Algebra II

General data

Course ID:	0600-MS1-2ALG2
Erasmus code / ISCED:	11.102 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (unknown)
Course title:	Algebra II
Name in Polish:	Algebra II
Organizational unit:	(in Polish) Instytut Matematyki.
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	obligatory courses
Requirements:	Algebra I 0600-FS1-2ALG1 Algebra I 0600-MS1-2ALG1 Elementary Number Theory 0600-FS1-1ETL Elementary Number Theory 0600-MS1-1ETL 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 i Algebry I.
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.
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
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.
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
Assessment methods and assessment criteria:	The overall form of credit for the course: final exam

This course is not currently offered.

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Copyright by University of Bialystok.