Linear Analysis (Michaelmas 2018)

Time and Location: M-W-F, 9-10am; room MR3

Linear Analysis is an introductory Functional Analysis course, in Part II of the Cambridge Tripos.


Lecture Notes from 2018

Lecture Notes from 2017

Example Sheets

The example sheets will be posted here during the course of the term.

List of lectures

  1. Normed vector spaces. The spaces l^p. Hoelder and Minkowski inequalities.
  2. Banach spaces. Bounded operators.
  3. Bounded operators. The dual space.
  4. Finite-dimensional spaces. Completion.
  5. Completion, products, quotients.
  6. Baire Category Theorem.
  7. Principle of uniform boundedness, Banach-Steinhaus Theorem. Open mapping theorem.
  8. Conclusion of proof of open mapping theorem. Examples. Closed graph theorem. Normal topological spaces.
  9. Urysohn-Tietze Extension Theorem.
  10. Compactness in metric spaces. Arzelà-Ascoli theorem.
  11. Compact operators. Application of the Arzelà-Ascoli theorem: Peano's Existence Theorem.
  12. Conclusion of Peano's Existence Theorem. Babylonian method to compute square roots.
  13. Stone-Weierstrass Theorem.


There are many classic textbooks on the subject. They can usually be found under the name Functional Analysis. However, I will mostly follow notes from in previous years: