University of Bialystok - Central Authentication SystemYou are not logged in | log in
course directory - help

Algebra and Number Theory

General data

Course ID: 0600-MS2-1ATL Erasmus code / ISCED: 11.103 / (unknown)
Course title: Algebra and Number Theory Name in Polish: Algebra i teoria liczb
Department: (in Polish) Zakład Algebry
Course groups: (in Polish) 2L stac. II st. studia matematyki - przedmioty obowiązkowe
ECTS credit allocation (and other scores): (not available)
view allocation of credits
Language: Polish
Type of course:

obligatory courses

Requirements:

Algebra I 0600-MS1-2ALG1
Algebra II 0600-MS1-2ALG2
Elementary Number Theory 0600-MS1-1ETL
Linear Algebra I 0600-MS1-1AL1
Linear Algebra II 0600-MS1-1AL2

Short description:

Course objectives: The skill to use the notation of an algebraic field extension, to find the Galois group of field extensions and intermediate fields of Galois extensions, the expertise of a complete characterization of Galois extension and fundamental theorems of the Galois Theory, the skill to notice the Galois Correspondence between a field extension and its Galois group, the understanding of 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, the skill to solve polynomial equations of both 3rd and 4th degree, the expertise of the Cardano Formula; the skill to use the notion of an algebraic integer, to solve Diophantine equations using the unique factorization of the ring of algebraic integers in some quadratic number fields, to find an integral basis of both quadratic number fields and cyclotomic fields; the skill to discuss the problem of the distribution of prime numbers

Full description:

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

Bibliography: (in Polish)

1. Andrew Baker, An introduction to Galois Theory (writen for a University of Glasgow level 4 Honours degree course). http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf

2. Jerzy Browkin, Teoria ciał, Wydawnictwo Naukowe PWN, Warszawa 1977.

3. Maciej Bryński, Elementy Teorii Galois, Wydawnictwo Alfa, Warszawa 1985.

4. Ian Steward, Galois Theory, third edition, Chapman & Hall/CRC, A CRC Company Boca Ration, London, New York 2004.

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.K_W04, K_W05, K_W07, K_W08, K_U01, K_U02, K_U03, K_U04, K_U10, K_U13, K_U14

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.K_W04, K_U01, K_U02, K_U03, K_U04, K_U10, K_U13, K_U14

A student discusses the problem of the prime numbers distribution.K_W04, K_U01, K_U02, K_U03, K_U04, K_U13, K_U14

A student obtains basic skills of creative development of algebra.K_K01, K_K02, K_K07

A graduate understands that modern technologies result from scientific discoveries including algebra.K_K08, K_K05

Assessment methods and assessment criteria:

The overall form of credit for the course: final exam

This course is not currently offered.
Course descriptions are protected by copyright.
Copyright by University of Bialystok.