Valid from: Spring 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-03-02
Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: MATM16
Teaching language: English
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.
Knowledge and Understanding
For a passing grade the doctoral student must
Competences and Skills
For a passing grade the doctoral student must
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.
Munkres, J.: Topology. Pearson New International Edition. Pearson, 2017. ISBN 9780134689517.
Paperback of second edition from 2000.
Types of instruction: Lectures, seminars
Examination formats: Written exam, oral exam.
Compulsory assignments may occur,
Grading scale: Failed, pass
Examiner:
Admission requirements: FMAA05 Calculus in one variable, FMAB20 Linear algebra, FMAB30 Calculus in several variables , FMAF01 Analytic Functions and FMAF05 Systems and Transforms.
Course coordinators:
Web page: http://www.ctr.maths.lu.se/course/top/