Alessandro Carlotto: Katalogdaten im Frühjahrssemester 2020

NameHerr Dr. Alessandro Carlotto
LehrgebietMathematik
E-Mailalessandro.carlotto@math.ethz.ch
DepartementMathematik
BeziehungAssistenzprofessor

NummerTitelECTSUmfangDozierende
401-2554-00LTopology Information Belegung eingeschränkt - Details anzeigen 6 KP3V + 2UA. Carlotto
KurzbeschreibungTopics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces.
LernzielAn introduction to topology i.e. the domain of mathematics that studies how to define the notion of continuity on a mathematical structure, and how to use it to study and classify these structures.
LiteraturWe will follow these, freely available, standard references by Allen Hatcher:

i) http://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf

(for the part on General Topology)

ii) http://pi.math.cornell.edu/~hatcher/AT/ATch1.pdf

(for the part on basic Algebraic Topology).

Additional references include:

"Topology" by James Munkres (Pearson Modern Classics for Advanced Mathematics Series)

"Counterexamples in Topology" by Lynn Arthur Steen, J. Arthur Seebach Jr. (Springer)

"Algebraic Topology" by Edwin Spanier (Springer).
Voraussetzungen / BesonderesThe content of the first-year courses in the Bachelor program in Mathematics. In particular, each student is expected to be familiar with notion of continuity for functions from/to Euclidean spaces, and with the content of the corresponding basic theorems (Bolzano, Weierstrass etc..). In addition, some degree of scientific maturity in writing rigorous proofs (and following them when presented in class) is absolutely essential.
401-5350-00LAnalysis Seminar Information 0 KP1KM. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, L. Kobel-Keller, T. Rivière, Uni-Dozierende
KurzbeschreibungForschungskolloquium
Lernziel
InhaltResearch seminar in Analysis
406-2554-AALTopology
Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.
6 KP13RA. Carlotto
KurzbeschreibungTopics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces.
LernzielAn introduction to topology i.e. the domain of mathematics that studies how to define the notion of continuity on a mathematical structure, and how to use it to study and classify these structures.
SkriptSee lecture homepage: https://metaphor.ethz.ch/x/2017/fs/401-2554-00L/
LiteraturJames Munkres: Topology
Voraussetzungen / BesonderesThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.