Course Objectives

Mathematics 2 –Module 1 covers the topics of function theory and didactics. In this course, the students will acquire insight into the fundamental concepts and methods of function theory and how they are used to carry out standard analyses of the characteristics of functions. It is particularly important that the students develop a broad and reliable understanding of the concept of functions as it is expressed dynamically/analytically and algebraically, and that they grasp the relationship between the graph of a function and its properties. The students will gain insight into the possibilities and limitations of the function concept, and be able to demonstrate this understanding by expanding the central concepts in function theory to include functions of several real variables. In addition, the students will expand their knowledge of the basic concepts of integration and differentiation, and explore how these concepts are a natural result of the concepts and relationships which are covered in the lower secondary-school. The students will gain insight into how function theory can be used to model important phenomena and situations, and they will learn to evaluate the accuracy of such models with respect to reality.

The students must be able to use electronic graphing programs to present and analyze function diagrams in both two and three dimensions, and they will learn how such programs may be used for teaching.

The students will gain experience in a realistic teaching situation involving both planning and carrying out instruction in mathematics, and they must demonstrate that they can consider and evaluate their options.

In the specialisation unit Mathematics 2, a major objective will be development of the students’ technical knowledge of the subject. In this course, the students will encounter mathematics as a school subject, where the inductive method is preferred, but they will also view mathematics on its own premises and acquire experience in how it is practiced as a logical-deductive science.

Course Description

Module 1 provides an introduction to function theory in relation to the topics:

The function concept (how it occurs naturally and is used in the formulation and solution of practical problems) – the analysis of linear and polynomial functions – differentiation and differentiation techniques – rational functions and asymptotes – limits and continuity – L’Hôpital’s rule – exponential functions and logarithms – the origin and properties of the trigonometric functions sine and cosine – angular measurement in radians – numerical sequences and series (particularly geometric and arithmetic) – modeling with functions – indefinite integrals and anti-differentiation – the use and interpretation of definite integrals – integration techniques – real functions with two variables – simple differential equations

The students will carry out a subject didactics project in mathematics where the theme will be the use of IT in teaching mathematics. The students will become familiar with the requirements for the use of IT in the ”Knowledge Promotion” school reform, and consider how the objectives of this reform may be achieved. They will orient themselves concerning the resources available on internet, and gain insight into the use of standard programs for mathematics.

Learning Methods

Mathematics 2 - Module 1 runs over one academic year, with final examinations in May / June. 4 hours of teaching per week will be offered in each of the modules (the teaching weeks are specified in the semester schedule). A teaching sequence will consist of both lectures and exercises; a flexible approach is used with regard to how the teaching hours are utilised. In addition, individual instruction is offered with regard to exercises.
Mathematics 2 includes subject didactics. The subject didactics work is divided into two parts, with a submission at the end of each semester.

Assessment Methods

The grade in Mathematics 2 is calculated on the basis of the grades in the two 5-hour written examinations, and the subject didactics work. The two written examinations count for 80% of the grade and subject didactics work 20%.
All components must be passed before the final grade can be awarded.
Letter grades from A to F will be awarded, where A represents the highest grade, and E the lowest passing grade. Candidates who fail will receive the grade F.

Minor adjustments may occur during the academic year, subject to the decision of the Dean