Academic Year/course:
2017/18
453 - Degree in Mathematics
27041 - Differentiable Manifolds
Syllabus Information
Academic Year:
2017/18
Subject:
27041 - Differentiable Manifolds
Faculty / School:
100 - Facultad de Ciencias
Degree:
453 - Degree in Mathematics
ECTS:
6.0
Year:
4
Semester:
First semester
Subject Type:
Optional
Module:
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5.1. Methodological overview
Methodology for the course:
-Lectures
-Problem sessions in small groups
-Office hours.
-Students' individual work.
5.2. Learning tasks
At the end of each chapter there will be an exercise to prove the understanding of the contents and guarantee the learning process.
5.3. Syllabus
Contents
Differentiable manifolds.
The topology of a manifold . Partitions of the unity.
Differntiation on a manifold
Submanifolds
Quotient manifolds
Vector fields
Embedding theorems.
Transversality.
5.4. Course planning and calendar
See the academic calendar of the Universidad de Zaragoza.
Dates for exercises will be announced in class and posted on the online platform Moodle.
The same will be done with the date, place and time of the final exam.
5.5. Bibliography and recommended resources
Auslander,L - Mackenzie, R.E. Introduction to Differentiable Manifolds. Mc.Graw-Hill. 1963.
Boothby,W.M. An introduction to Differentiable Manifolds and Riemannian Geometry . Ac. Press. 1975.
Brickell,F.-Clark,R.S. . Differentiable Manifolds . Van Nostrand, 1970.
Burns, K – Gidea ,M . Differentiable Geometry and Topology. Chapman & Hall /CRC. 2005
Conlon,L. Differentiable Manifolds. A First Course. Birkhäuser , 1993
Gamboa J.M. - Ruiz J.M. Iniciación al estudio de las Variedades Diferenciables. Sanz y Torres 2016
Lee , J.M. Introduction to smooth manifolds. Springer-Verlag 2002.
Outerelo, E. - Ruiz, J.M - Rojo J.A. Topología Diferencial. Sanz y Torres 2014.