# Mathematics 2, module 2 Statistics and Probability Theory 15MAT22

## Course Objectives

*Mathematics 2 –Module 2* covers the topics *statistics, probability and didactics*. In this course, the students will acquire insight into the fundamental methods and models of statistics and how they are used for analyzing realistic situations. This means that the students must also learn how numerical values can represent insight in numerical materials, how to evaluate uncertainty in numerical materials, and they must develop insight into what conclusions may be drawn on such a basis. In order to gain this understanding, the students will learn the concept apparatus of statistics, they will practice reading and interpreting the tables and diagrams which are normally used to present numerical materials, and they will study those applications of these mediums which are relevant to science and social life.

The students will also acquire a thorough knowledge of the probability concept, and will be able to discern between the empirical and the theoretical approaches to this concept. They will also gain insight into the relationship between probability and statistics. The students will practice combinatorics and combinatorial probability, and learn how various kinds of games and choice-situations may be analyzed.

They must be able to use spread-sheets to analyze collected numerical data and create simulations, they will expand their knowledge of how spread-sheets may be used for instruction in schools, and they will learn to organize spread-sheets so that they are comprehensible and useful to others.

Students will gain experience in realistic communication situations, where both planning and implementation of teaching mathematics are included, and they must also be able to demonstrate that they can reflect upon this.

For the specialization unit Mathematics 2, development of pure knowledge of the subject will be an essential goal. Students will of course become acquainted with the mathematics that is taught in schools, where inductive methods are central, but they must also study the discipline mathematics, and gain some experience of how it is pursued as a logical-deductive science.

## Course Description

Module 2 provides an introduction to statistics and probability calculations based on the topics:

*Basic statistical concepts such as probability, variance and standard deviation - analysis of data using charts and graphs - the interpretation and implications of the concept of probability - probability models, and application of such models in model building and problem solving - combinatorial selection methods and principles - the interpretation and application of stochastic variables - the normal probability distributions: binomial, hypergeometric, normal and Poisson - the main principles of hypothesis testing and application to practical problems - the basic theory of correlation and regression. *

Students will complete subject didactics work, where the theme will be the use of ICT in mathematics teaching. Students will become familiar with the Knowledge Promotion curriculum’s requirements concerning the use of ICT in mathematics teaching, and reflect on how Knowledge Promotion competence aims may be achieved. They must inform themselves about what is available on the Internet, and they will gain insight into the use of standard applications for mathematics.

## Learning Methods

Mathematics 2 - Module 2 is taught over one academic year, with final examinations in May / June. Four hours teaching per week will normally be offered in each of the modules during the teaching weeks (teaching weeks will be specified in the semester schedule). A teaching sequence will consist of both lectures and exercises; however, students can expect a degree of flexibility with regards to the organization of the teaching). In addition, individual instruction will be offered in work on exercises.

The subject-didactics work described above is two-fold, with a submission at the end of each semester.

## Assessment Methods

The grade in Mathematics 2 is calculated on the basis of the grades for the two 5-hour written examinations, one grade for each of the two modules, and the subject-didactics work. In calculating the final grade, the written examinations count for 80% and the subject-didactics work counts 20%.

All components must receive passing marks before the final grade may be awarded.

Letter grades from A to F will be awarded, where A is the highest grade, and E is the lowest passing grade. F is a failing grade.

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

Publisert av / forfatter Ian Harkness <Ian.HarknessSPAMFILTER@hit.no>, last modified Ian Hector Harkness - 11/11/2009