Monday 2-3pm. L4.
Tuesday 10-11am. L5.
Thursday 12-1pm. L4.
L4 and L5 are over in the Science Concourse (opposite the library).
Support classes with Alexander Norlund-Matthiessen:
Week 2: Thursday 4-5 pm, in B2.04/5 in the Science Concourse.
Weeks 3-10 (unless otherwise advertised): Thursday 2-3 pm, B3.03 (Zeeman Bldg).
MA225 Differentiation, MA231 Vector Analysis. Also, MA222 recommended, but not essential.
Curves in the plane and 3-space. Frenet frames. Existence and uniqueness of curves with prescribed curvature and torsion. Parameterised surfaces in 3-space. Tangent spaces and normals. The first fundamental form. Definitions of embedded surfaces. Charts and transition maps. The second fundamental form. Principal and Gauss curvatures. Covariant derivatives of tangential vector fields on surfaces. Dependence on the first fundamental form. Parallel transport and geodesics. Gauss curvature is an intrinsic property. A local version of the Gauss-Bonnet theorem. Some global properties of closed surfaces. [Depending on time, abstract riemannian surfaces.]
100% written examination.
The 2013 examination will have a similar format to that of 2012.
That is, there will be one compulsory question worth 40%. In addition you should attempt three out of four optional questions worth 20% each.
Paper copies are available from the maths office.
Section 11 of the notes ``2-manifolds'' is NOT examinable in the 2013 examination.
Solutions to exercises by Tom Collyer are available via his homepage.
Geometry of Surfaces course notes
by Nigel Hitchin at the University of Oxford
(particularly Chapter 4, a.k.a. "Chapter 3, Surfaces in R^3"!) give a very nice concise introduction.
I used some material from this in preparing the course.
This course has a
where you can find some ``archived material'' from long ago.
It also has an Official page, which I can't edit (or I would have put a link there to this page).
Animation (Mathematics Museum, Ibaraki University.)
Interactive (Visual geometry, Technische Universitat, Berlin.)
Stills (Minimal surfaces, Indiana University.)
(1) John McCleary, "Geometry from a differential viewpont" :
Cambridge University Press 1994. (QA 641 M2).
[A more modern account of some classical material. Some material was used in preparing this course.]
(2) Dirk J. Struik, "Lectures on classical differential geometry" :
Addison-Wesley 1950 (QA 641 S8).
[Classical treatment, good reference for much of the material].
(3) Manfredo P. do Carmo, "Differential geometry of curves and surfaces" :
Prentice-Hall 1976 (QA 641 C2).
[More traditional approach. Lots of examples.]
(4) Barrett O'Neill, "Elementary differential geometry" :
Academic Press 1 1966 (QA 641 O6).
[More general introduction to classical differential geometry, with sections on curves and surfaces.]
(5) Sebastian Montiel, Antonio Ros, "Curves and surfaces",
American Mathematical Society 1998 (QA 643 M6613).
[More modern and advanced treatment.]
(6) Alfred Gray, "Modern differential geometry of curves and surfaces" :
CRC Press 1993 (QA 641 G7).
[Practical introduction to curves and surfaces, with many illustrations.]