The intention of the boot camp is to help new graduate students to review undergraduate real analysis and get prepared for the Math 240 series, real analysis, in UCSD.
We won't cover topics in full details since Math 240 will go over those very carefully.
Qingyuan Chen, qic069@ucsd.edu
Zilu Ma, zim022@ucsd.edu
The following are loose plans and we will adjust them accordingly later.
Practice problems will be given later and exercises in Rudin's books are pretty good.
Monday: real numbers, axiom of choice, Zorn's lemma. basic topology, metric spaces.
Tuesday: Cauchy, continuity. series, differentiation, Taylor
Wednesday: Riemann-Stieltjes Integral. uniform convergence, Arzela-Ascoli, Stone-Weierstrass
Thursday: normed space, Baire category Lp space, Fourier series
Friday: sigma-algebra, measures. Lebesgue integration, monotone convergence theorem, dominated convergence theorem, etc.