# Mathematics for the natural sciences - programme subject in programmes for Specialization in General Studies (MAT3-01)

Denne læreplanen utgår gradvis fra 1.8.2021

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## Main subject areas

### Geometry

Mathematics R1

The main subject area deals with the measurement, calculation and analysis of figures in the plane. Central to the main subject area are two approaches to geometry, which complement each other. The first focuses on the use of geometric loci, congruence and symmetry to solve problems by pure geometrical arguments. Geometric construction using a compass and straightedge is based on these concepts. The other focuses on the use of vectors and coordinates to convert geometrical problems to algebra. In addition, the main subject area deals with the development of formal logical arguments and proofs in a geometrical context.

Matematics R2

The main subject area deals with the measurement, calculation and analysis of figures in space. It also focuses on coordinates, equations and vectors, which are used to determine figures and calculate lengths, angles, area and volume. It also includes three-dimensional vectors, scalar and vector products and parameter presentation.

### Algebra

Mathematics R1

The main subject area deals with the fundamental language of symbols in mathematics. Calculation, manipulation and argumentation using mathematical symbols are therefore absolutely central to the main subject area. Argumentation involves the use of different types of proof and logical relations. In addition, the main subject area covers key concepts such as polynomials, polynomial division and rational, logarithmic and exponential expressions.

Mathematics R2

The main subject area deals with the analysis and calculation of numerical patterns, finite sums and infinite series. Basic methodologies in the main subject area are recursion and induction. It also focuses on series, convergence and proof by induction.

### Functions

Mathematics R1

The main subject area deals with the analysis of the dependence between two quantities. It focuses on relations between quantities from algebra, geometry or practical areas, which are analyzed by functions and graphs. The main subject area also deals with the relation between a function and its derivative. It covers polynomial functions, power functions, rational functions, logarithmic functions, exponential functions and combinations of these. Core concepts in the main subject area are boundedness, continuity and differentiability.

Mathematics R2

The main subject area deals with the application of periodic functions for modelling periodic phenomena. It also involves the derivation and integration of central functions in modelling and calculations. Central functions included in the main subject area are polynomial functions, power functions, rational functions, logarithmic functions, exponential functions, periodic functions and combinations of these.

### Combinatorics and probability

The main subject area deals with systematic counting methods that form the basis for calculating probability. It also focuses on the fundamental concepts of statistical independence and conditional probability and about random and non-random selection.

### Differential equations

The main subject area deals with applying mathematics for the analysis and calculation of dynamic phenomena. This main subject area includes standard methods for linear and separable differential equations that are applied to practical problems. The subject area also involves key concepts such as initial conditions, vector diagrams and integral curves.

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