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.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 
Students MUST have passed:
Honours Algebra (MATH10069) AND
Geometry (MATH10074)

Corequisites  
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 prerequisite courses, but they are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, 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 )

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 
Hours & Minutes 

Main Exam Diet S1 (December)  Differential Geometry (MATH11235)  2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Explain the concept of a manifold and give examples
 Perform coordinatebased and coordinatefree 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

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  Dr Gerben Oling
Tel:
Email: gerben.oling@ed.ac.uk 
Course secretary  Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk 

