Algebra II 360-FS1-2ALG2
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 15x2h = 30h
preparation for classes 15x2h = 30h
completing notes after exercises and lectures 15x1h = 15h
consultations 5x2h = 10h
preparation for control works 2x5h = 10h
the final examination: preparation.and take 12h + 3h = 15h
Quantitative description
Direct interaction with the teacher: 63 h., 2 ECTS
Type of course
Requirements
Algebra I
Linear Algebra I
Linear Algebra I
Linear Algebra II
Linear Algebra II
Elementary Number Theory
Elementary Number Theory
Prerequisites (description)
Course coordinators
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). KA6_WG03, KA6_WG04.
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. KA6_WG01, KA_WG02, KA6_WG04.
A student can identify a concrete example of application of algebra in reality (i.e. counting of combinatorial objects by the Burnside lemma). KA6_WG04, KA6_UU01.
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. KA6_WK01, KA6_UU02.
Additional information
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