Syllabus academic year 2010/2011
(Created 2010-07-25.)
Credits: 4,5. Grading scale: UG. Cycle: G1 (First Cycle). Main field: Technology. Language of instruction: The course will be given in Swedish. Compulsory for: Pi1. Course coordinator: Studierektor, Anders Holst,, Mathematics. Recommended prerequisits: Knowledge from courses in calculus and linear algebra which are taught in parallel. Assessment: Written and oral reports of project works, 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, demonstrating the need for rigour through simple examples. Furthermore, the student should practise his or her ability to seek information, and to put forward and present mathematical reasoning, even in popular form. The student should also get some notions of current and modern mathematical research.

Knowledge and understanding
For a passing grade the student must

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

be able to informally describe the mathematical sciences (geometry, algebra, analysis and probability theory) and to give examples of research in classical as well as modern mathematics.

know the procedure for getting a mathematical work published, and know of some important mathematical journals.

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, and be able to provide references according to the accepted standards.

orally as well as in writing, with proper terminology, in a well-structured way and with clear logic be able to explain solutions (produced by the student or by others) to a mathematical problem, and be able to present, orally as well as in writing, a mathematical problem in a manner accesible to laypersons.

Judgement and approach
For a passing grade the student must

develop an attitude to the world around him or her, according to which 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.
Gowers, T: Mathematics: a very short introduction. Oxford University Press. ISBN 0-19-2853619.
Supplementary material.