Dept of Mathematics

MAM604 Mathematics D 30.0 ECTS credits

DENNA SIDA FINNS OCKSÅ PÅ SVENSKA

General information about studying at Luleå University
TIMEPERIOD:

LANGUAGE: Swedish

EXAMINER
T Gunnarsson Univ lekt

PREREQUISITES
MAM603

COURSE AIM
The course aims to give broad and deeper knowledge and understanding of mathematics and aims at developing the students ability to to use his or her mathematical knowledge.

CONTENTS
The course consists of a seminar, courses and a D-paper. a) Seminar Participation in a seminar on the history of mathematics (2 credits). The participants give seminars on selected parts from the history of mathematics. Attendance is mandatory. b) Courses The following courses ( each 4 credits) 1. Geometry 2. Computer algebra with Maple. Geometry (4 credits) The course treats euclidean geometry, projective geometry and differential geometry for curves and surfaces. Literature: Roe, John: Elementary Geometry, Oxfor University Press (latest edition) Computer algebra with Maple (4 credits) Maple is a computer program which supports symbolic manipulation. This means that apart from numerical computations, plotting of curves and diagrams one can perform symbolic manipulations - differentiation, determination of primitive functions, solving equations, studying of differential equations etc. Hence one can let the computer do all routine computations, test hypotheses etc. It is also possible to write program (or to use othe peoples programs) and to define your own functions in Maple. The teaching is for the most part in the form of computer laborations. Literature: Redfern, Darren: The Maple Handbook, Springer-Verlag, latest edition (1996) Heck, AndrŽ: Introduction to Maple, latest edition (1996) c) D-paper (thesis) 10 credits Alternatively one can choose a 20 credit paper, which is required for "magisterexamen". For magisterexamen one may also do a C-paper and a D-paper (each 10 credits). In this case the D-paper should be a continuation and deepening of the C-paper. The work with the paper should be a deeper study of some part of mathematics. The work with the paper includes planning and carrying out of an independent work. The work is done with the supervision of the examiner of the paper and can in some cases be attached to some of the departments internal or external research projects. Topics can, for example, be chosen from the following areas: Linear algebra Mechanical systems The calculus of variations Stochastic processes, ergodic theory and information theory The history of mathematics Mathematical didactics The choice of topic has to be done in concensus with the examiner Work with the D-paper may not commence until MAM603 or a corresponding course i completed. The D-paper has to be presented at a seminar. Literature: The literature is chosen in cooperation with the examiner.

TEACHING
The teaching consists of lectures, computer exercises and tutorials. The course can in its entirety and in part be taught in english.

EXAMINATION
The examination consists of written and oral examination.
COURSE GRADE SCALE: G, VG

ITEMS AND CREDITS 
Thesis                                                      	15.0 ECTS
Written exam                                                	6.0 ECTS
Written exam (Geometry)                                     	6.0 ECTS
                                                            	3.0 ECTS

COURSE LITERATURE
See the individual courses.

REMARKS
Recommended prerequisites MAM603. For the D-paper the following holds: MAM603 or a corresponding course must be completed before work with the D-paper is started. The course Computer algebra is taught together with MAM074. The course Geometry is taught together with MAM097. The Seminar on the history of mathematics is taught together with MAM605 and MAM095.
Last modified 97-03-05
Back to departement menu