# TMA4150 - Algebra

### Examination arrangement

Examination arrangement: Written examination

Evaluation form Weighting Duration Examination aids Grade deviation
Written examination 100/100 4 hours D

### Course content

The course gives examples of the axiomatic framework of mathematics, and it deals with groups, subgroups, homomorphisms of groups, cyclic groups, permuation groups, finite abelian groups, the fundamental theorem for finite abelian groups, normal subgroups, factor groups, group action on a set, Sylow theorems, elementary ring and finite fields, vector spaces over an arbitrary field, combinatorial counting results, elementary number theory with applications to linear congruences and codes.

### Learning outcome

1. Knowledge. The student is familiar with fundamental concepts and methods of group theory, including normal subgroups and factor groups, permutation groups and cyclic groups. The student has knowledge about the classification of cyclic and abelian groups, about Lagrange's and Cayley's theorem, in addition to Burnside's theorem for group actions. The student knows the fundamental theorem for group homomorphisms and the Sylow theorems. The student also knows the fundamental concepts from elementary ring theory with emphasis on commutative ring theory, and field theory and vector spaces over arbitrary fields. The student has some knowledge of application of group theory in enumeration and number theory in secret codes (RSA). The student has some knowledge about the axiomatic framework within mathematics, in addition to basic logic concepts and different structure of proofs.

2. Skills. The student is able to recognize group and ring structures and group actions, and to analyze simple aspects of these. Furthermore the student masters the theoretical base of application of group theory in enumeration and the number theoretical base for secret codes (RSA). In addition the student can preform elementary mathematical proofs.

### Learning methods and activities

Lectures and exercises. Retake of examination may be given as an oral examination.

### Further on evaluation

see «Teaching methods and activities».

### Course materials

Will be announced at the start of the course.

### Credit reductions

Course code Reduction From To
MA2201 7.5
SIF5021 7.5
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Third-year courses, level III

Coursework

Term no.: 1
Teaching semester:  SPRING 2020

No.of lecture hours: 4
Lab hours: 2
No.of specialization hours: 6

Language of instruction: Norwegian

Location: Trondheim

Subject area(s)
• Mathematics
• Technological subjects
Contact information
Course coordinator:

Department of Mathematical Sciences

Phone:

# Examination

#### Examination arrangement: Written examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam
Spring ORD Written examination 100/100 D 2020-05-22 09:00
• * The location (room) for a written examination is published 3 days before examination date.
If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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