# GRA 6035 Mathematics

## GRA 6035 Mathematics

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 graduate student go beyond the material usually taught in undergraduate courses, and this course will teach the beginning graduate student more advanced mathematical models, theories, and methods. In particular, it will introduce the students to coding using Excel. The course is taught in the first semester of the master programme. Topics include linear algebra and matrix methods, optimisation in several real variables, and differential and difference equations.

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 linear algebra and matrix methods, optimisation in several real variables, and differential and difference equations, and specialized understanding of how these 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, and to use Excel to model, solve and visualize differential and difference equations. 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.

- Linear algebra and matrix methods
- Optimisation in several real variables
- Differential and difference equations

The course is taught over one semester, and consists of lectures (36 hours) and plenary problem solving sessions (12 hours).

For each lecture, there will be a work program consisting of exercises and reading assignments. The student must learn the material presented in the reading assignments, and work through the exercises. Some of the exercises will be reviewed in lectures and plenary problem solving sessions. It is assumed that the student has worked with the exercises in order to take full advantage of the review. By allocating some time in class to short assignment related to new topics, students will be activated and learning objectives achieved.

Wolfram Alpha is used in lectures and problem solving sessions to illustrate taught material. Excel will be used to model, solve and visualize linear differential and difference equations.

Please note that while attendance is not compulsory in all courses, it is the student’s own responsibility to obtain any information provided in class.

All parts of the assessment must be passed in order to receive a final grade in the course.

All courses in the Masters programme will assume that students have fulfilled the admission requirements for the programme. In addition, courses in second, third and/or fourth semester can have specific prerequisites and will assume that students have followed normal study progression. For double degree and exchange students, please note that equivalent courses are accepted.

**Disclaimer**

Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.

Exam category | Weight | Invigilation | Duration | Support materials | Grouping | Comment exam |
---|---|---|---|---|---|---|

Exam category:Submission Form of assessment:Written submission Exam code:GRA60352 Grading scale:ECTS Grading rules:Two examiners Resit:- | 20 | Yes | 1 Hour(s) | - BI-approved exam calculator
- Simple calculator
- Bilingual dictionary
| Individual | Written examination under supervision. Retake is offered in January and not during May/June in the spring semester. |

Exam category:Submission Form of assessment:Written submission Exam code:GRA60353 Grading scale:ECTS Grading rules:Two examiners Resit:- | 80 | Yes | 3 Hour(s) | - BI-approved exam calculator
- Simple calculator
- Bilingual dictionary
| Individual | Final written examination under supervision. Retake is offered in January and not during May/June in the spring semester. |

All exams must be passed to get a grade in this course.

Activity | Duration | Comment |
---|---|---|

Teaching | 36 Hour(s) | Lectures |

Feedback activities and counselling | 12 Hour(s) | Plenary session |

Group work / Assignments | 16 Hour(s) | Exercise sessions |

Examination | 4 Hour(s) | Midterm exam 1h and Final exam 3h |

Student's own work with learning resources | 92 Hour(s) | Read theory and prepare for lectures, own work with problems |

A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 6 ECTS credits corresponds to a workload of at least 160 hours.