Joseph H. Silverman

Office: 202 Kassar House Phone (direct): (401) 863-1124 Phone (dept office): (401) 863-2708 Fax: (401) 863-9013 Email: joseph_silverman@brown.edu Mailing Address: Mathematics Department Box 1917 Brown University Providence, RI 02912 USA

Teaching Schedule: 

Academic 2024/2025

Fall - Math 1540 - Topics in Abstract Algebra

Fall - Math 0750 - Introduction to Higher Mathematics

Spring - Math 2540 - Number Theory

Academic 2023/2024

Fall - Math 2530 - Number Theory

Spring - Math 0420 - Number Theory

Academic 2022/2023

Sabbatical Leave

Academic 2021/2022

Fall - Math 2530 - Number Theory

Spring - Math 1530 - Algebra

Advice for those requesting a Letter of Recommendation

Research Interests: Number theory, elliptic curves, arithmetic and Diophantine geometry, number theoretic aspects of dynamical systems, cryptography

Mathematical genealogy and list of Ph.D. students

CV and Publications

Click here for further information and a link to a CV and list of publications.

Books

1. Abstract Algebra: An Integrated Approach, AMS Pure and Applied Undergraduate Texts.
2. Moduli Spaces and Arithmetic Dynamics, CRM Monograph Series 30, AMS, 2012.
3. An Introduction to Mathematical Cryptography, with Jill Pipher and Jeffrey Hoffstein, Springer-Verlag, UTM, 2008. 2nd Edition 2014.
4. The Arithmetic of Dynamical Systems, Springer-Verlag, GTM 241, 2007.
5. A Friendly Introduction to Number Theory, Pearson, 1997. 4th Edition 2012.
6. Diophantine Geometry: An Introduction, with Marc Hindry, Springer-Verlag, GTM 201, 2000.
7. Advanced Topics in the Arithmetic of Elliptic Curves, Springer-Verlag, GTM 151, 1995.
   
8. Rational Points on Elliptic Curves, with John Tate, Springer-Verlag, UTM, 1992. Expanded 2nd Edition, 2015.
   
9. The Arithmetic of Elliptic Curves, Springer-Verlag, GTM 106, 1986. Expanded 2nd Edition, 2009.

Edited Volumes

1. Cryptography and Lattices Conference (CaLC 2001), editor, Lecture Notes in Computer Science 2146, Springer-Verlag, 2001.
2. Modular Forms and Fermat's Last Theorem, co-editor with Gary Cornell and Glenn Stevens, Springer-Verlag, 1997.
3. Arithmetic Geometry, co-editor with Gary Cornell, Springer-Verlag, 1986.

Selected Preprints and Reprints

Presentations

Reference Sheets

The following reference sheets are being made available as a service to the general mathematical community. They should be printed landscape (i.e., rotated 90 degrees).

Links to Number Theory Sites, Elliptic Curve Sites and Other Sites of Interest

• On-Line Number Theory Seminars
  • ADIOS – Arithmetic Dynamics International Online Seminar
  • VaNTAGe – Virtual math seminar on open conjectures in number theory and arithmetic geometry
  • Number Theory Web Seminar – Online seminar associated with the Number Theory Web
  • Online Math Seminars Listing – Extensive sortable and filterable list of online math seminars
• ABC Conjecture Web Site (Abderrahmane Nitaj)
• Algorithmic Number Theory Links (Noam Elkies)
• ArXiv Number Theory Preprint Server
• ArXiv Algebraic Geometry Preprint Server
• Groups: Table of small groups with names and notation (Tim Dokchitser)
• Lehmer's Conjecture Web Site (Michael Mossinghoff)
• LMFDB: The L-Series and Modular Form Database (also with lots of elliptic curve data)
• Magma Online Calculator
• Mathematics Geneaology Project
• NTRU Cryptosystems (Security Innovation)
• Number Theory Web
• Practical Suggestions For Mathematical Writing by Bjorn Poonen
• Sage: Open Source Mathematics Software
• XKCD: The Best of (Math and Crypto) from XKCD