Mathematical Modeling, 7.5 Credits

Contents

Mathematical models are used in many contexts to describe systems, analyze questions and solve various problems. This is done by reformulating the part of the world you are interested in into a mathematical model. By describing real phenomena in terms of mathematics, mathematical tools and methods can be used to systematically analyze properties and questions related to everything from physical and technical systems to economic and social science processes.

In the course, you practice creating mathematical models to analyze real issues. The models are implemented in suitable software and algorithms are constructed to carry out calculations and simulations. The results and solutions from the analyses are then linked back to the question and its original context.

The course combines knowledge from previous courses and the student gets training in applying the theory from these. In addition, the course provides increased skills in solving problems in a structured way and the student also gets an insight into how mathematical models are used in various industries.

The course is divided into two modules:
Module 1 (2.5 credits) Theory for mathematical modelling,
Module 2 (5 credits) Project work in mathematical modelling.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• account for different types of modeling approaches
• account for a selection of graph algorithms and simulation methods
• account for how to use vectorization to make calculations more efficient

Skills and Abilities

• formulate real problems as mathematical problems
• construct and adapt mathematical models to answer different types of questions
• construct and use functions to write structured programs
• implement algorithms in mathematical problem solving software
• interpret results from mathematical models in their original context
• report results and analyses from mathematical modeling problems orally and in writing
• plan and organize project work

Judgement and approach

• assess reliability, validity and generalizability for different models
• assess and critically relate to models and the use of models connected to ethics and sustainability

Form of instruction

The teaching on Module 1 takes the form of lectures and lessons. The teaching in Module 2 takes the form of supervised lab work and seminars.

Examination modes

Module 1 is examined by a programming test and a written exam. On the exam, one of the following grades is given: Fail (U), Pass (3), Pass with distinction (4), Pass with special distinction (5). Module 2 is examined by written and oral presentations of the project work. The grades for the project work are Fail (U), Pass (3), Pass with distinction (4), Pass with special distinction (5). The entire course is given one of the following grades: Fail (U), Pass (3), Pass with distinction (4), Pass with special distinction (5).

To pass the whole course, all modules must have been passed. The course grade constitutes a summary assessment of the results on both modules. A student who has received a passing grade on a test is not allowed to retake the test in order to receive a higher grade.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Examiners may decide to deviate from the modes of assessment in the course syllabus. Individual adaption of modes of assessment must give due consideration to the student's needs. The adaption of modes of assessment must remain within the framework of the intended learning outcomes in the course syllabus. Students who require an adapted examination must submit a request to the department holding the course no later than 10 days before the examination. The examiner decides on the adaption of the examination, after which the student will be notified.

Credit transfer
All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be addressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics.

In the event that the syllabus ceases to apply or undergoes major changes, students are guaranteed at least three examinations (including the regular examination opportunity) according to the regulations in the syllabus that the student was originally registered on for a period of a maximum of two years from the time that the previous syllabus ceased to apply or that the course ended.