Course contents *

Mathematics as a logical system. The number system, especially Peano's axioms for the natural numbers and Dedekinds construction of the real numbers. Cardinality. Basic set theory. Groups, rings, fields, linear spaces. Metric spaces, convergence, continuity, compactness, connections. Contractions and fix point theorems with applications. Analysis, in particular in R and Rⁿ: The definition of the elementary functions and the derivation of their properties. Advanced study of differential and integral calculus. The concept of area and volume.

An independent work within an area from the current mathematical literature.

Intended learning outcomes *

After the course the student should be able to

• explain basic concepts and theorems within the parts of algebra and analysis described by the content of the course,
• apply concepts, theorems and methods to solve and present the solutions of problems within the parts of algebra and analysis described by the content of the course,
• Explain and summarize results from the current mathematics literature.

Course Disposition

No information inserted

Specific prerequisites *

Completed basic course SF1626 Calculus in Several Variable and SF1662 Discrete Mathematics.

Recommended prerequisites

SF1633 Differential Equations I or similar. 

Equipment

No information inserted

Literature

No information inserted

Grading scale *

A, B, C, D, E, FX, F

Examination *

• TEN1 - Examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

An exam which may be replaced, in part och fully, by examination determined in consultation between the teacher and the students.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Kristian Bjerklöv

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Offered by

SCI/Mathematics

Main field of study *

Mathematics

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

Kristian Bjerklöv (bjerklov@kth.se)

Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.