Syllabus academic year 2007/2008

Higher education credits: 4,5. Grading scale: UG. Level: G1 (First level). Language of instruction: The course will be given in Swedish. Compulsory for: Pi1. Optional for: N3. Course coordinator: Studierektor, Lars-Christer Böiers,, Matematik. Recommended prerequisits: Knowledge from courses in calculus and linear algebra which are taught in parallell. Assessment: Written and oral report of project work, individually and group-wise. Compulsory attendance at the project reports. Home page:

The aim of the course is to increase the awareness of and understanding of mathematical reasoning. The course gives an introduction to the construction of mathematical theory in which the need of a strict theory is demonstrated through simple examples. Furthermore, the student should train his or her ability to seek information, and to put forward and present mathematical reasoning, even in a popular form, and to get some glimpse of current and modern mathematical research.

Knowledge and understanding
For a passing grade the student must

be able to use fundamental concepts in mathematical theory construction, and to understand their meaning.

be able to informally describe the mathematical sciences and to give examples of research in classical as well as modern mathematics.

Skills and abilities
For a passing grade the student must

be able to use logical reasoning to analyse and solve mathematical problems which require a division into several subproblems.

be able to search for articles and journals in data bases and libraries containing mathematical literature.

orally as well as in writing, with proper terminology, in a well structured way and with clear logic be able to explain the solution to a theoretical mathematical problem.

be able to present a mathematical question in a popular way, as well orally as in writing.

Judgement and approach
For a passing grade the student must

develop an attitude to the world around him or her where mathematics is a natural and precise instrument for communication and reasoning.

The construction of mathematical theories. A presentation of the mathematical sciences. A glimpse of modern mathematics.

Courant-Robbins: What is mathematics? 2nd ed. Oxford University Press. ISBN 0-19-510519-2.
Stewart: From here to infinity. Oxford Univeristy Press 1996. ISBN 0-19-283202-6.
Supplementary material.