(in Polish) Algebraic topology 1000-OG-EN-TA

(in Polish) Lecture : 30 h. Exercise classes: 30 h. Self-study: reading reference materials, completion of notes:30 h. Self-study: solving problems: 45 h. Preparation to the exam -15 h Total: 150 h. – 6 ECTS

(in Polish) W1: Knows the concept of homotopy, fundamental group and higher homotopy groups. (K_W01, K_W03) W2: Knows the role of covering spaces in determining the fundamental group. . (K_W02, K_W03) W3: Understands the construction of singular homology groups, their basic properties, in particular exact sequence of homology groups. . (K_W02, K_W03) W4: Is aware of axiomatic approach to homology theory. (K_W03) W5: Understands the functorial nature of the constructions of homology (homotopy) groups. (K_W03) W5: Knows selected applications of methods of algebraic topology.and the functoriality of this construction.(K_W04)

(in Polish) U1: Knows how to calculate fundamental groups in selected examples. (K_U01, K_U06, K_U10) U2: Determines homology groups of selected spaces, in particular using long exact sequence of homologies. .(K_U01, K_U06, K_U10) U3: Applies algebraic topology concepts to prove selected facts from topology and geometry. .(K_U01, K_U06) U4: Uses the terminology of algebraic topology and related branches of mathematics.(K_U10)

(in Polish) K1: Is able to evaluate his/her own knowledge and skills and to develop it independently. (K_K03)

(in Polish) Lecture accompanied by exercise classes

- informative (conventional) lecture

- practical

(in Polish) Knowedge of basic concepts of general topology and algebra (groups).

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• Description of 1000-OG-EN-TA in USOSweb