learning in the subject.

General competence

The students should:

• be able to reflect on their own teaching practice in mathematics, further develop their own mathematics education competence through professional literature, research and experience, and contribute to both colleagues' and the school's development.
• be able to communicate mathematics education issues, orally and in writing.
• be able to orient themselves in, and critically relate to, professional literature.