Algebra II
General data
Course ID:  0600MS12ALG2#a  Erasmus code / ISCED:  11.102 / (0541) Mathematics 
Course title:  Algebra II  Name in Polish:  Algebra II 
Department:  Faculty of Mathematics and Informatics  
Course groups: 
(in Polish) 3L stac. I st. studia matematyki  przedmioty obowiązkowe 

ECTS credit allocation (and other scores): 
5.00 view allocation of credits 

Language:  English  
Type of course:  obligatory courses 

Prerequisites:  Algebra I 0600MS12ALG1#a 

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 

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. nonsolvability by radicals of polynomial equations, nonconstructability 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 
Classes in period "Academic year 2018/2019" (in progress)
Time span:  20181001  20190630 
see course schedule 
Type of class: 
Class, 30 hours more information Lecture, 30 hours more information 

Coordinators:  Jarosław Kotowicz  
Group instructors:  (unknown)  
Students list:  (inaccessible to you)  
Examination:  Examination 
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