[Forside] [Hovedområder] [Perioder] [Udannelser] [Alle kurser på en side]
LEARNING OBJECTIVES: The objective of the course is to give the participants a basic knowledge of the notions and methods of mathematical analysis with emphasis on arguments and rigorous mathematical proofs. At the end of the course, the participants should be able to give rigorous proofs of elementary statements involving metric spaces, limits, continuity, differentiability and series and sequences of functions defined on Euclidian or metric spaces.
COURSE DESCRIPTION: The course gives a rigorous definition of real and complex numbers and treats the fundamental notions of mathematical analysis such as: finite dimensional spaces, basic topology and metric spaces, limits and continuity, derivatives of functions of one or several variables, sequences and series of functions, and integral notions.
COURSE SUBJECT AREAS: Real and complex numbers and finite dimensional spaces, basic topology, metric spaces, limits and continuity, derivatives of functions of one or several variables, sequences and series of functions, and integral notions.
LECTURER: Jørgen Hoffmann-Jørgensen
TEACHING METHOD: Lectures and take-home problem sets
TEACHING LANGUAGE: English
LITERATURE: Textbook: Rudin, Walter. Principles of Mathematical Analysis , 3. edition, Ed. McGraw-Hill, 1976. Chap.1 p.1-17 (not the Appendix), Chap.2 p.24-43, Chap.3 p.47-75 (not Sec.3.52-3.55), Chap.4 p.83-95 (not Sec.4.28-4.31), Chap.5 p.103-113, Chap.7 p.143-161 (not Sec.7.27-7.33).
Lecture Notes: Hoffmann-Jørgensen, Jørgen. Supplementary Notes to Rudin's book:
Principles of Mathematical Analysis. p.1-43
FORM OF ASSESSMENT: A 4-hour written final exam
EXAMINATION AIDS ALLOWED: All - except any means of electronic communication including calculators, mobile phones and PCs.
