Courses
| Course title: | Abstract Arithmetic |
|---|---|
| Faculty: | Faculty of Education |
| Department: | Department of Mathematics with Didactics |
| Course code: | KMD / E-AG3 |
| Credits: | 5 |
| Semester: | Winter / Summer |
| Level of study: | Mgr. |
| Format of study: | Lecture 1 [Hours/Week], Seminar 1 [Hours/Week] |
| Name of the lecturer: | Ing. Tomáš Barot, Ph.D. (G) |
| Language: | English, German |
| ISCED F broad: | Natural sciences, mathematics and statistics |
| Annotation: | The course introduces methods of construction of number fields - construction of natural numbers using Pean's axioms, natural numbers in the sense of an algebraic structure, a splitting group and a splitting field, construction of the ring of integers and rational numbers, embedding of a lattice into a complete lattice, MacNeil's hull, construction of real numbers in the sense of completion rational numbers, two method of construction - Dedeknid's cuts, topological completion using Cauchy sequences, an algebraic complete field, construction of the field of complex numbers, an algebraic complete field of complex numbers, divisibility in integral domains, special types of integral domains with special arithmetic properties, Gauss rings, a principal ideal ring, Euclidean rings. |
