Course syllabus for Mathematical modelling and problem solving

Course syllabus adopted 2022-01-27 by Head of Programme (or corresponding).

Overview

  • Swedish nameMatematisk modellering och problemlösning
  • CodeDAT026
  • Credits7.5 Credits
  • OwnerTKITE
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentCOMPUTER SCIENCE AND ENGINEERING
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 52129
  • Block schedule
  • Open for exchange studentsYes

Credit distribution

0107 Written and oral assignments 7.5 c
Grading: TH		7.5 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

The compulsory courses in mathematics on the Software Engineering programme or their equivalent (i.e. discrete mathematics, linear algebra, analysis and mathematical statistics). A course in algorithms and data structures complements this course in a good way, but is not a requirement.

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.

With carefully selected exercises this course teaches mathematical modelling as a tool for solving real problems. Problems are taken from computing and traditional engineering disciplines, as well as from other areas, such as economics, medicine and games.

The course is primarily intended as an introduction to mathematical modelling for students with limited experience in the use of mathematics in engineering, but which may come to work in different areas where mathematics is useful. With application oriented exercises, and by teaching modelling and problem solving, the course then bridges the gap between the theoretical courses in mathematics and relevant applications.

For the most updated information about the course, please see the course home page.

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

  • Describe different model types and their properties, as well as the processes of modelling and problem solving. Describe main aspects of mathemtical thinking.
  • Explain the role of mathematics in different areas of application.
  • 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.
  • Mathematical 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.
  • Communicate with and about mathematics.
  • Use different computational tools as a natural part of working mathematically.
  • Show an ability to balance own thinking and using knowledge from others.
  • Show a reflective attitude to the contents of the course and to the student's own thinking.
  • Show accuracy and quality in all work. 

Content

The core of the course is a number of application oriented exercises, 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 exercises illustrate many areas of application and are organized after the main model types. In the list below one can find examples indicating the more detailed scope:

  • 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.
  • One to two more modules with mixed and/or current topics.
  • With the exercises as a starting point, we actively teach modelling and problem solving with a supervision style that develops the independence of the student. During lectures, we also discuss different problem solving strategies, reflect on solutions and compare different ways to solve the same problem.
  • The course also demonstrates the importance of building mathematical computer models for different kinds of applications.

Organisation

The course is organized in weekly modules, one for every model type. A module consists of an introductory lecture, exercises for the week, and a compulsory follow-up lecture giving feedback to the solved exercises.
An emphasis is placed on an interactive teaching style with a lot of direct contact between students and teachers. This is done in supervision sessions where students solve the exercises and regularly discuss with the teachers. The students can then receive individual feedback and appropriate guidance in their own problem solving, and develops their independent problem solving ability.
As a follow up to each module, the students are asked to reflect on their own and alternative solutions, and on their own problem solving.

Literature

Since the exercises are the core of the course there is no course literature in the traditional sense. For handout material and additional reading, see the course home page.

Examination including compulsory elements

The course is examined through written assignments and a final report, where the students are encouraged to summarize the course in their own way. Additionally, the course includes compulsory follow-up lectures for each modules, and during the examination week there is also compulsory final meeting where the report is discussed. Both the weekly assignments and the final report are normally done in groups of two.

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.