course-details-portlet

TMA4145 - Linear Methods

About

Examination arrangement

Examination arrangement: Written examination
Grade: Letters

Evaluation Weighting Duration Grade deviation Examination aids
Skriftlig 100/100 4 timer

Course content

Linear and metric spaces. Completeness, Banach spaces and Banach's fixed point theorem. Picard's theorem. Linear transformations. Inner product spaces, projections, and Hilbert spaces. Orthogonal sequences and approximations. Linear functionals, dual space, and Riesz' representation theorem. Spectral theorem, Jordan canonical form, and matrix decompositions.

Learning outcome

1. Knowledge. The student has knowledge of central concepts in the theory of metric spaces, vector spaces and Hilbert spaces. In the theory of metric spaces a key objective is that the student understand the Banach fixed point theorem. This includes an understanding of metric spaces, convergence of sequences and continuous functions. In the theory of vector spaces the main objective is that the student understand the transition from Euclidean spaces to general vector spaces. This includes an understanding of isomorphisms and bases of finite dimensional vector spaces and the relationship between linear transformations and matrices. The student is familiar with principles of matrix factorization. The student masters the basic concepts from the theory of Hilbert spaces, including orthogonality, closest point and duality. The student understands the Riesz representation theorem.

2. Skills. The student is able to apply his or her knowledge of the theory of metric spaces, vector spaces and Hilbert spaces to solve concrete problems. A key skill is that the student is able to combine results and construct new proofs using the theory acquired in the course.

Learning methods and activities

Lectures and mandatory exercises. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. Retake of examination may be given as an oral examination.

Compulsory assignments

  • Exercises

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5020 7.5
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Third-year courses, level III

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2015

Language of instruction: English, Norwegian

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Subject area(s)
  • Mathematics
  • Technological subjects
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences

Examination

Examination arrangement: Written examination

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD Skriftlig 100/100 2015-12-17 09:00
Room Building Number of candidates
Summer KONT Skriftlig 100/100 2016-08-18 09:00
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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