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).