|
| Udgave: |
Efterår 2012 NAT |
| Point: |
7,5 |
| Blokstruktur: |
2. blok |
| Skemagruppe: |
A |
| Fagområde: |
mat |
Semester: |
Efterår |
| Varighed: |
9 uger. |
| Institutter: |
Institut for Matematiske Fag |
| Uddannelsesdel: |
Kandidat niveau |
| Kontaktpersoner: |
postdoc Ehud Meir, kontor 04.3.01, telefon: 3532 0687, email:meir@math.ku.dk |
| Skema- oplysninger: |
 Vis skema for kurset
Samlet oversigt over tid og sted for alle kurser inden for Lektionsplan for Det Naturvidenskabelige Fakultet Efterår 2012 NAT |
| Undervisnings- periode: |
19. november 2012 - 27. januar 2013 |
| Undervisnings- form: |
5 timers forelæsninger og 4 timers øvelser per uge. |
| Indhold: |
Modules, tensor products, exact sequences.
Categories, functors, natural transformations.
Chain complexes and homology, resolutions, derived functors.
Topics from:
Category theory: Adjoint functors, universal constructions, limits and colimits, abelian categories.
Homology theory: Spectral sequences, derived categories, simplicial methods, differential graded algebra.
Applications: Dimension theory for rings, Group cohomology, Hochschild cohomology, singular homology.
|
| Kompetence- beskrivelse: |
I området svarende til det faglige indhold skal man kunne følge og gengive beviser på højeste abstrakte niveau, og løse abstrakte problemer. |
| Målbeskrivelse: |
At the end of the course the student should
Be well versed in the basic theory of modules over a ring (direct sums and products, tensor products, exact sequences, free, projective, injective and flat modules.)
Understand the basic methods of category theory and be able to apply these in module categories (isomorphisms of functors, exactness properties of functors, adjoint functors, pushouts and pullbacks).
Have a thorough understanding of constructions within the category of chain complexes (homology, homotopy, connecting homomorphism, tensor products, Hom-complexes, mapping cones).
Have ability to perform calculations of derived functors by constructing resolutions (Ext and Tor).
Be able to interpret properties of rings and modules in terms of derived functors (homological dimensions, regularity).
Have ability to solve problems in other areas of mathematics, such as commutative algebra, group theory or topology, using methods from homological algebra.
|
| Lærebøger: |
P.J. Hilton and U. Stammbach, A Course in Homological Algebra, Graduate Texts in Mathematics 4, Springer-Verlag
and supplementary notes, depending on the chosen topics.
S. Maclane- Homology, Classics in mathematics, Springer.
J. J. Rotman- An introduction to homological algebra
|
| Tilmelding: |
Kursus- og eksamenstilmelding og afmelding sker på
www.kunet.dk
Tilmelding skal ske i perioden den 15. maj – 1. juni 2012.
|
| Faglige forudsætninger: |
Alg2, Top
|
| Eksamensform: |
Løbende evaluering, baseret på 3 opgavesæt. Karakter efter 7-trin skalaen, ekstern censur.
Reeksamen: 30 minutters mundtlig eksamen med forberedelse. Karakter efter 7-trin skalaen, ekstern censur.
|
| Eksamen: |
Løbende evaluering.
Reeksamen: Mundtlig prøve den 18. april 2013. |
| Kursus hjemmeside: |
 |
| Pensum: |
Fastlægges løbende. |
| Undervisnings- sprog: |
Engelsk
|
| Sidst redigeret: |
24/10-2012 |