Learning outcomes and verification methods:
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). - Oral/written Exam Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation
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. - Oral/written Exam Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation
A student can identify a concrete example of application of algebra in reality (i.e. counting of combinatorial objects by the Burnside lemma). - Oral/written Exam Quizzes Test/ midterm exam Homework presentation of solutions
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. - Oral/written Exam Homework continous evaluation