Discrete mathematics 2: algebra

• give the definition of a group
• apply group theory to solve counting problems
• describe symmetries of geometric object
• give the definition of a ring
• explain the notion of an ideal and use this to construct quotient rings
• understand the construction of fields from rings (especially finite fields)
• indicate how finite fields are applied
• carry out a mathematical proof

Algebra is the foundation of many applications, especially in coding theory and cryptography.
The goal with this course is to introduce several algebraic constructions (groups, rings and fields). These constructions will be exemplified in different areas, among others geometry and discrete mathematics. Also an impression is given as to how this theory is applied and as such the course is a preparatory course for further courses in discrete mathematics.

01017/01019/01001/01003/01005/01006/01015/01016, The following topics from Discrete Math 1 (01017) will be used: the induction principle, the extended Euclidean algorithm (both for integers and for polynomials), modular arithmetic.

The following topics from 01001/01005 will be used: linear algebra, among others matrix arithmetic, linear maps, kernel and image of a linear map.

Lectures and exercise sessions