| Unit name | Algebra 2 |
|---|---|
| Unit code | MATH21800 |
| Credit points | 20 |
| Level of study | I/5 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. McGillivray |
| Open unit status | Not open |
| Pre-requisites |
MATH11501, MATH11002 and MATH11003 |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Many important objects in mathematics can be thought of as number-systems in the sense that they have both addition and multiplication. Examples include the integers, the rational numbers, the complex numbers, integers mod( (n) ), polynomials, etc. We shall study some of these systems with the two aims of providing general results and immediately applying the theory to solving problems. For instance we shall consider unique factorisation in such systems, and use the uniqueness of factorisation of Gaussian integers to prove Fermat's assertion that every prime number of the form 4 n + 1 is the sum of two squares. Also we shall develop the sort of mathematics which is used to show that certain geometrical constructions are not possible, and we shall use it to prove the impossibility of squaring the circle. We shall also construct some examples of finite field; this area has now become hugely important because of its use in coding theory. Throughout the unit there will be an emphasis on applying the general theory to solving problems with actual numbers in them.
