3/2: I proved the Theorem ¡­

3/2: I proved the Theorem 1.3.10 (local embedding theorem). Note that this theorem is (obviously) wrongly stated in the text book.A correct formulation of the theorem can you find

here

I lectured the remaining part of 1.3, then i started on section 1.4,constructed bump functions, proved Theorem 1.4.3 (that every compact manifold can be embedded into some Euclidean space. Then I refered Whitney Embedding Theorem (that every smooth m-manifold can be immersed into R^2m and embedded into R^(2m+1)).

10/2: I constructed partions of unity on a smooth manifold and showed that manifols are paracompact (section 1.5). I started on chapter 2 lectured 2.1 and 2.2. On 17/2 I will start lecturing 2.3, then I will jump to 3.2 and talk about vectorbundles in general. In the third hour I will do some exercises namely 1.3, 1.4 and 1.6 together with the following

two