| An exact sequence of weighted Nash complexes |
submitted |
Submitted to Illinois Journal of Mathematics.
Given a three-dimensional complex algebraic variety with isolated singular point and a sufficiently fine complete resolution of the singularity, we can make a careful choice of hyperplane that allows us to construct an exact sequence of weighted Nash complexes.
Preprint in .pdf format |
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| p-Coloring classes of torus knots |
pending revisions |
Pending revisions, to appear in
the Missouri Journal of Mathematical Sciences.
Written with Anna-Lisa Breiland and Layla Oesper.
We develop a theorem for determining the p-colorability of any
(m,n) torus knot, and prove that any p-colorable
(m,n) torus knot has exactly one p-coloring class.
Preprint in .pdf format |
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| Taking Sudoku Seriously |
to appear |
To appear in Math Horizons.
We investigate the main open questions concerning Sudoku puzzles by examining
these questions in the 4x4 case. Many research questions suitable for undergraduate
research projects are included.
Preprint in .pdf format |
| |
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| Counting m-coloring classes of knots and links |
2006 |
Pi Mu Epsilon Journal, Volume 12, Number 5, Fall 2006.
Written with Kathryn Brownell and Kaitlyn O'Neil.
We develop a general formula for the number of fundamentally different
m-colorings of a knot based on its m-nullity, and apply
this result to the class of pretzel knots.
Preprint in .pdf format |
| |
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| Problem Zero: Getting students to read mathematics |
2005 |
MAA Innovative Teaching Exchange, April 2005.
An idea for a simple way to encourage students to read their textbooks and
to take ownership of and responsibility for the material.
Article on the MAA website |
| |
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| Integrated Calculus Textbook |
2004 |
Published nationally by Houghton Mifflin in 2004, ISBN 0-618-21950-1.
This textbook combines calculus, precalculus, and algebra into one two-semester
course sequence. Integrated Calculus addresses the needs of students
who need more background in precalculus and algebra, but covers calculus
material at a level that is suitable even for math and science majors.
Used at James Madison University since 2001, where it is the required text for
Math 231 and 232 (Calculus with Functions I and II). Also appeared as
a custom publication from Houghton-Mifflin as ISBN 0-618-30822-9 in 2002.
Has been used at
California State University Long Beach, Centre College, Gustavus Adolphus College, Harvard University, Hope College, James Madison University, Knox College, Loyola University Chicago, Miami Dade Community College, Monash University, North Central College, Oxford College of Emory University, Trinity College Hartford, Tulane University, University of St. Thomas, and Urbana University.
www.integratedcalculus.com
|
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| Simplicity is Not Simple: Tesselations and Modular
Architecture |
2002 |
Cover article for Math Horizons, September 2002.
Co-written with Eugenie Hunsicker, Lawrence University.
An investigation of 2-dimensional tesselations and 3-dimensional
space-filling polyhedra and their use in modular architecture, in particular
in the work of artist and architect Gregg Fleishman.
Winner of the MAA Trevor Evans Award.
Cover photo
Article in pdf format
|
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| Complete Resolutions, Hsiang-Pati Coordinates,
and the Nash Sheaf |
2001 |
Manuscripta Mathematica 106, 2001, no. 2, 249-270.
In this paper we show that if V is a 3-dimensional complex
algebraic variety with isolated singular point, then there exists a
"complete" resolution of V, i.e. a resolution over which the Nash sheaf
is locally free, and the maximal ideal sheaf and a certain Fitting ideal sheaf
are locally principal. Over such a resolution, the Nash sheaf is generated by
the differentials of monomial functions whose exponents are a Hsiang-Pati
ordered set.
Abstract
Review of article
Article in pdf format
|
| |
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| Calculus/Precalculus Coursepack and Laboratory Manual |
1999 and 2000 |
| John Wiley Custom Publishing, ISBN 0-471-40965-0 and
0-471-37785-6. Co-written with Jack Bookman, et al,
Duke University.
