Differentiable Manifolds

Code:

M4051

Acronym:

M4051

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2013/2014 - 2S

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	4	Plano de Estudos do M:Matemática	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

Acquire fundamental knowledge of differentiable manifolds, important examples of Lie groups,  tensorial calculus, calculus on manifolds, de Rham cohomology, principal and vector bundles, connections on princial and vector bundles, semi-riemannian geometry.

Learning outcomes and competences

Acquire fundamental knowledge of differentiable manifolds, important examples of Lie groups,  tensorial calculus, calculus on manifolds, de Rham cohomology, principal and vector bundles, connections on princial and vector bundles, semi-riemannian geometry.

Working method

Presencial

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

Linear Algebra, Calculus in one and several real variables,  Vector Analysis.

Program

Differentiable manifolds, important examples of Lie groups,  tensorial calculus, calculus on manifolds, de Rham cohomology, principal and vector bundles, connections on princial and vector bundles, semi-riemannian geometry.

Mandatory literature

Carlos Menezes; Notas de aula
Warner Frank W.; Foundations of differentiable manifolds and Lie groups

Teaching methods and learning activities

Exposion of the syllabus by the teacher in the theoretical and practical classes.

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Calculation formula of final grade

The final mark is the mark of the final exam.