Algebra II 0600-MS1-2ALG2

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

The overall form of credit for the course: final exam

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

• Description of 0600-MS1-2ALG2 in USOSweb