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General information

Contact

Schedule

Problem modules

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## Lecture slides and other reading

### Mathematical thinking and some follow-up

• What is mathematical thinking? (week 1)
Lecture slides

• History of mathematical thinking (week 2)
Lecture slides

• Where and how is mathematical thinking used? (week 3)
Lecture slides

• Follow-up functions and equations (follow-up 2 - week 3)
Lecture slides (most of the lecture not published online)

• Comments on mathematical thinking (mid-course - week 5)
Thinking slides

• Follow-up dynamic systems (follow-up 5 - week 6)
Lecture slides (most of the lecture not published online)

### Final lecture

All introductory lectures will be posted. Sometimes we will not use word processed slides at all or there may be other reasons why a lecture is not published here.

Note that the slides do not necessarily correspond to the entire lecture since we will also write on the board. Making your own notes is also a way to learn. We do not recommend replacing a lecture with reading of the slides, and they should be used as a complementary backup.

## 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

The most important element of this course is to learn a skill by doing the problems, so we have no coursebook. So you are not recommended to buy any books immediately. Besides, no book that I know of covers the full scope of this course. However, some nice books to look at are:

• Devlin. Introduction to mathematical thinking (). Emphasizes the logical reasoning aspect. (2012)
• Ellenberg. How not to be wrong: the power of mathemtical thinking (). Discusses many ways of how reasoning can go wrong and sorts them out, also when probabilites are involved. (2014)
• Giordano et.al. A first course in mathematical modeling (4th edition, 2008). An extensive and broad introduction.
• Gerlee and Lundh. Scientific models (2016). A mostly non-mathematical book, which in a nice and general way broadens the understanding of models and how they can be used.
• Meerschaert. Mathematical modeling (3rd edition, 2007).
• Polya. How to solve it. (2nd edition, 1957). A classic book about mathematical problem solving.

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