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Valid for year : 2010
 
TATA55 Abstract Algebra, 6 ECTS credits.
/Abstrakt algebra /

For:   C   CS   D   IT   Mat   Y  

 

Prel. scheduled hours: 40
Rec. self-study hours: 120

  Area of Education: Science

Main field of studies: Mathematics, Applied Mathematics

  Advancement level (G1, G2, A): G2

Aim:
The course is intended to give basic skill and proficiency in the concepts and methods of abstract algebra and its applications, particularly in computer science, coding theory and cryptology. In particular, students should, after completing the course:
  • Be able to use the Chinese remainder theorem to solve system of congruences
  • Be proficient in the use of Burnside's theorem for solving combinatorial problems involving group actions
  • Know how to calculate with permutations
  • Be able to explain and prove Cayley's and Lagrange's theorem of elementary group theory.
  • Know the basic facts in the theory of finite fields
  • Be able to calculate the splitting field of a low-degree polynomial
  • Be able to state the fundamental theorem of finite abelian groups
  • Be able to state the tower theorem and primitive element theorem for finite field extensions


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Mathematics corresponding to basic courses in discrete algebra and linear algebra.

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Organisation:
The theory is dealt with in lectures and office hours.
The course runs over the entire autumn semester.
Course contents:
Groups, subgroups, quotient groups, group homomorphisms, rings, esp. PID:s, ideals, ring homomorphisms, fields, extension fields, finite fields, the Chinese Remainder Theorem.
Course literature:
T. Judson: Abstract Algebra, Theory and Applications, Lolab ("on demand") or P-A.Svensson: Abstract Algebra, Studentlitteratur.

Examination:
Hand-in assignments
 6 ECTS
 


Course language is Swedish (under certain circumstances the course might be offered in English).
Department offering the course: MAI.
Director of Studies: Göran Forsling
Examiner: Jan Snellman
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 01/27/2015