Required text for all sections of the laboratory calculus/precalculus sequence
at Duke University. |
| MAA Contributed Paper Session at the New Orleans Joint
Math Meetings |
Spring 2007 |
|
Organizer of the contributed paper session The Mathematics of Sudoku and Other
Puzzles, which featured 16 contributed talks about Sudoku, Kakuro, Knight's Tours,
and the game of SET, over two three-hour sessions.
|
| |
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| MAA Fall MD/DC/VA Sectional Meetings |
Fall 2006 |
Program Chair of the fall sectional meeting, which was hosted jointly by
Hampden-Sydney College and Longwood University in Farmville, Virginia.
The two-day meeting consisted of 19 contributed
faculty talks, Project NExT activities,
and four invited speakers (Eve Torrence of Randolph-Macon College delivered the
Workshop, Thomas Hull of Merrimack College gave the Banquet Address, and the Saturday
invited addresses were given by Betty Mayfield of Hood College and John Osoinach
of Millsaps College).
Fall MAA meeting website
|
| |
| |
| Shenandoah Undergraduate Mathematics and Statistics
Conference (SUMS II) |
Fall 2006 |
Co-Director of the second annual JMU SUMS Conference, which consisted of
22 undergraduate contributed talks, 27 student poster presentations, three
panel sessions, and two invited addresses (Ed Burger of Williams College and Tim Chartier
of Davidson College).
SUMS 2006 website
|
| |
| |
| Shenandoah Undergraduate Mathematics and Statistics
Conference (SUMS I) |
Fall 2005 |
Co-Director of the first annual JMU SUMS Conference, which consisted of
16 undergraduate contributed talks, 11 student poster presentations, a
panel session, and two invited addresses (Art Benjamin of Harvey-Mudd College and
Greg Warrington of Wake Forest University).
SUMS 2005 website
|
| |
| |
| MAA Panel Session at the Baltimore Joint Math Meetings |
Spring 2003 |
|
Organizer for the panel session Integrating Calculus, Precalculus, and Algebra,
which featured authors of combined calculus/precalculus textbooks and materials
(Nancy Baxter-Hastings of Dickinson College, Jack Bookman of Duke University,
Dennis Ebersole of Northampton Community College,
Robin Gottleib of Harvard University, and Robert Hostetler of Penn State Erie).
|
| |
| |
| Project NExT Session at the New Orleans
Joint Math Meetings |
Spring 2001 |
|
Co-organizer of the Pedagogy Swap Session at the Project NExT portion of the
AMS/MAA Joint Meetings in New Orleans.
|
| |
| |
| Panel discussion: Getting your first textbook published |
| Part of a panel organized by Project NExT at the AMS/MAA
Joint Meetings in New Orleans. |
Spring 2007 |
| |
| |
| Panel discussion: Strategies for Establishing Your
Research/Scholarship Agenda |
| Part of a panel for the JMU Center for Faculty Innovation,
Faculty Workshop Series |
Fall 2006 |
| |
| |
| Sudoku: Questions, Variations, and Research |
| Invited colloquium talk, Harvey Mudd College Department of
Mathematics, Claremont, California. |
Spring 2007 |
| Invited talk in the Graduate Minicourse
Series, University of Maryland
Department of Mathematics, College Park, Maryland. |
Fall 2006 |
| Invited colloquium talk, Washington and Lee
Department of Mathematics, Lexington, Virginia. |
Fall 2006 |
| Invited talk at the Gems of Recreational
Mathematics Special Session at MathFest 2006, Knoxville, Tennessee. |
Summer 2006 |
| Invited colloquium talk, Wake Forest University
Department of Mathematics, Winston-Salem, North Carolina. |
Spring 2006 |
| Invited one-hour address, MAA Spring MD/DC/VA Sectional
Meetings, Loyola College, Baltimore, Maryland. |
Spring 2006 |
| Invited one-hour closing address, Project NExT meeting
at the MAA KY Sectional Meetings at Centre College, Danville, Kentucky. |
Spring 2006 |
| |
| |
| Panel discussion: Tenure and Pre-Tenure Review |
| Part of a panel at the Project NExT meeting at MathFest 2006, Knoxville. |
