# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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# Undergraduate Course: Differentiable Manifolds (MATH10088)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 10 (Year 4 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 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
 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
 Pre-requisites None High Demand Course? Yes
 Academic year 2017/18, 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 Manifolds 2:00
 On completion of this course, the student will be able to: Explain the concept of a manifold and give examples.Perform coordinate-based 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. Explain the concept of a Riemannian metric.
 Recommended : (*) John Lee, Introduction to smooth manifolds, Springer 2012 Michael Spivak, Calculus on manifolds, Benjamin, 1965 Theodor Bröcker & Klaus Jänich, 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
 Graduate Attributes and Skills Not entered Keywords DMan
 Course organiser Dr Pieter Blue Tel: (0131 6)50 5076 Email: P.Blue@ed.ac.uk Course secretary Mrs Alison Fairgrieve Tel: (0131 6)50 5045 Email: Alison.Fairgrieve@ed.ac.uk
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