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Algebra I

General data

Course ID: 0600-MS1-2ALG1 Erasmus code / ISCED: 11.102 / (unknown)
Course title: Algebra I Name in Polish: Algebra I
Department: (in Polish) Zakład Algebry
Course groups: (in Polish) 2 rok 1 stopnia sem. zimowy Matematyka spec. Teoretyczna
(in Polish) 3L stac. I st. studia matematyki - przedmioty obowiązkowe
ECTS credit allocation (and other scores): 4.00
view allocation of credits
Language: Polish
Type of course:

obligatory courses

Requirements:

Elementary Number Theory 0600-FS1-1ETL
Elementary Number Theory 0600-MS1-1ETL
Elements of Logic and Set Theory 0600-FS1-1WDM
Elements of Logic and Set Theory 0600-MS1-1WDM
Linear Algebra I 0600-FS1-1AL1
Linear Algebra I 0600-MS1-1AL1
Linear Algebra II 0600-FS1-1AL2
Linear Algebra II 0600-MS1-1AL2

Prerequisites:

Elementary Number Theory 0600-FS1-1ETL
Elementary Number Theory 0600-MS1-1ETL
Elements of Logic and Set Theory 0600-FS1-1WDM
Elements of Logic and Set Theory 0600-MS1-1WDM
Linear Algebra I 0600-FS1-1AL1
Linear Algebra I 0600-MS1-1AL1
Linear Algebra II 0600-FS1-1AL2
Linear Algebra II 0600-MS1-1AL2

Prerequisites (description):

(in Polish) Student posiada podstawową wiedzę ze Wstępu do matematyki, Elementarnej teorii liczb oraz Algebry liniowej.

Short description:

Course objectives: A student can recognize the structure of a group (a ring, a field) in well-known algebraic objects. The student can formulate well-known mathematical facts in the language of group and ring theory.

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: 2, semester: 3

Prerequisities: Linear Algebra II, Elementary Number Theory

lecture 30 h. exercise class 30 h.

Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.

ECTS credits: 4

Balance of student workload:

attending lectures15x2h = 30h

attending exercise classes 7x4h + 2h(preliminary teaching) = 30h

preparation for classes 7x3h = 21h

completing notes after exercises and lectures 7x2h = 14h

consultations 5x2h = 10h

the final examination: preparation.and take 15h + 4h = 19h

Quantitative description

Direct interaction with the teacher: 74 h., 2 ECTS

Practical exercises: 75 h., 3 ECTS

Bibliography: (in Polish)

1. R. R. Andruszkiewicz „Wykłady z algebry”, strona internetowa wykładowcy

2. R. R. Andruszkiewicz „Wykłady z algebry ogólnej I” Wydawnictwo UwB, Białystok 2005

3. Cz. Bagiński „Wstęp do teorii grup” Wydawnictwo Script, Warszawa 2002

4. M. Bryński, J. Jurkiewicz „Zbiór zadań z algebry” PWN, Warszawa 1978

5. K. Szymiczek „Zbiór zadań z teorii grup” PWN, Warszawa 1989

6. J. Rutkowski „Algebra abstrakcyjna w zadaniach” PWN, Warszawa 2006

7. M. Woronowicz, "Zadania z algebry ogólnej" - materiały dydaktyczne przesyłane studentom przez prowadzącego ćwiczenia.

Learning outcomes:

Learning outcomes:

A student knows that algebraic structures, which are known, are important in a variety of mathematical theories.K_U17, K_W05, K_W03

A student knows the basic concepts of algebra and can provides appropriate examples (permutation groups, polynomial rings, fields GF(p^n)).K_W03

A student is able to formulate the most important theorems of abstract algebra, in particular the fundamental theorem of algebra. A student knows importance of this theorem.K_W04, K_W02

A student knows how to apply abstract algebra in a variety of branches of mathematics (for example, Fermat’s little theorem in number theory).K_U17

A student knows how to use the main theorems of abstract algebra to solve standard exercises.K_U17, K_U38

A student understands problems formulated in the language of abstract algebra.K_W04, K_W05

A student sees parallels between the properties of various algebraic structures.K_W04, K_W05, K_U37

A student can indicate a specific example of the use of algebra in real life (for example, in cryptography).K_U25, K_U17

Assessment methods and assessment criteria:

The overall form of credit for the course: final exam

Classes in period "Academic year 2017/2018" (past)

Time span: 2017-10-01 - 2018-06-30
Choosen plan division:


magnify
see course schedule
Type of class: Class, 30 hours more information
Lecture, 30 hours more information
Coordinators: Romuald Andruszkiewicz
Group instructors: Romuald Andruszkiewicz, Karol Pryszczepko
Students list: (inaccessible to you)
Examination: Examination

Classes in period "Academic year 2018/2019" (future)

Time span: 2018-10-01 - 2019-06-30
Choosen plan division:


magnify
see course schedule
Type of class: Class, 30 hours more information
Lecture, 30 hours more information
Coordinators: (unknown)
Group instructors: (unknown)
Students list: (inaccessible to you)
Examination: Examination
Course descriptions are protected by copyright.
Copyright by University of Bialystok.