Douglas Ulmer — Teaching and Mentoring
“The only success which is ours to command is to bring to our work a mighty heart” (Oliver Wendell Holmes, slightly paraphrased)
Recent student projects
- R. Knak, D. Lewis, S. Nelson, T. Phillips, B. Savoie, B. Wei, Spring 2021 (readings on rational points)
- Madison Delmoe, Fall 2020 - Spring 2021 (congruences for the number of points on superelliptic curves)
- Tristan Phillips, Fall 2019 - Spring 2020 (readings on elliptic curves)
- Justice Harasha, Fall 2019 - Spring 2020 (readings in linear algebra)
- Shuangcai Zhang, visiting Xi'an University student, Spring 2014 (explicit points on elliptic curves)
- Michael Lane, Spring 2014 (combinatorics of orbits under a balanced subgroup)
- Sam Kim, Summer 2012 through Fall 2013 (senior project on representations and lattices)
- David Turk, Spring 2012 (senior project, generalizing Cipolla's algorithm to calculate n-th roots)
- David Hollis, Spring and Fall 2011 (combinatorics and “balanced” subgroups of the multiplicative group)
- Mahadi Osman, Summer 2011 (REU, representation theory of a semi-direct product of cyclic groups)
- David Turk and Zach Wilt, Spring 2011 (computing subgroups of the multiplicative group that are “balanced” in various senses)
- Ryan Carlin, Summer and Fall 2010 (representation theory calculations related to elliptic curves of high rank)
- Chris Pryby, Summer 2010 (background work on algebraic geometry and elliptic curves)
- Harrison Brown, Spring 2010 (linear algebra calculations related to elliptic curves of high rank)
Graduate students and postdocs
- PhD students
- Tommy Occhipinti, 2010. First position: 3-year post-doc, UC Irvine
- Lisa Berger, 2007. First position: Tenure-track assistant professor, Stony Brook University
- Geoffrey Cunningham, 2000. First position: Cryptologic mathematician, National Security Agency
- Master's students
- Boonyarit Intiyot, 2001
- Paul Baloun, 2000
- Postdocs mentored
- Arvind Suresh 2021-2024
- Padmavathi Srinivasan 2016-2017
- Kit Ho Mak 2012-2014
- Saikat Biswas 2011-2013
- Cetin Urtis 2002-2005
- Mugurel Barcau 2001-2004
- Shuzo Takahashi 2000-2004
- Dennis Eichhorn 2001-2003
- Carl Lienert 1998-2000
- Antonios Broumas 1998-2000
Course Archive
 |
At the Georgia Institute of Technology: |
||
| Honors Multivariable Calculus | Math 2561 | Spring 2016 | |
| Linear Algebra with Abstract Vector Spaces | Math 1564 | Fall 2015 | |
| Algebraic Geometry I | Math 6421 | Fall 2013 | |
| Honors Calculus II | Math 1512 | Fall 2012 | |
| Algebra I | Math 6121 | Fall 2011 | |
| Abstract Vector Spaces | Math 2406 | Fall 2010 | |
 |
At the University of Arizona: |
||
| Algebraic Geometry | Math 536AB | Fall 2008 - Spring 2009 | |
| Topics in Arithmetical Algebraic Geometry | Math 519 | Spring 2007 | |
| Theory of Graphs and Networks | Math 443/543 | Fall 2006 | |
| Complex Analysis (Riemann surfaces) | Math 520B | Spring 2006 | |
| Complex Analysis | Math 520A | Fall 2005 | |
| Algebraic Geometry | Math 536B | Spring 2005 | |
| Introduction to Cryptography | Math 445 | Spring 2004 | |
| Lie Groups and Lie Algebras | Math 559B | Spring 2003 | |
| Basic Statistics | Math 160 | Fall 2002 | |
| Lie Groups and Lie Algebras | Math 559A | Fall 2002 | |
| Calculus I | Math 125 | Fall 2001 | |
| Algebraic Topology | Math 531 | Fall 2001 | |
| Algebraic Geometry | Math 536B | Spring 2001 | |
| Business Mathematics II | Math 115B | Fall 2000 | |
| Calculus II (honors) | Math 129 | Fall 2000 | |
| Business Mathematics II | Math 128B | Spring 2000 | |
| Topology-Geometry | Math 534B | Spring 2000 | |
| Business Mathematics I | Math 128A | Fall 1999 | |
| Topology-Geometry | Math 534A | Fall 1999 | |
| Topics in Number Theory (Modular Forms) | Math 519 | Spring 1999 | |
| Math in Modern Society | Math 122 | Fall 1998 | |
| Introduction to Ordinary Differential Equations | Math 254 | Fall 1998 | |
| Topology-Geometry | Math 534B | Spring 1997 | |
| Introduction to Ordinary Differential Equations | Math 254 | Fall 1996 | |
| Topology-Geometry | Math 534A | Fall 1996 | |
| Matrix Analysis | Math 410 | Summer 1996 | |
| Algebraic Number Theory | Math 514B | Spring 1996 | |
| Linear Algebra | Math 215 | Fall 1995 | |
| Algebraic Number Theory | Math 514A | Fall 1995 | |
| Vector Calculus (2 sections) | Math 223 | Fall 1994 | |
| Second Course in Abstract Algebra | Math 416/516 | Spring 1994 | |
| Calculus II | Math 125B | Fall 1993 | |
| Abstract Algebra | Math 415/515 | Fall 1993 | |
| Algebraic Geometry | Math 536B | Spring 1993 | |
| Calculus I | Math 125A | Fall 1992 | |
| Algebraic Geometry (new course, ran as 538: Topics in Geometry and Topology) |
Math 536A | Fall 1992 | |
| Calculus I | Math 125A | Fall 1991 | |
| Algebra | Math 511A | Fall 1991 | |
 |
At the California Institute of Technology: |
||
| Topology and Geometry | Math 151c | Spring 1991 | |
| Number Theory | Math 160a | Winter 1990 | |
| Introduction to Complex Variables | Math 104 | Winter 1990 | |
| Abstract Algebra | Math 120c | Spring 1990 | |
| Algebraic Curves | Math 191e | Winter 1989 | |
| Projective Geometry | Math 91a | Fall 1989 | |
 |
At the Massachusetts Institute of Technology: |
||
| Algebraic Number Theory (Cyclotomic Fields) | 18.776 | Spring 1989 | |
| Calculus (Integrated Studies Program recitation) | 18.02 | Spring 1989 | |
| Calculus (Integrated Studies Program recitation) | 18.01 | Fall 1988 | |
| Calculus (One ISP recitation and one standard recitation) | 18.02 | Spring 1988 | |
| Calculus (Recitation) | 18.02 | Fall 1987 | |
| Applied Calculus (Recitation) | 18.013 | Fall 1987 |
| email: ulmer@math.arizona.edu | phone: 520-621-2868 | offices: Math 109 & ENR2 S311 |
