
Course unit
HOMOLOGY AND COHOMOLOGY
SC02111817, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/03 
Geometry 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
3 Omologia e Coomologia  a.a. 2018/2019 
01/10/2018 
30/09/2019 
CHIARELLOTTO
BRUNO
(Presidente)
BALDASSARRI
FRANCESCO
(Membro Effettivo)
BERTAPELLE
ALESSANDRA
(Supplente)
CAILOTTO
MAURIZIO
(Supplente)
FIOROT
LUISA
(Supplente)
LONGO
MATTEO
(Supplente)

Prerequisites:

we expect the student knows that it is possible to associate some invariants (fundamental group..) to topological spaces and he knows the existence of some topologies as the Zariski's one. 
Target skills and knowledge:

basic commutative algebra and algebraic geometry 
Examination methods:

taylored on the basis of the students attitudes: oral and homeworks. 
Assessment criteria:

some new techniques will be introduced: we expect the student shows how to master them. 
Course unit contents:

Starting from the basic definition of the algebraic topology we will introduce the definition of homology and cohomology for a topological space. Later we will see how such a idea can be "realized" in other cases by specializing the basic space in an algebraic variety and/or a complex analytic space (de Rham). 
Planned learning activities and teaching methods:

in class and homeworks 
Additional notes about suggested reading:

we will indicate them during the class: as a part of a book or/and notes. 
Textbooks (and optional supplementary readings) 

Innovative teaching methods: Teaching and learning strategies
 Problem based learning
 Interactive lecturing
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex
 Mathematica
 Matlab
Sustainable Development Goals (SDGs)

