If you are interested to learn about unique continuation of elliptic equations using Carleman inequalities, you may look into my slides.
I have done M.Sc. project in Analytic Number theory under the guidance of Dr. Saurabh Kumar Singh. My project mainly focuses on the Riemann zeta function and consequences of Riemann hypothesis. My project report can be accessed here.
I have attached some problems which would be helpful for under graduates.
Functional Set 1 (with solution)
Measure Set 1 (with solution)