## Mathematical Structures

Course Material Autumn 2012

Notice
If you enjoyed this module, and would like to
have similar challenges in the rest of your course,
I recommend the following:

#### Module description

The module has three main aims:

1. to introduce the basic objects of mathematics (numbers, sets and functions), and their properties;
2. to emphasize the fact that mathematics is concerned with proofs, which establish results beyond doubt, and to show you how to construct proofs, how to spot false "proofs", how to use definitions, etc.;
3. to get you involved in the excitement of doing mathematics.

The module description, with the syllabus and learning outcomes, can be found here in the list of modules on the School's web page.

#### Course information

The course information sheet is here.

#### Lecture notes

There are ten chapters, on the following topics:

Each chapter of the notes includes a section on study skills.

Here is an index to the notes, which might help you to find your way around; and here are the study skills collected into a single document.

#### Problem sheets

The timing for problem sheets has been changed, starting from Sheet 4. The dates on the sheet will be the week in which the material will be discussed in tutorials; you can hand it in any time between the end of the tutorial and the beginning of the following week's tutorial.

My response to the questionnaires is here.

#### Extra questions

A sample exam paper can be found here. Solutions to the sample exam will not be published, but the lecturer is happy to go through your attempts at this paper with you; please email for an appointment.

I have put the sample test and test papers here. I have also posted a list of statements made on test papers; you are asked to explain what is wrong with each, and to try to clear up the misunderstanding of the person who wrote it.

Here are some questions on sets, functions and relations and some questions on numbers that you might like to practise on.

#### Resources

There is no compulsory textbook for the module. The recommended books are:

• Timothy Gowers, Mathematics: A very short introduction, Oxford University Press, Oxford (2002)
• Kevin Houston, How to think like a mathematician, Cambridge University Press, Cambridge (2009)

I gave the LMS-Gresham lecture about the Mathematical Structures module on 14 May. Slides of the talk are available: screen version, printer version.

Some websites you might find useful:

Peter J. Cameron
17 January 2013