DRE 7017 Mathematics, Ph.D.
The language of mathematics is extensively used to analyse problems in economics and finance, and mathematical models, theories, and methods are extensively used to solve problems. The mathematical requirements of a doctoral student go beyond the material usually taught in courses at the bachelor and master level, and this course will teach the beginning doctoral student more advanced mathematical models, theories, and methods. Topics include linear algebra and matrix methods, introduction to function spaces and functional analysis, optimisation in several real variables, differential and difference equations, optimal control theory, and fixed point theory.
The course is designed for students in the following programmes:
Ph.D. specialisation in Economics
Ph.D. specialisation in Finance
After completing the course, the student will have advanced knowledge of mathematical concepts, models, theories, and methods. The student will have an advanced understanding of selected mathematical topics, and specialized understanding of how mathematical models and methods can be used in economics and finance.
After completing the course, the student will be able to analyse quantitative problems using the mathematical language, and be able to use mathematical models and methods to solve these problems. The student will be able to assess solution strategies, be able to carry out necessary computations correctly and precisely. The student will be able to give mathematical arguments for his conclusions, and be able to formulate written answers that explain the methods used and interpret the solutions obtained. The students will be able to see connections between mathematics and other subjects, especially economics and finance.
After completing the course, the student will be able to reflect upon central assumptions for the models and theories used, and critically assess if they are met in applications. The student will be capable of critical thinking. The student will be able to reflect upon the results obtained, and critically assess if they are reasonable.
The course will be based around the following topics:
- Sets and point set topology
- Vectors and linear algebra
- Real analysis in one and several variables
- Unconstrained and constrained optimization
- Correspondences and fixed points
- Differential equations and dynamical systems
- Control theory in continuous and discrete time
There will be twelve lectures, and a program for each lecture will be given (including reading assignments and exercises).
Mathematical software may be used during lectures for illustration purposes.
Enrollment in a PhD programme is a general requirement for participation in PhD courses at BI Norwegian Business School.
External candidates are kindly asked to attach confirmation of enrollment in a PhD programme when signing up for a course. Other candidates may be allowed to sit in on courses by approval of the course leader. Sitting in on a course does not permit registration for the course, handing in exams or gaining credits for the course. Course certificates or confirmation letters will not be issued for sitting in on courses.
Due to the Covid-19 pandemic, there may be deviations in teaching and learning activities as well as exams, compared with what is described in this course description.
|Exam category||Weight||Invigilation||Duration||Support materials||Grouping||Comment exam|
Form of assessment:
Internal and external examiner
Examination when next scheduled course
|Form of assessment:||Written submission|
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|Resit:||Examination when next scheduled course|
Student's own work with learning resources
A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 4 ECTS credit corresponds to a workload of at least 110 hours.