Algebra and Number Theory 360-MS2-1ATL
Course profile: academic
Form of study: stationary
Course type: obligatory
Academic discipline: Mathematics, field of study in the arts and science: mathematics
Year: 1, semester: 1
Prerequisities: none
lecture 30 h. exercise class 30 h.
Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.
ECTS credits: 5
Balance of student workload:
attending lectures15x2h = 30h
attending exercise classes 15x2h = 30h
preparation for classes 7x3h = 21h
completing notes after exercises and lectures 7x2h = 14h
consultations 12x1h = 12h
the final examination: preparation.and take 12h + 3h = 15h
control works: repeating the material and preparation 3x4h = 12h
Quantitative description
Direct interaction with the teacher: 75 h., 3 ECTS
Practical exercises: 77 h., 3 ECTS
Type of course
Prerequisites
Prerequisites (description)
Course coordinators
Learning outcomes
Learning outcomes: A student uses the notion of an algebraic field extension; knows a complete characterization of a Galois extension and fundamental theorems of the Galois Theory; finds the Galois group of field extensions and intermediate fields of Galois extensions; understands the importance of the Galois Theory in the solution of the problem of solving polynomial equations by radicals, and of the Three Geometric Problems of Antiquity. KA7_WG01, KA7_WG02, KA7_WG03, KA7_WG04, KA7_WG05, KA7_WG06, KA7_UW02, KA7_UW03, KA7_UW04, KA7_UW10, KA7_UW13, KA7_UK01, KA7_UK02, KA7_UK03, KA7_UU01, KA7_UU02, KA7_KK01, KA7_KK02.
A student examines the unique factorization of the ring of algebraic integers in quadratic number fields; solves Diophantine equations using the unique factorization of the ring of algebraic integers in some quadratic number fields; understands the importance of the unique factorization of the ring of algebraic integers in some quadratic number fields in the solution of some problems in the Number Theory. KA7_WG01, KA7_WG02, KA7_WG03, KA7_WG04, KA7_WG05, KA7_WG06, KA7_UW02, KA7_UW03, KA7_UW04, KA7_UW10, KA7_UW13, KA7_UK01, KA7_UK02, KA7_UK03, KA7_UU01, KA7_UU02, KA7_KK01, KA7_KK02.
A student discusses the problem of the prime numbers distribution. KA7_WG01, KA7_WG02, KA7_WG03, KA7_WG04, KA7_WG05, KA7_WG06, KA7_UW02, KA7_UW03, KA7_UW04, KA7_UW10, KA7_UW13, KA7_UK01, KA7_UK02, KA7_UK03, KA7_UU01, KA7_UU02, KA7_KK01, KA7_KK02.
A student obtains basic skills of creative development of algebra. KA7_WG01, KA7_WG02, KA7_WG03, KA7_WG04, KA7_WG05, KA7_WG06, KA7_UW02, KA7_UW03, KA7_UW04, KA7_UW10, KA7_UW13, KA7_UK01, KA7_UK02, KA7_UK03, KA7_UK04, KA7_UU01, KA7_UU02.
A graduate understands that modern technologies result from scientific discoveries including algebra. KA7_WG05.
Assessment criteria
The overall form of credit for the course: final exam
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: