Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMAN10F valid from Autumn 2013

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  • English
  • Every spring semester
  • The course is established in order to give the doctoral students knowledge about basic concepts of abstract algebra, which is useful for further studies in mathematics as well as within digital technology and coding theory.
  • Rings: Polynomial rings. Ideals and quotient rings. Ring homomorphisms and isomorphisms.

    Groups: Lagrange's theorem. Permutation groups. Normal subgroups and quotient groups. Group homomorphisms and isomorphisms.

    Fields: Characteristic. Finite fields. Field extensions.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to describe basic properties of integers and polynomials, and be able to compute with congruences modulo these objects.

    be able to describe basic properties of the important concepts in abstract algebra; ring, ideal, quotient ring, group and field.

    be able to explain, in writing and orally, the contents of some central definitions and proofs.

    be able to give examples of and illustrate some important applications of the course contents.

    have acquired basic knowledge for further studies in algebra or subjects based on algebraic methods.
Competences and Skills
  • For a passing grade the doctoral student must
  • For a passing grade the student must

    be able to independently construct proofs of simple statements within the framework of the course.

    be able to show a good ability to independently, in writing and orally, explain mathematical reasoning in a well structured way, with clear logic.
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Exercises
Examination Formats
  • Written exam
  • Oral exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • In terms of content, basic courses in calculus (in one and several variables) and linear algebra are sufficient. However, the mathematical maturity provided by one or more further courses in mathematics is helpful .
Selection Criteria
  • Hungerford, T.: Abstract Algebra: An Introduction. Cengage Learning, 2012. ISBN 9781111573331.
Further Information
Course code
  • FMAN10F
Administrative Information
  •  -01-27
  • FN1/Anders Gustafsson

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