This syllabus is valid: 2016-01-18
and until further notice
Course code: 5MA161
Credit points: 7.5
Education level: First cycle
Main Field of Study and progress level:
Mathematics: First cycle, has at least 60 credits in first-cycle course/s as entry requirements
Grading scale: VG Pass with distinction, G Pass, U Fail
Responsible department: Department of Mathematics and Mathematical Statistics
Established by: Faculty Board of Science and Technology, 2016-02-22
The course covers the basic theory of groups rings and field, including concepts like residue classes, ideals, and isomorphisms. Applications of the underlying theory is given in combinatorics, cryptology, coding theory, and geometric constructions.
Further, polynomials with coefficients in a field are studied, and how zeros of a polynomial can be found in a larger field. The general theory for such field extensions is then connected to three classical geometric problems; trisection of an angle, doubling the cube, and squaring a circle, and why these are unsolvable.
Expected learning outcomes
For a passing grade, the student must be able to
Knowledge and understanding
account for definitions and basic properties of groups, ring, and fields.
account for the basic theory of polynomials and field extensions
Skills and abilities
use structure theorems to describe finite groups
use symmetry groups and groups actions on sets
factorize polynomials over finite fields
apply algebraic codes
translate geometric construction problems to number field problems
Judgment and approach
decide the applicability of symmetries of mathematical objects.
The course requires 60 ECTS in mathematics or at least two years university studies and in both cases courses in Discrete Mathematics and Linear Algebra or equivalent. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
Form of instruction
The teaching takes the form of lectures.
The course is examined by written exam. On the written exam and for the whole course, one of the following grades is assigned: Fail (U), Pass (G), Pass with distinction (VG). In order to receive a passing grade on the course, all parts must be completed with a passing grade.
A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.
Credit transfer All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications
In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics.