Introduction to Topology

Code:

M3008

Acronym:

M3008

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	2	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	0	Official Study Plan	2	-	6	56	162
			3
L:G	1	study plan from 2017/18	3	-	6	56	162
L:M	9	Official Study Plan	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	6	56	162

Teaching language

Portuguese

Objectives

To introduce the theory of metric and topological spaces; to show that metric spaces are more general than Euclidean spaces and that topological spaces are yet more general than metric spaces.
To introduce some topological invariants and to be able to distinguish spaces.

Learning outcomes and competences

To be able to understand that the concepts introduced in the first and second year analysis can be extended to more general spaces to prove some powerful results used in may parts of mathematics . To be able to understand the concept of topological invariant and its use to distinguish and classify spaces.

Working method

Presencial

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

Real Analysis I, II and III.

Program

Mandatory literature

Sutherland W. A.; Introduction to metric and topological spaces. ISBN: 0-19-853161-3
Lima Elon Lages 1929-; Espaços métricos. ISBN: 978-85-244-0158-9
Schubert Horst; Topology. ISBN: 356-02077-0

Complementary Bibliography

Lima Elon Lages; Elementos de topologia geral
Mendelson Bert; Introduction to topology

Comments from the literature

The most important "bibliography" is what is given in the lectures.

Teaching methods and learning activities

Exposure of the program and resolution of exercises.

Resolution, by the students, of the proposed exercises and answering questions about the resolution of problems and proposed work.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	92,50
Participação presencial	7,50
Total:	100,00

Eligibility for exams

Terms of frequency: If the limit of absences is exceeded the student will not be admited access to examination, either in time or normal use (except for students exempted from frequency).

Calculation formula of final grade

Formula Evaluation: There wil be two components of assessment:

• Continuous Evaluation based on level of participation and performance in class (PP)
• Final written exam (EF)
-.-.-.-.-.-.-.-.-.-.-.-.-.- 

PP - Continuous Evaluation
EF - Final written exam
0,925*EF + 0,075*PP

Special assessment (TE, DA, ...)

According to the General Evaluation Rules.

Classification improvement

According to the General Evaluation Rules. The student can only improve the mark of the written exam.

Observations

Pre-requirements:

Real Analysis I, II and III.