# Mathematics

### Stær2ÞA05

This course is designed to allow students to become more skilful in certain procedures in mathematics such as precision in presentation, argumentation, and the solution of assignments and problems. The main topics are algebra, powers and roots, percentages, Euclidian geometry and trigonometry.

### Stær2HJ05

This course is designed to allow students to become more skilful in certain procedures in mathematics such as understanding the concept of function, as well as acquiring adequate algebraic skills. The main topics are sets, quadratic equations, inequations, polynomials, functions and Cartesian coordinate system.

### Stær2PÞ05

This course is designed to allow students to become more skilful in certain procedures in mathematics such as precision in presentation, argumentation, and the solution of assignments and problems. The main topics are algebra, powers and roots, percentages, Euclidian geometry, trigonometry and the Cartesian coordinate system.

### Stær2MM05

This course is designed to allow students to become more skilful in certain procedures in mathematics such as understanding the concept of function, as well as acquiring adequate algebraic skills. The main topics are sets, quadratic equations, inequations, polynomials, functions and Cartesian coordinate system.

### Stær2LT05

This course is designed to allow students to become more skilful in certain procedures in mathematics such as understanding probability and statistics. Students also study propositional logic; databases, frequency tables, pictograms; averages, weighted average, standard deviation, mean deviation, actual range; probability calculus, permutations and combinations; normal distribution, binomial distribution and Poisson distribution; confidence limits; correlation and conjectures tests.

### Stær3VH05

This course is designed to allow students to become more skilful in certain procedures in mathematics such as vectors and trigonometrical functions, the connection of algebra and geometry in a system of coordinates, and an introduction to combinatorics. Furthermore, the historical evolution of trigonometry and the practical knowledge of trigonometrical functions are addressed, for instance regarding geodetic surveys. It is emphasised that students acquaint themselves with plane geometry in a coordinate system and learn to prove and apply the major theorems concerned. Certain proofs are selected for discussion.

### Stær3DF05

This course is designed to allow students to become more skilful in certain procedures in mathematics such as dealing with exponential and logarithmic functions, limits and the differentiation of common functions. This course discusses differentiation and limits from a historical viewpoint, as well as practical problems where differential calculus provides the solution. The stress is on students' gaining clear insight into differential calculus and being able to argue the most significant rules involved.

### Stær3HR05

In this course, students are expected to further their knowledge gained in the coursesSTÆR3DF05. The main emphasis of the course is on integration; the fundamental theorem of calculus, the definite integral, rules of integration and techniques of integration (integration by parts, the method of substitution and integrals of rational functions/partial fraction decomposition). Students further study some applications of integral calculus, i.e. area, volume and surface area calculations. An introduction to first-order separable and homogeneous differential equations is provided and some application of differential equations are studied. Furthermore, a short introduction to series and sequences (geometric and arithmetic sequences) and inverse trigonometric functions is provided.

### Stær3FF05

In this course, emphasis is placed on how mathematics touches on things in nature and society. Students will work with exponential- and logarithmic functions, differentiation of simple functions and introduction to the application of differentiation. Students study the infinite sequences and series with relation to interest calculations. There is an introduction to the concept of vectores.

### Stær3HF05

In this course, emphasis is placed on integration and integration used to find the area between functions. Students learn different types of integration methods. Students also study first order differential equations. Students are introduced to matrix calculations and the least squares method.

### Stær3BD05

The topic of this course is diverse and covers various aspects of mathematics. The main topics are matrices, hyperbolic functions, proof by induction, complex numbers, second order linear differential equations, Taylor polynomials, and finding a numerical approximation to a solution of a differential equation using Euler‘s method. Furthermore, there is a short introduction to series and sequences (geometric and arithmetic sequences). In this course the emphasis is on learning structured presentation of formal proofs.

### Stær4CA05

The course provides an introduction to calculus where the main emphasis is laid on the theoretical aspects of the material. Several different types of mathematical proofs are studied in detail (e.g. direct proofs, indirect proofs and proofs by mathematical induction). Students are introduced to the construction of the real number system and use the axioms for the real numbers to proof simple rules. Sequences and series are studied in more detail than in prior courses, with emphasis on the limits of sequences and convergence tests for series. The main properties of continuous and differentiable functions are studied and students apply, for instance, the definition of limits of functions, and the mean- and intermediate-value theorems in proofs. The rule of l'Hopital is further used for computation of limits. The mathematical typesetting system LaTeX is introduced and students are expected to use it.

### Stær2RT05

In this course, students are expected to further their knowledge in dealing with exponential and logarithmic functions, differentiation of polynomials, sigma and Pi notation for summation and multiplication, sequences and series, and statistics. Students also study propositional logic; databases, frequency tables, pictograms; averages, weighted average, standard deviation, mean deviation, actual range; probability calculus; normal distribution, binomial distribution and Poisson distribution; confidence limits; correlation and conjectures tests.

### Stær3LD05

In this course, the main focus is on the three following topics; probability, functions and vectors. Students study sets, propositional logic, the foundation of probability with finite possibilities by using permutations and combinations. Students will learn diffentiation rules for simple functions and its applications. The concept of vector will be introduced.

### Stær3RF05

The main emphasis of the course is on understanding the concept of mathematical proof in geometry. The main topics are analytic geometry in three dimensions, spherical geometry and finite geometry.