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:

- Introduction to the p-means.
- HÃ¶lder’s Theorem.
- Problem set 1.
- Problem set 2.

- Minkowski’s Theorem and a theorem of Hadamard.
- Chebyshev’s inequality, Resolving Powers.
- Symmetrical Means and Muirhead’s Theorem.
- More on symmetry and majorization.