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DAT026 / DIT993 Mathematical modelling and problem solving lp1 HT26 (7.5 hp)

Course is offered by the department of Computer Science and Engineering

Contact details

Examiner and Course Responsible: Robin Adams <robinad@chalmers.se>

Teaching Assistants:

Useful Links

Course purpose

Welcome to the course on mathematical modelling and problem solving! This course is quite different to most others at Chalmers and GU.

Mathematical modelling is descriptive mathematics. We have a problem we want to solve, or a question we want to answer, about the real world. We construct a mathematical model - a mathematical object (function, equation, set, graph, ...) that behaves like the real world situation in the important respects. By investigating the mathematical model (on paper or with a computer), we hope to solve the problem that we started with.

There is no algorithm that can tell you the correct mathematical model to choose. It is a creative process requiring original ideas, and an iterative process requiring trial-and-error to find out what works, and successively refining and improving your model.

To teach these higher-order problem solving skills, each week we present you with a number of problems where it is not obvious what you have to do to solve them. We will discuss the problems with you in the supervision sessions using Socratic questioning - instead of telling you the next step, we ask questions that will hopefully help you find the correct ideas yourself. After you submit your solutions, we will show you the correct solutions in a video, and then ask you to reflect on your process, and see how you could improve your problem solving skills in the future.

Schedule

TimeEdit

Course literature

There is no textbook or compulsory literature for the course. A number of suggestions for students who want further reading about mathematical modelling or problem solving are on the page Complementary literature

Course design

The core of the course is a number of problems in six weekly modules. The normal schedule of a module is the following:

  • Introductory lecture (Wednesday). A general introduction to the the type of models considered in the module and preparation for the problems.
  • Problem solving work during the week. The students work together on the problems in groups of three. There are several supervision sessions when the students can discuss their ideas with the supervisors. We give advice interactively and incrementally, so you are encouraged to come back and discuss the same exercise several times. You will then get more help every time.
  • The problems are completed and handed in on Canvas.
  • After you submit your solution to each problem, you will get access to a video giving you the solution to the problem and additional context about the problem's true purpose.
  • After you have submitted a solution for each problem in a module and seen the solutions, you are asked to reflect on your problem solving and your learning in a final submission for each module.

In the final week of the course, you are asked to write a final report summarising what you consider to be the most important aspects of the course for you.

Changes made since the last occasion

The follow-up lecture for each module has been replaced by a set of videos giving the solutions to the problems, one for each problem.

Learning objectives and syllabus

Learning objectives:

  • 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. 

Links to the syllabus: 

Chalmers syllabus

GU syllabus

Examination form

The course is examined through the written assignments and a final report, where the students are encouraged to summarize the course in their own way. Both the weekly assignments and the final report are normally done in groups of three.

AI Policy

Since this course focuses on developing your own thinking skills and problem solving abilities, use of generative AI (ChatGPT etc.) is contrary to the learning objectives.

Additionally, I would never require a student who (like me) considers generative AI to be an inherently unethical technology to use it.

However, simple policies that forbid AI use have problems:

  • If the policy is not enforced, then students who are honest are at a disadvantage to students who succumb to temptation (as deadlines approach and workloads are high) and use a chatbot to get some answer for a difficult problem
  • If the policy is enforced, then some innocent students will be unfairly accused of using generative AI. There is no reliable way to detect AI output, false positives are impossible to defend against, and students spend more time worrying about how to dodge the AI detector than about the content of the course.

For this course, we therefore adopt the following policy (originally by Ploum):

For each problem, you may choose one of the following two options:

Option A: I will not use any generative AI. Any use of generative AI will be considered cheating.

Option B: I may use generative AI as it’s part of my toolbox. I will then respect the following rules:
1) I will clearly indicate in my solution each time information come from a chatbot
2) I will share the prompts I used so the teacher understands how I use the tool
3) I will identify mistakes in answers from the chatbot and explain why those are mistakes

Not following those rules will be considered cheating. Mistakes made by chatbots will be considered more important than honest human mistakes, so a higher standard of solution will be expected from students who choose Option B.

I emphasise that choosing Option A for every problem is the way that the course is intended to be taken.

Course summary:

Course Summary
Date Details Due