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Algebra II

Informacje ogólne

Kod przedmiotu: 360-MS1-2ALG2a Kod Erasmus / ISCED: 11.102 / (0541) Matematyka
Nazwa przedmiotu: Algebra II
Jednostka: Wydział Matematyki
Grupy:
Punkty ECTS i inne: 5.00
zobacz reguły punktacji
Język prowadzenia: angielski
Rodzaj przedmiotu:

obowiązkowe

Wymagania (lista przedmiotów):

Algebra I 0600-FS1-2ALG1
Algebra I 0600-MS1-2ALG1
Algebra liniowa I 0600-FS1-1AL1
Algebra liniowa I 0600-MS1-1AL1
Algebra liniowa II 0600-FS1-1AL2
Algebra liniowa II 0600-MS1-1AL2
Elementarna teoria liczb 0600-FS1-1ETL
Elementarna teoria liczb 0600-MS1-1ETL

Założenia (opisowo):

The student has basic knowledge of Introduction to Mathematics, Elementary Number Theory and Linear Algebra and Algebra I.

Skrócony opis:

Course objectives: A student can apply the Sylow theorem to describe selected finite groups.A student efficiently uses permutation groups and the classification theorem for finitely generated abelian groups. A student understands the relationship between ideals and algebraic sets. A student understands and can use the Galois theory.

Pełny opis:

Course profile: academic

Form of study: stationary

Course type: facultative

Academic discipline: Mathematics, field of study in the arts and science: mathematics

Year: 2, semester: 4

Prerequisities: Algebra I, Elementary Number Theory, Linear Algebra II

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 7x4h + 2h(preliminary teaching) = 30h

preparation for classes 7x3h = 21h

completing notes after exercises and lectures 7x2h = 14h

consultations 5x2h = 10h

preparation for control works 2x5h = 10h

the final examination: preparation.and take 12h + 3h = 19h

Quantitative description

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

Practical exercises: 85 h., 3 ECTS

Literatura:

1. Paul M. Cohn " Basic Algebra: Groups, Rings and Fields", Springer Science & Business Media 2004.

2. Joseph J. Rotman "A First Course in Abstract Algebra: With Applications" Pearson Prentice Hall 2006.

3. Joseph Gallian "Contemporary Abstract Algebra" Cengage Learning 2016.

4. Gregory T. Lee "Abstract Algebra: An Introductory Course" Springer 2018.

5. I. N. Herstein "Abstract Algebra" Macmillan Pub 1990.

6. David S. Dummit, Richard M. Foote" Abstract Algebra" Wiley. 1999.

7. Thomas W. Hungerford "Algebra" Springer Science & Business Media, 2003.

Efekty uczenia się:

Student can formulate the most important theorems of general algebra, knows the basic theorem of algebra and understands its meaning KA6_WG03.

Student knows examples of applications of general algebra methods in various branches of mathematics (for example, Fermat's little theorem in number theory) KA6_UW25.

Student is able to use the most important theorems of general algebra to solve standard problems KA6_UW25.

Student knows the basic structures and concepts of general algebra and can illustrate them with examples (permutation groups, polynomial rings, GF (p ^ n) fields) KA6_WG04.

Student knows that the known algebraic structures exist and are important in various mathematical theories and can point out a specific example of the application of general algebra in reality (e.g. cryptography) KA6_WG02, KA6_WK01, KA6_WK03.

Student notices analogies between the properties of various algebraic structures KA6_UW24.

Metody i kryteria oceniania:

The overall form of credit for the course: final exam

Zajęcia w cyklu "Rok akademicki 2022/23" (jeszcze nie rozpoczęty)

Okres: 2022-10-01 - 2023-06-30
Wybrany podział planu:


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Typ zajęć: Ćwiczenia, 30 godzin więcej informacji
Wykład, 30 godzin więcej informacji
Koordynatorzy: Romuald Andruszkiewicz, Tomasz Czyżycki, Aneta Sliżewska
Prowadzący grup: (brak danych)
Lista studentów: (nie masz dostępu)
Zaliczenie: Egzamin
Opisy przedmiotów w USOS i USOSweb są chronione prawem autorskim.
Właścicielem praw autorskich jest Uniwersytet w Białymstoku.