i.uoh.kau.magl12.31071.20191MAGL12
2019-02-12T15:59:37.314+01:002025-01-01T00:00:00.000+01:00Matematik II med didaktisk inriktningMathematics and Mathematics Teaching IIKursen är den andra kursen i matematik och matematikdidaktik på ämneslärarprogrammet och är en fortsättning på kursen MAGL11. Kursen behandlar linjär algebra, sannolikhetslära och statistik, geometri och modellering med ordinära differentialekvationer samt didaktisering kring motsvarande områden i skolans matematikundervisning.Module 1 Linear algebra, 7.5 ECTS crLinear 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 crDiagrams, 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 crTranslate 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. false30.0Genomgången kurs MAGL11 varav minst 10hp G, eller dokumenterade motsvarande kunskaper från kurser som tidigare ingått i ämneslärarprogrammet.MAGL11 with at least 10 ECTS cr completed, or documented equivalent knowledge acquired through courses previously part of the teacher education programgrundlaggande