(in Polish) Teoria Morse'a

General data

Course ID:	1000-1M19TM
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	(unknown)
Name in Polish:	Teoria Morse'a
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
Course homepage:	http://www.mimuw.edu.pl~mcboro/morse.html
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Prerequisites (description):	The student knows existence and uniqueness theorems in ODE's. He's supposed to know some basics of algebraic topology.
Mode:	Remote learning
Short description:	We describe the rudiments of Morse theory.
Full description:	Elementary theorems in Morse theory. Rearrangement and cancellation theorems. Morse--Witten chain complex. Proof of h-cobordism theorem.
Bibliography:	Milnor ,,Lectures on h-cobordism theorem'' Nicolaescu ,,Invitation to Morse theory" Banyaga, Hurtubise ,,Lectures on Morse theory" Borodzik, Nemethi, Ranicki "Morse theory for manifolds with boundary" Borodzik, Powell "Embedded Morse theory"
Learning outcomes:	The student understands the rudiments of knot theory and is capable of reading research papers on the subject as well as conducting independent research in the field.
Assessment methods and assessment criteria:	Oral exam online. Knowledge of theorems from the lecture and at least sketches of proofs is required.

This course is not currently offered.

Course descriptions are protected by copyright.
Copyright by University of Warsaw.