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\noindent{}These are the PI's most relevant publications.  They are on
Sage or use Sage extensively for applications to education and
research in number theory.


\head{Most Relevant Publications}%
\begin{itemize}\setlength{\itemsep}{0ex}

\item \emph{Elementary Number Theory: Primes, Congruences, and
    Secrets} (166 pages), Undergraduate Texts in Mathematics
  (Springer-Verlag), 2009. (Extensively uses Sage.)

 \item \emph{Opinion: Open Source Mathematical Software} (2007), Notices
of the AMS, {\bf 54}, no. 10.

 \item \emph{Explicitly {C}omputing {M}odular {F}orms} (284 page),
 Graduate Studies in Mathematics (AMS), 
 2007, with an appendix by Paul Gunnells. (Extensively uses Sage.)

 \item {\ptitle Verification of the Birch and Swinnerton-Dyer
      Conjecture for Specific Elliptic Curves}, with G. Grigorov, A.
    Jorza, S. Patrikis, and C. Patrascu (26 pages), 2009, 
    to appear in Mathematics of Computation.

\item {\ptitle Average {R}anks of
  {E}lliptic {C}urves: {T}ension {B}etween {D}ata and {C}onjecture},
  with  B.~Bektemirov, B.~Mazur, W.~Stein, and 
  M.~Watkins, Bulletins of the AMS (2006).
  
\item {\ptitle Visible Evidence for the Birch and Swinnerton-Dyer
Conjecture for Rank 0 Modular Abelian Varieties} (31 pages), with
A.~Agashe, Math. of Comp.%

\end{itemize}
\head{Other Relevant Publications}%
\begin{itemize}\setlength{\itemsep}{0ex}

  \item {\ptitle Studying the Birch and Swinnerton-Dyer Conjecture
for Modular Abelian Varieties Using Magma} (22 pages), 
chapter in the Springer-Verlag book ``Computational Experiments
in Algebra and Geometry''.%

    
\item {\ptitle The Modular Degree, Congruence Primes and Multiplicity One},
with A. Agashe and K. Ribet (16 pages), 2005, Documenta
Math.

\item {\ptitle Computation of $p$-Adic Heights and Log Convergence},
with B. Mazur and J. Tate (36 pages), 2006, Documenta
Mathematica. 

\item {\ptitle Shafarevich-Tate Groups of Nonsquare Order},
  Progress in Math., {\bf 224} (2004), 277--289, Birkhauser.
  
\item {\ptitle Constructing Elements in Shafarevich-Tate Groups of
Modular Motives}, (19 pages) with N.~Dummigan and M.~Watkins, 
``Number theory and algebraic geometry---to Peter
Swinnerton-Dyer on his 75th birthday'', Ed.
 by   M. Reid and A. Skorobogatov.%

\end{itemize}




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