MATB33 Introduction to Higher Analysis, 7.5 credits, is a compulsory course for a Bachelor of Science degree in mathematics. The course can be taken as an stand-alone course. The course is given at half-study pace during the second half of each semester. The course is given in English.

Course Content
The course treats:

Properties of the real numbers R: completeness axiom, Cauchy sequences, cardinality of rational and irrational numbers.
Topology in Rⁿ: open and closed sets, p-norms, convergence, compactness and the Bolzano-Weierstrass theorem, connected sets.
Continuous functions in Rⁿ: intermediate value theorem, min-max theorem, uniform continuity, continuity of inverse functions, implicit function theorem.
Convergence of sequences and series of functions: pointwise, absolute and uniform convergence, termwise differentiation and integration, power series.
Examples of applications to selected topics relevant to mathematical research at the Centre for mathematical sciences.

Teaching
The teaching consists of lectures and seminars. A mandatory project assignment is included in the course.

Assessment
The examination consists of the following parts:

project assignment, 2.5 credits (grading scale: Fail, Pass)
written examination at the end of the course, 2.5 credits, (grading scale: Fail, Pass)
oral examination at the end of the course, 2.5 credits, (grading scale: Fail, Pass, Pass with distinction)

The project assignment is examined in writing during the course and presented orally at the end of the course. Peer response is included in the requirements for the project.

The oral examination is only given to those students who have passed the written examination and also concerns questions about the project assignment.

In order to obtain the grade Pass on the entire course, it is required to pass the project assignment as well as the written and oral examinations. The final grade for the entire course is determined by the grade on the oral examination.

Course Literature

Jan-Fredrik Olsen: Introduction to Higher Analysis, Lecture Notes, compendium handed out by the department)

Official Course Description

Syllabus in English
Kursplan på svenska

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science