Mathematical modelling and problem solving

Lecture slides and other reading

• 2019-09-02 Introduction to Module 1: Functions and Equations Recordings:

• 2019-09-05 General Perspectives on Modelling and Problem Solving Recordings:

• 2019-09-10 Optimization Problems Recordings:

• 2019-09-16 Discrete Models Recordings:

• 2019-09-23 Modelling Languages Recordings:

• 2019-09-23 Dynamic Models Recordings:

• 2019-09-23 Reflections on Modelling and Problem Solving Please note: this lecture was given twice, once to students on DAT026/DIT992 and once to students on LGMA65. Both recordings are below.

• 2019-09-30 Bouncing Balls

• 2019-09-30 Independence in Problem Solving

• 2019-09-30 Rumsliga Modeller

• 2019-10-07 Dynamic Systems: Slides

• 2019-10-14 Probability Models: Slides (Probabilistic Models)

  Part 1 (download recommended) and Part 2 (download recommended)

• 2019-10-21 Course summary: Slides (course summary)

  No video available for this lecture due to technical problems with the file from the recordning

Links and literature related to Mathematica

Mathematica is available on the lab systems. There is also an online version of Mathematica called the Wolfram programming lab. (Chalmers students can download Mathemtica to their own computers through the Chalmers site license).

Stephen Wolfram has written a quite friendly introduction to programming in Mathematica: Introduction to the Wolfram programming language. This online book is a useful entry point for understanding how Mathematica works.

One of the great benefits of Mathematica is its coherent and comprehensive help system.

Complementary literature

Here is the paper mentioned in one of the lectures:
A Mathematical Theory of Communication

The main element of this course is to learn a skill by doing the problems, so we have no coursebook. However, as complementary reading about models, I highly recommend the following book

• Gerlee och Lundh. Vetenskapliga modeller (Studentlitteratur 2012).

This is an easy-to-read and mostly non-mathematical book, which in a nice and general way deepens the understanding of models and how they can be used.

Then, there are many books about mathematical modelling. Books that are relatively close to the spirit of this course are

• Giordano et.al. A first course in mathematical modeling (5th edition, Brooks/Cole, 2014).
• Meerschaert. Mathematical modeling (4th edition, Elsevier, 2013).

A classic book about mathematical problem solving is

• Polya. How to solve it. (2nd edition, Princeton, 1957)

and I highly recommend you to read it some time. However, no book that I know of covers the entire scope of this course. You are not recommended to buy any of these books now! If you would like a book about mathematical modelling after you have solved the problems and for future reference then Giordano would be the first choice.