Undergraduate Course: Differential Geometry (MATH11235)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This 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 the following topics:
- Smooth manifolds, the manifold topology and submanifolds as level sets
- Tangent and cotangent spaces, derivative of a smooth map.
- Tangent bundle, vector fields, derivations, flows, Lie derivative.
- Vector bundles, tensor fields.
- Differential forms, Cartan calculus, de Rham complex.
- Orientation, integration, Stokes's theorem.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Honours Algebra (MATH10069) AND
Geometry (MATH10074)
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Co-requisites | |
| Prohibited Combinations | Students MUST NOT also be taking
|
Other requirements | Students MUST have not taken Differentiable Manifolds (MATH10088).
Note that PGT students on School of Mathematics MSc programmes are not required to have taken pre-requisite courses, but they are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
Information for Visiting Students
| Pre-requisites | This is a Year 4/5 advanced, Honours level course. Visiting students are expected to have an academic profile equivalent to at least the first three years of the BSc (Hons) Mathematics programme (UTMATHB), and should be confident that their background has equipped them to undertake a course at this level. Students should have passed courses equivalent to Honours Algebra (MATH10069) and Geometry (MATH10074). Students must not have taken Differentiable Manifolds (MATH10088). |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
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 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 20%, Examination 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S1 (December) | Differential Geometry (MATH11235) | 120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Explain the concept of a manifold and give examples
- Perform coordinate-based and coordinate-free calculations on manifolds
- Describe vector fields from different points of view and indicate the links between them
- Work effectively with tensor fields and differential forms on manifolds
- State and use Stokes' theorem
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Reading List
Recommended in addition to materials provided:
(*)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
(*)Loring Tu, Introduction to Manifolds, Springer 2010
(*) are available to download from the University Library |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | DG,Differential geometry,smooth manifolds |
Contacts
| Course organiser | Prof José Figueroa-O'Farrill
Tel: (0131 6)50 5066
Email: j.m.figueroa@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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