Undergraduate Materials:

  1. A note on Ordered Fields (some material borrowed from a lecture by K K Chatterjee of Budrwan University); it describes topology of Ordered Fields, and 10 equivalent characterizations of $\mathbb R$. See it here.
  2. A proof of Schröeder Bernstein Theorem pdf file
  3. Schwarz's theorem in Calculus, which states something about a sufficient condition that the partial derivatives would commute. pdf file
  4. My notes on Peter-Weyl Theorem, which essentially says that if you have a compact group $G$, then the representative functions are dense in the space of continuous functions $C(G)$ in sup norm. dvi file
  5. An elementary, but self contained, introduction to Characteristic classes of vector bundles on topological spaces. pdf file
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