Principles of Mathematical Analysis
About the course
Can be taken as a single course.
Who has to apply for admission?
• PhD students at UiT that wishes to take a PhD level course which is not going to be a part of the PhD degree they study for at UiT.
• PhD students from other institutions than UiT.
• Applicants that has achieved a master’s degree (five year master or three year bachelor degree + two year master degree), but isn’t a PhD student.
This course provides PhD students with the tools necessary for modelling and analyzing complex optimization problems, involving continuous change and uncertainty.
Admission requirements
- This course is aimed at PhD candidates from engineering disciplines, but is open to postdoc fellows if seats are available.
- PhD candidates from both UiT and NORDTEK universities may be admitted to the course. PhD candidates not registered at UiT must upload a document from their university stating that they are registered PhD candidates.
If there are 5 applicants or fewer, the course responsible will evaluate whether the course will take place.
Required prerequisites: In addition to the general admission requirements for the PhD program at UiT, the following courses must be passed before taking this subject:- Mathematics 2, 3
Recommended prerequisites: The following prior knowledge is recommended:
- Number Theory
- Set Theory
- Continuity
- Calculus
Objectives of the course
The objective of the course is to give a good understanding of some basic and advanced concepts in mathematical analysis.
Concepts from real analysis are discussed. Rational and real numbers, countable and uncountable sets are introduced. Also, basic topological concepts such as open, closed, bounded, and compact sets are introduced. Numerical sequences, series, and properties of continuous and differentiable functions are thoroughly discussed. The Riemann integral is introduced, and its properties are studied. Sequences and series of functions are studied in connection with continuity, integration, and differentiation.
Upon successful completion of the course, the following learning outcomes are expected to be achieved:
Knowledge:
After passing the course, the student is expected to be able to
- Account for the main concepts of real analysis.
- Understand and use the basic principles in mathematical analysis on a relatively high level, at the forefront of knowledge in the field.
- Contribute to the development of new knowledge, new theories, methods, interpretations, and forms of documentation in research fields connected to engineering and sciences.
Skills:
After passing the course, the student is expected to be able to:
- Solve relatively advanced problems connected to mathematical analysis of a high international standard.
Competence:
After passing the course, the student is expected to be able to
- Formulate and solve complicated problems devoted to Mathematical Analysis in a way that enables communication of research on a high level in the field.
Teaching methods
Language of instruction and examination
EnglishSchedule
The schedules are normally finalized and published well in advance of the start of the semester, often a few weeks beforehand. This gives students the opportunity to organize their studies and prepare for upcoming activities.
It is recommended to check the schedule regularly, as changes may occur.
Examination
| Oral exam | Duration: 30 Minutes |
Grade: Passed / Not Passed |
To take an examination, the student must have passed the following coursework requirements
| Report | Grade: Approved – not approved |
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