Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course MATM16F valid from Spring 2018

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  • The aim of the course is to consolidate and generalize resultats which the student already has encountered in earlier courses in analysis, to equip him or her with an adequate language for higher studies in mathematics, and to develop his or her ability to work with abstract concepts, which are defined through of axioms. In particular the course should form a bridge between the mathematics courses at the Faculty of Engineering and more advanced mathematics courses.
  • The fundamentals of the theory of metrical, topological and compact spaces. The Tietze extension theorem and Stone-Weierstrass approximation theorem. Elementary properties of Banach and Hilbert spaces.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to define and explain basic concepts in general topology, such as topological space, connected space, continuous map…

    be able to describe some common classes of av topologies

    be able to account for the different ways to define compactness.
Competences and Skills
  • For a passing grade the doctoral student must
  • be able to prove the theorems in the course

    be able to determine if a given family of sets forms a topological space

    be able to prove the compactness of a given topological space

    be able to actively reason with use of the terms in the course.
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Seminars
Examination Formats
  • Written exam
  • Oral exam
  • Compulsory assignments may occur,
  • Failed, pass
Admission Requirements
  • FMAA05 Calculus in one variable, FMAB20 Linear algebra, FMAB30 Calculus in several variables , FMAF01 Analytic Functions and FMAF05 Systems and Transforms.
Assumed Prior Knowledge
Selection Criteria
  • Munkres, J.: Topology. Pearson New International Edition. Pearson, 2017. ISBN 9780134689517.
  • Paperback of second edition from 2000.
Further Information
Course code
  • MATM16F
Administrative Information
  • 2018-03-02
  • Professor Thomas Johansson

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