\documentclass[12pt]{ucbletter}12\name{William A.~Stein}3\signature{William Stein}4\location{1075 Evans}5\telephone{(510)643-0893 (office), \,\,\,(510)883-9938 (home)}6\email{was@math.berkeley.edu}7\address{8William A.~Stein\\92041 Francisco Street, \#14\\10Berkeley, CA 94709}1112\letterheadanyway13\signature{William A.~Stein}14\adjustmargins{-.25in}1516\begin{document}1718\begin{letter}{19}2021\opening{Dear Application Committee:}2223I wish to apply for a [job]24My application, curriculum vitae, list of abstracts,25and statement of future research plans are enclosed.26I have arranged for \nobreak{letters} of recommendation from27K.~Buzzard, R.~Coleman, H.~Lenstra, B.~Mazur, L.~Merel,28and K.~Ribet to be sent separately.2930I am a graduate student at the University of California at31Berkeley and expect to receive my Ph.D.\ degree in May 2000 from32the Department of Mathematics. Under the33guidance of Professor Hendrik W.~Lenstra, I am currently writing my34dissertation which is entitled {\em Explicit approaches to modular35abelian varieties}. My interests are in the36areas of number theory, modular forms, special values of37$L$-functions, Galois representations, and algorithms.38I have had frequent conversations with [...].394041In my dissertation work, I develop methods for42explicitly working with modular forms and abelian43varieties, and then apply my results to study Mazur's notion44of visibility of Shafarevich-Tate groups in connection with the45Birch and Swinnerton-Dyer conjecture.46In addition, I give new examples of modular icosahedral Galois47representations, and have developed a package of modular forms software.4849I have four years of teaching experience, and have given many50seminar talks. I have taught three courses51in the areas of Discrete Mathematics and College Algebra, and52served as a teaching assistant for Calculus53and Linear Algebra courses as well as for a graduate level54course at the IAS/Park City conference.55I wrote educational {\sc Matlab} software as part of56an NSF sponsored curriculum development effort.5758I am very committed to pursuing a research59career in academia, and look forward60to hearing from you regarding my application. If you have any61further questions, please send email to62{\sf was@math.berkeley.edu} or call me at 510-883-9938.63Thank you for your time and consideration.646566\closing{Sincerely,}676869\end{letter}7071\end{document}7273