First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
HOMOLOGY AND COHOMOLOGY
SC02111817, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track ALGANT [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination HOMOLOGY AND COHOMOLOGY
Website of the academic structure http://matematica.scienze.unipd.it/2019/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge BRUNO CHIARELLOTTO MAT/03

Mutuating
Course unit code Course unit name Teacher in charge Degree course code
SC02111817 HOMOLOGY AND COHOMOLOGY BRUNO CHIARELLOTTO SC1172

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

Syllabus
Prerequisites: we expect the student knows that it is possible to associate some invariants (fundamental group..), basic commutative algebra.
Target skills and knowledge: The student should understand the meaning of invariants for a topological space
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. Singular, simplicial, cellular, relative, excisin, mayer-vietoris. Tor and Ext: universal coefficients theorem. Cup and cap product: teh ring structure on the cohomology of a projective space. Poincare' duality
Planned learning activities and teaching methods: in class and homeworks
Additional notes about suggested reading: we will indicate them during the class: as part of books or/and notes.

J.Rotman "Introduction to algebraic topology" Springer
A. Hatcher "Algebraic Topology"
Textbooks (and optional supplementary readings)

Innovative teaching methods: Teaching and learning strategies
  • Problem based learning
  • Questioning
  • Problem solving
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex

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