Topology

Code:

M4050

Acronym:

M4050

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:M	6	Plano de Estudos do M:Matemática	1	-	6	56	162
			2

Teaching language

Suitable for English-speaking students

Objectives

Introduce the students to the theory of topological spaces and continuous functions. Basic notions of algebraic topology, mainly those related to homotopy.

Learning outcomes and competences

A working knowledge of the fundamental concepts of general topology and a first encounter with the methods of algebraic topology.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

The theory of metric spaces, including normed spaces.

Program

Topological spaces and continuous functions. Comparison of topologies. Basis and subbasis. Products and sums. Separation axioms. First and second countable spaces. Compacteness and related properties. Connectedness and related properties. Metrizable topological spaces.
Homotopy. Basic properties. The fundamental group.

Mandatory literature

Munkres James R.; Topology. ISBN: 0-13-925495-1

Complementary Bibliography

Willard Stephen; General topology. ISBN: 0-201-08707-3
May J. P.; A concise course in algebraic topology. ISBN: 0-226-51182-0
Munkres James R.; Elements of algebraic topology. ISBN: 0-201-04586-9

Teaching methods and learning activities

Classroom presentation of the theory and resolution of exercises.

keywords

Physical sciences > Mathematics > Geometry > Algebraic topology

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	75,00
Participação presencial	5,00
Trabalho prático ou de projeto	20,00
Total:	100,00

Calculation formula of final grade

FG - grade in the final exam
CP - grade for classroom participation
AE - grade in the assignements

0,75*FG+0,05*CP+0,20*AE