Teaching language: English
Application code: 20119
Open for exchange students: Yes
Module 

Credit distribution 

Examination dates 
Sp1 
Sp2 
Sp3 
Sp4 
Summer course 
No Sp 
0107 
Examination 
7,5 c 
Grading: TH 



7,5 c





19 Mar 2021 pm J, 
08 Jun 2021 am J, 
16 Aug 2021 am J

In programs
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
TKTEM ENGINEERING MATHEMATICS, Year 3 (elective)
Examiner:
Per Salberger
Go to Course Homepage
Eligibility
General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Basic course in linear algebra
Aim
In swedish only
Learning outcomes (after completion of the course the student should be able to)
 define and explain what a binary operation is.
 define the most important algebraic structures: groups rings and fields.
 give exmples of groups consisting of congruences of integers, matrices, permutations, and symmetries of geometric objects.
 define what a subgroup and a coset of a subgroup is.
 use equivalence relations to study cosets and to prove Lagrange’s theorem.
 form quotient objects of groups and rings by means of normal subgroups and ideals.
 define the concepts: homomorphism, isomorphism, kernel and image of a homomorphism.
 use the Euclidean algoritm for integers and polynomials over a field and describe the corresponding theories of unique prime factorization.
 explain the relation between finite field extensions and zeros of polynomials over the base field.
Content
Operations, groups, subgroups, symmetries, permutations, equivalence relations and partitions, prime numbers, the fundamental theorem of arithmetic, congruences, orders of groups and elements in groups, cyclic groups, cosets and Lagrange's theorem, isomorphisms, direct product of groups, isomorphism types of finite Abelian groups, Cayley's theorem, group homomorphisms, image and kernel, normal subgroups, quotient groups, the fundamental homomorphism theorem, orbits, stabilizers, Burnside's theorem, Sylow's theorem, definition of rings and fields, integral domains, characteristic of a field, polynomial rings, the division algorithm, irreducible polynomials,Euclidean rings, unique factorization domains, ring homomorphisms, ideals, principal ideals, quotient rings, adjunction of roots of polynomials, something about the existence and construction of finite fields, zeros of polynomials, factorization in polynomial rings, various number systems.
Organisation
The course consists of about 15 lectures and 15 lessons. Classes are devoted to demonstrations of the exercises in the textbook.
Literature
Durbin: Modern Algebra, John Wiley & Sons
Examination including compulsory elements
Written exam