Mathematical Structures
Matematiska strukturer

FMAN65F, 6 högskolepoäng

Gäller från och med: Spring 2023
Beslutad av: Maria Sandsten
Datum för fastställande: 2023-01-14

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMAN65
Undervisningsspråk: Swedish

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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).

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

Sets. Real numbers. Metric spaces. Algebra (groups and linear spaces). Banach spaces and Hilbert spaces with applications.

Kurslitteratur

Kaplansky, I.: Set Theory and Metric Spaces. American Mathematical Society. 2001. ISBN 9780821826942.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, seminarier

Kursens examination

Examinationsformer: Skriftlig tentamen, muntlig tentamen. 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.
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: FMAF01 Analytic functions and FMAF05 Systems and Transforms, or equivalent.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: https://canvas.education.lu.se/courses/20374