| TATA55 |
Abstract Algebra, 6 ECTS credits.
/Abstrakt algebra /
For:
CS
D
DAV
IT
Mat
U
Y
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Prel. scheduled
hours: 36
Rec. self-study hours: 124
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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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
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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.
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Organisation:
The theory is dealt with in lectures and office hours.
The course runs over the entire autumn semester.
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Course contents:
Groups, subgroups, quotient groups, group homomorphisms, rings, esp. PID:s, ideals, ring homomorphisms, fields, extension fields, finite fields, the Chinese Remainder Theorem.
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Course literature:
T. Judson: Abstract Algebra, Theory and Applications, Lolab ("on demand") or P-A.Svensson: Abstract Algebra, Studentlitteratur.
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Examination: |
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Hand-in assignments
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6 ECTS
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Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Jan Snellman
Link to the course homepage at the department
Course Syllabus in Swedish
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