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Abstract Algebra, 6 credits
Abstrakt algebra, 6 hp
TATA55
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Jan SnellmanDirector of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 36 hRecommended self-study hours: 124 h
ECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2XCourse offered for
- Mathematics
- Computer Science and Engineering, M Sc in Engineering
- Information Technology, M Sc in Engineering
- Computer Science and Software Engineering, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Computer Science, Master's programme
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Mathematics corresponding to basic courses in discrete algebra and linear algebra.Intended learning outcomes
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
Course content
Groups, subgroups, quotient groups, group homomorphisms, rings, esp. PID:s, ideals, ring homomorphisms, fields, extension fields, finite fields, the Chinese Remainder Theorem.
Teaching and working methods
The theory is dealt with in lectures and office hours.
The course runs over the entire autumn semester.
Examination
| UPG2 | Assignments | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Jan SnellmanCourse website and other links
http://www.mai.liu.se/und/kurser/index-amne-tm.htmlEducation components
Preliminary scheduled hours: 36 hRecommended self-study hours: 124 h
Course literature
Additional literature
Books
- P-A.Svensson, Abstract Algebra, Studentlitteratur
- T. Judson, Abstract Algebra, Theory and Applications
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG2 | Assignments | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Books
P-A.Svensson, Abstract Algebra, Studentlitteratur
T. Judson, Abstract Algebra, Theory and Applications
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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X
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UPG2
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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UPG2
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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X
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UPG2
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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| 3.3 Communication in foreign languages |
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X
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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