Algebra II
General data
| Course ID: | 0600-MS1-2ALG2 | Erasmus code / ISCED: |
11.102
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(unknown)
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| Course title: | Algebra II | Name in Polish: | Algebra II |
| Department: | (in Polish) Zakład Algebry | ||
| Course groups: |
(in Polish) 3L stac. I st. studia matematyki - przedmioty obowiązkowe |
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| ECTS credit allocation (and other scores): |
5.00  view allocation of credits |
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| Language: | Polish | ||
| Type of course: | obligatory courses |
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| Requirements: | Algebra I 0600-FS1-2ALG1 |
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| Prerequisites (description): | (in Polish) Student posiada podstawową wiedzę ze Wstępu do matematyki, Elementarnej teorii liczb oraz Algebry liniowej i Algebry I. |
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| Short description: |
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. |
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| Full description: |
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 |
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| Bibliography: |
(in Polish) 1. R. Andruszkiewicz, Wykłady z algebry ogólnej II, Wydawnictwo Uniwersytetu w Białymstoku, Białystok 2016. 2. Cz. Bagiński „Wstęp do teorii grup” Wydawnictwo Script, Warszawa 2002 3. M. Bryński, J. Jurkiewicz „Zbiór zadań z algebry” PWN, Warszawa 1978 4. Paulo Ney de Souza, Jorge-Nuno Silva, Berkeley Problems in Mathematics, Berkeley, 1998. 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. |
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| Learning outcomes: |
Learning outcomes: A student knows that the algebraic structures occurs and are important in various mathematical theories; A student knows the basic concepts of general algebra II and is able to illustrate them on examples (a group action, simple groups, solvable groups, noetherian rings, algebraic sets). A student is able to formulate main theorems of general algebra II (the Sylow theorem, the Galois theorem). A student knows the importance of the Galois theorem in mathematics (i.e. non-solvability by radicals of polynomial equations, non-constructability in geometry). A student knows the contemporary problems of algebra (i.e. the classification of simple groups).K_U17, K_W05, K_W04, K_W01, K_W02 A student can take advantage of the most important general theorem of general algebra II to solve classical exercises. A student can classify finite abelian groups. A student understands problems formulated in the language of abstract algebra and he can formulate problems in this language. A studen can apply euclidean rings to solve diophantine equations.K_U38, K_W02, K_W04 A student can identify a concrete example of application of algebra in reality (i.e. counting of combinatorial objects by the Burnside lemma).K_U29, K_U25, K_W03 A student can present the three famous problems of antiquity and briefly explain the main algebraic ideas which are used in the solution of these problems. K_K02, K_U36, K_W01, K_W03, K_U17 |
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| Assessment methods and assessment criteria: |
The overall form of credit for the course: final exam |
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Classes in period "Academic year 2017/2018" (past)
| Time span: | 2017-10-01 - 2018-06-30 |
 
 see course schedule |
| Type of class: |
Class, 30 hours more information Lecture, 30 hours more information |
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| Coordinators: | Romuald Andruszkiewicz | |
| Group instructors: | Romuald Andruszkiewicz, Mateusz Woronowicz | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination |
Classes in period "Academic year 2018/2019" (in progress)
| Time span: | 2018-10-01 - 2019-06-30 |
see course schedule |
| Type of class: |
Class, 30 hours more information Lecture, 30 hours more information |
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| Coordinators: | Romuald Andruszkiewicz | |
| Group instructors: | Romuald Andruszkiewicz, Małgorzata Hryniewicka | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination |
Copyright by University of Bialystok.