THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

University Homepage
DRPS Homepage
DRPS Search
DRPS Contact
DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Differentiable Manifolds (MATH10088)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis course is an introduction to differentiable manifolds from an intrinsic point of view, leading to classical theorems such as the generalised Stokes' theorem. It extends the subject matter of Y3 Geometry from surfaces (embedded in R^3) to differentiable manifolds of arbitrary dimension (not necessarily embedded in another space). This provides the necessary concepts to start studying more advanced areas of geometry, topology, analysis and mathematical physics.
Course description The course will include many of the following topics: -
- Definition of topological manifolds
- Smooth manifolds and smooth maps, partitions of unity
- Submanifolds and implicit function theorem
- Tangent spaces and vector fields from different points of view (derivations, velocities of curves)
- Flows and Lie derivatives
- Tensor fields and differential forms
- Orientation, integration and the generalised Stokes' Theorem
- Basic notions of Riemannian geometry
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Honours Differential Equations (MATH10066) AND Honours Algebra (MATH10069) AND Geometry (MATH10074))
Co-requisites Students MUST also take: General Topology (MATH10076) OR General and Algebraic Topology (MATH10075)
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Academic year 2018/19, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 5%, Examination 95%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)Differentiable Manifolds2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Explain the concept of a manifold and give examples.
  2. Perform coordinate-based calculations on manifolds.
  3. Describe vector fields from different points of view and indicate the links between them.
  4. Work effectively with tensor fields and differential forms on manifolds.
  5. State and use Stokes' theorem. Explain the concept of a Riemannian metric.
Reading List
Recommended :

(*) John Lee, Introduction to smooth manifolds, Springer 2012
Michael Spivak, Calculus on manifolds, Benjamin, 1965
Theodor Broecker & Klaus Jaenich, Introduction to Differential Topology, CUP 1982
Frank Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer 1983
(*) Loring Tu, Introduction to Manifolds, Springer 2010
(*) are available to download from the University Library
Additional Information
Graduate Attributes and Skills Not entered
KeywordsDMan
Contacts
Course organiserProf Josť Figueroa-O'Farrill
Tel: (0131 6)50 5066
Email: j.m.figueroa@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
Navigation
Help & Information
Home
Introduction
Glossary
Search DPTs and Courses
Regulations
Regulations
Degree Programmes
Introduction
Browse DPTs
Courses
Introduction
Humanities and Social Science
Science and Engineering
Medicine and Veterinary Medicine
Other Information
Combined Course Timetable
Prospectuses
Important Information