Course syllabus for Mathematical modelling and problem solving

Course syllabus adopted 2023-02-05 by Head of Programme (or corresponding).

Overview

  • Swedish nameMatematisk modellering och problemlösning
  • CodeDAT605
  • Credits4 Credits
  • OwnerTKGBS
  • Education cycleFirst-cycle
  • Main field of studyGlobal systems, Mathematics
  • DepartmentCOMPUTER SCIENCE AND ENGINEERING
  • GradingUG - Pass, Fail

Course round 1

  • Teaching language Swedish
  • Application code 74128
  • Maximum participants70
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0123 Written and oral assignments 4 c
Grading: UG		4 c0 c0 c0 c0 c0 c

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

DAT435 Applied mathematical thinking

Aim

Mathematical models are used in science and engineering to describe and represent different objects and systems, to analyze, understand and predict, and for finding the best design or strategy. Mathematical modelling is therefore a basic engineering skill. The course also aims to develop a problem solving ability with a particular attention to problem solving in engineering. The problems are taken from several different areas to create variation and to make it possible to see patterns in modelling and problem solving across different areas of application.

Learning outcomes (after completion of the course the student should be able to)


Knowledge and understanding

• Describe different model types and their properties, as well as the processes of modelling and problem solving. Describe main aspects of mathemtical thinking.

Competence and skills

• Mathematical modelling: investigate real problems, suitably translate into a mathemtical model and draw conclusions with the help of the model. This includes to create a precise formulation, simplify, make suitable assumptions and selecting how the problem can be described e.g. with the help of equations or in other mathematical ways.
• Problem solving: solving complex and unknown problems with an investigative and structured approach. This includes analyzing and understanding, working in smaller steps and trying things out.
• Technical problem solving: ability to solve practical engineering problems.
• Show ability to tackle large and more complex modelling problems
• Use different computational tools as a natural part of working mathematically.

Judgement and approach

• Identify how own thinking can be used to solve a problem, and to what extent previous knowledge can be used.
• Show a reflective attitude to the course contents and to their own thinking.
• Show care for precision and quality in all work.

Content


The core of the course is a number of application oriented problems, which are used as a starting point for the student's own learning. The problems have been carefully selected to develop the student's own skills in modelling and solving problems in a investigative way.

The problems illustrate several areas of application and will make use of different kinds of mathematical models:

• Functions and equations, for example how different mathematical statements can be motivated and how to select and fit functions to empirical data.
• Optimization models, e.g. mathematical programming in economics and decision support.
• Dynamic models, e.g. simulation in biology, physics and engineering.
• Probability models, e.g. stochastic simulation, Markov models for text and Bayesian inference.
• Discrete models, e.g. graphs and networks for modelling projects and activities, modelling with discrete standard problems and boolean logic, planning.

Within the course we will also engage in at least one larger modelling problem and also illustrate different aspects of problem solving in engineering, like for example the design process and different practical aspects.

Organisation


The course is mainly organized in modules. For every module there is problem set, and lectures adapted to the content of the modules, where follow-up is an important part.

The learning is supported by an interactive way of teaching with a lot of contact
between students and teachers. This occurs during supervision hours where students work with the problems and regularly discuss with the supervisors. They will then receive individual feedback and guidance in their own problem solving, and develop their independent abilities.

Literature

The course does not have any specific course literature beyond what is provided in the modules.

Examination including compulsory elements


The course is examined through written assignments and with a final report, where the students are encouraged to summarize and reflect over the course in a personal way. The assignments and the final report are normally written in groups of two persons. In addition, each group reads reports from other groups, and discusses them in a final seminar. To pass the course, attendance of selected lectures and the final seminar is also required.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.