It is unfortunately rather easy to complete a math major, and even go to graduate school, without learning much about what one might call “practical real analysis”. In this course, we try to remedy that situation by presenting a week’s worth of material that every working mathematician (especially in applied math) would be helped by knowing.

The basic text for the course is the classic Inequalities, by Hardy-Littlewood-Polya, but I’ll supplement it rather generously with material from the (excellent) The Cauchy-Schwartz Master Class by Steele.

Every day will have two lectures (about an hour each) and two problems to work on together (about an hour each).

Lecture Notes:

  1. Introduction to the p-means.
  2. Hölder’s Theorem.
    1. Problem set 1.
    2. Problem set 2.
  3. Minkowski’s Theorem and a theorem of Hadamard.
  4. Chebyshev’s inequality, Resolving Powers.
  5. Symmetrical Means and Muirhead’s Theorem.