Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMAN65F valid from Spring 2023

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  • Besides mere knowledge imparting, the course aims to give training in theorem proving, and to bring out the possibilities of a more abstract representation of mathematical concepts and the connections between them. The intention is to give an overall view elucidating the foundations of the mathematical theories in the basic courses.
  • Sets. Real numbers. Metric spaces. Algebra (groups and linear spaces). Banach spaces and Hilbert spaces with applications.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be familiar with and in his or her own words be able to explain the concepts within analysis, algebra and geometry touched upon in the course.

    be able to give examples of how these concepts are abstractions of concepts in the basic courses, and show understanding for how the abstractions serve to simplify and clarify the theory.

    in his/her own word be able to describe the logical connections between the concepts (theorems and proofs).

Competences and Skills
  • For a passing grade the doctoral student must
  • be able to demonstrate ability to identify problems which can be modelled with the concepts introduced.

    in the context of problem solving be able to demonstrate ability to, in simple situations, develop the theory further.

    with proper terminology, in a well-structured manner, and with clear logic be able to explain the connections between various concepts in the course.

    with proper terminology, suitable notation, in a well-structured manner and with clear logic be able to explain the solution to a problem or the proof of a theorem.

    have developed his or her ability to independently read and judge mathematical text at a high level.
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Seminars
Examination Formats
  • Written exam
  • Oral exam
  • The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • FMAF01 Analytic functions and FMAF05 Systems and Transforms, or equivalent.
Selection Criteria
  • Kaplansky, I.: Set Theory and Metric Spaces. American Mathematical Society. 2001. ISBN 9780821826942.
Further Information
Course code
  • FMAN65F
Administrative Information
  • 2023-01-14
  • Maria Sandsten

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