Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course MATP33F valid from Spring 2021

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  • English
  • Every other spring semester
  • The course aims to provide, in comparison with the course Algebraic structures, a deeper understanding of group theory and ring theory as a basis for further studies in algebraic subject areas, and to provide general mathematical knowledge.

  • • Groups: Permutation groups. Burnside's lemma with application to Pólya arithmetic. Sylow's theorems. Symmetric and alternating groups. The structure of finitely generated Abelian groups.
    • Rings: Noetherian and Artinian rings and modules. Artin-Wedderburn's theorem. Finitely generated modules over a principal ideal domain with application to Jordan's normal form of matrices.
    • Linear algebra: Multilinear mappings. Tensor products.

Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to, in detail, explain the concepts, theorems and methods included in the course,

    be able to identify the most important theorems in the course and present their proofs.
Competences and Skills
  • For a passing grade the doctoral student must
  • in connection with problem solving be able to demonstrate the ability to integrate knowledge from the different parts of the course,

    be able to independently identify problems that can be solved by methods that are part of the course and use appropriate solution methods,

    be able to explain the solution to a mathematical problem within the course framework, in speech and in writing, logically coherently and with adequate terminology.
Judgement and Approach
  • For a passing grade the doctoral student must
  • be able to argue for the importance of group theory and ring theory as tools in other areas such as algebraic geometry and algebraic number theory, and discuss their limitations.
Types of Instruction
  • Lectures
  • Seminars
Examination Formats
  • Written exam
  • Oral exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • FMAN10 Algebraic structures
Selection Criteria
  • Bhattacharya, P. B., Jain, S. K. & Nagpaul, S. R.: Basic Abstract Algebra. Cambridge University Press, 1994. ISBN 9780521466295.
Further Information
Course code
  • MATP33F
Administrative Information
  • 2020-09-24
  • Professor Thomas Johansson

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