Students should be familiar with first courses in algebraic number theory and in analytic number theory.

Preparatory Reading for certain mini-courses. Each of the following are about 30 pages long:

— Melanie Wood (Harvard): “Probability theory for random groups arising in number theory” https://ems.press/books/standalone/278/5565

— Ashvin Swaminathan (Harvard): “Counting Cubic Number Fields” by Niven Achenjang https://www.mit.edu/~NivenT/assets/pdf/Counting_Cubic_Number_Fields.pdf.

— Adam Harper “Moments of random multiplicative functions, III: A short review” https://arxiv.org/abs/2410.11523, & the introduction of “On the limiting distribution of sums of random multiplicative functions”  https://arxiv.org/abs/2508.12956

— Alexandra Florea (UC Irvine): “Traces of high powers of the Frobenius class in the hyperelliptic ensemble” by Zeev Rudnick, Acta Arithmetic, 143.1 (2010), 81-99, obtain from this LINK

— Alex Smith: “The Selmer group, the Shafarevich-Tate group, and the weak Mordell Weil theorem” by Bjorn Poonen https://math.mit.edu/~poonen/f01/weakmw.pdf

— Tim Browning (IST Austria): “Beginners guide  to the circle method” by Andrew Granville https://dms.umontreal.ca/~andrew/CircleMethodNotes.pdf