Mathematics: Algebraic Structures

<p>The course is an elective course for first-cycle studies for a Bachelor's of Science degree in mathematics. The overarching goal of the course is for the students to acquire knowledge of the basic concepts and structures in abstract algebra such as groups, rings and fields, which are of importance for further studies in mathematics as well as in applications in computer science, information theory, physics and chemistry.</p><p>The course treats:</p> <ul> <li>Number theory: the fundamental theorem of arithmetic, modular artithmetic.</li> <li>Groups: definition, basic examples of groups, subgroups, normal subgroups, factor groups, isomorphisms and homomorphisms, Lagrange's theorem, permutation groups, symmetric and alternating groups, finitely generated Abelian groups.</li> <li>Rings: definition, basic examples of rings, isomorphisms and homomorphisms, ideals, factor rings, polynomial rings, factorisation of polynomials as products of irreducible poynomials.</li> <li>Fields: characteristic, simple field extensions, finite fields.</li> </ul>