# MA247 Content

**Content**: A broad range of topics will be explored through problem solving and researching the literature, using material covered in the first and second year Mathematics core modules as the point of departure. The module will provide an opportunity to explore some of the deeper and more beautiful aspects of mathematics. The unity of the subject will be emphasized.

**The following is a short selection of worksheet topics from recent years: **

- Root-finding for polynomials,
- Approximation of irrational numbers by rational numbers,
- Infinite dimensional linear algebra,
- Knots,
- Calculus of variations,
- Critical points and level sets.

Extracts from SSLC evaluations of the module: The students were almost unanimously pleased with the module. There were some difficult problems, but they were by far my favourite ones. Assignment problems were found to be helpful with the understanding of some other modules. Projects were popular. The module required me to make substantial use of the library, more so than in other modules. A team spirit evolved among most students on the module. More students should take this module; it is not as daunting as it sounds and it is very rewarding and beneficial.

**Aims**:

- To provide an opportunity to explore some of the deeper and more beautiful aspects of mathematics and to exhibit its unity.
- To foster and maintain enjoyment of mathematics and inspire some students to consider seriously a career in mathematical teaching or research.
- To teach how to use the computer to solve mathematical problems and to discover, formulate and test mathematical conjectures.

**Objectives**:

- To develop problem solving skills.
- To teach how to write mathematics well.
- To give practice in presenting mathematics to a group.
- To develop research skills, including use of library, the internet, group discussions, etc.

**Books**:

A home produced problem list. The project will involve consulting a number of books, all of which are available from the library or from the module organiser. You need not purchase any books.