This is the (unofficial) website of MA3H5.
Support classes with Rhiannon Dougall
Starting week 2: Tuesday 4pm, B1.01.
Weeks 3-10: Thursday 10am, MS.03.
The course also has an Offical web page.
Note: These are have only recently been prepared. Almost certainly there are still some mistakes in them. I will post any significant corrections as they are noticed.
Prior to 2014, a course with the same title was given as a 4th-year module. The course notes above give a nice account of much of the material in the current 3rd year unit. Lots of pictures, more examples and explanations. I have used it in preparing my own notes. It covers most (but not all) of the current course, and lots more. (There is a lot of stuff about transversality which is not in the present course. Conversely, I was planning to say something about general vector bundles, which is not discussed in these notes.)
Sphere eversions: turning a sphere inside out through immersions: Scary video: Optiverse video and explanations: Optiverse page
Mechanical linkages: manifolds as configuration spaces: WP page, and a paper by (our very own) Magalhaes and Pollicott here, with reference to the Thurston-Weeks Linkage (surface of genus 2).
L. W. Tu, ``An Introduction to Manifolds'', Universitext Springer-Verlag (2010).
[Covers most of the material in the course fairly efficiently.]
J. M. Lee, ``Introduction to Smooth Manifolds'', Graduate Texts in
Mathematics, Springer (2013).
[Good introductory text. Develops the theory from basic material to more advanced topics. Covers most of the course. 600+ pages.]
``Foundations of differentiable manifolds and Lie groups'', Graduate Texts in
Mathematics, Springer (2010).
[A more formal treatment. Progresses quite quite quicky on to more advanced topics.]
W. Boothby, ``An introduction to differentiable manifolds and Riemannian geometry'', Academic Press (2003). QA614.3.B6.