Summer 2006 |
| |
| |
| Teaching the derivative one rule at a time |
| Contributed talk at MathFest 2006, Knoxville. |
Summer 2006 |
| |
| |
| Panel discussion: Finding your classrooom style |
| Part of a panel at the Project NExT meeting at the
MAA Spring Kentucky Sectional Meetings, Centre College. |
Spring 2006 |
| |
| |
| Sudoku Variations |
| Contributed Paper Session, MAA MD/DC/VA Fall Meetings, Montgomery College |
Fall 2005 |
| |
| |
| Brainwashing and Great Expectations: Thoughts about
teaching, persuasion, intimidation, expectations, bribes, and humor in the
classroom |
| Project NExT meeting at the MAA Fall MD/DC/VA Sectional
Meetings, Montgomery College (Germantown Campus). |
Fall 2005 |
| Invited talk, Alder Awards Session, MAA MathFest,
Albuquerque. |
Summer 2005 |
| |
| |
| An exact sequence of weighted Nash complexes |
| General Contributed Paper Session, MAA MathFest,
Albuquerque. |
Summer 2005 |
| |
| |
| How not to give a talk |
| Research for
Undergraduates Seminar, James Madison University 2005 REU
Program. |
Summer 2005 |
| |
| |
| Problem Zero: A simple way to encourage students to read
mathematics and make it their own |
| MAA Spring MD/DC/VA Sectional Meetings, University of Virginia. |
Spring 2005 |
| MAA Session: Getting Students to Explore Concepts Through Writing in
Mathematics, MAA MathFest, Providence. |
Summer 2004 |
| |
| |
| Tracking Student Success in an Integrated Calculus/Precalculus
Course
|
| General Contributed Paper Session, Joint AMS/MAA Meetings,
Phoenix. |
Spring 2004 |
| |
| |
| Integrated Calculus, Precalculus and Algebra:
Teaching calculus to underprepared students
|
| Invited talk, Mathematics Worshop Faculty Program,
Chicago. |
Spring 2004 |
| Invited talk, Mathematics Colloquium, American University. |
Spring 2002 |
| |
| |
| Panel Session on
Integrating Calculus, Precalculus, and Algebra
|
| Organizer and speaker at this panel session
featuring authors of combined calculus/precalculus textbooks, Joint AMS/MAA
Meetings, Baltimore. |
Spring 2003 |
| |
| |
| How I got here: an autobiographical talk
|
| Invited talk and discussion session,
Blue Ridge Chapter of the Association for Women in Science,
James Madison University. |
Spring 2003 |
| |
| |
| The Nash Bundle and the Nash Sheaf
|
| Mathematics Colloquium, James Madison University. |
Spring 2002 |
| |
| |
| Integrated Calculus: A combination course to effectively
train math and science majors
|
| MAA Contributed Paper Session, AMS/MAA Joint Meetings,
San Diego. |
Spring 2002 |
| |
| |
| Developing combined calculus/precalculus courses from
both traditional and reform perspectives
|
| Project NExT session at the MAA Spring MD/DC/VA Sectional
Meetings, Virginia Military Institute. |
Spring 2001 |
| |
| |
| Pedagogy Swap Session
|
| Co-organizer for this Project NExT session, AMS/MAA Joint
Meetings, New Orleans. |
Spring 2001 |
| |
| |
| Complete Resolutions, Hsiang-Pati Coordinates,
and the Nash Sheaf
|
| AMS Western Section Meetings, San Francisco State University.
Travel partially funded by the Association for Women in Mathematics. |
Fall 2000 |
| |
| |
| My thesis and why it isn't done yet: the evolution
of a Ph.D. thesis
|
| Graduate/Faculty Seminar, Duke University. |
Fall 1999 |
| |
| |
| The basics of teaching a combined precalculus/calculus course
|
| Teacher Training Program, Duke University. |
Summer 1999 |
| Teacher Training Program, Duke University. |
Summer 1998 |
| |
| |
| Chern Classes for Singular Hypersurfaces
|
| Graduate/Faculty Seminar, Duke University. |
Fall 1997 |
| |
| |
| Knot Theory from Two Perspectives (with Tim Culver)
|
| Graduate/Faculty Seminar, Duke University. |
Fall 1997 |
| |
| Divisors and Line Bundles
|
| Riemann Surfaces Seminar, Duke University. |
Spring 1997 |
| Program Chair, Mathematical Association of America MD/DC/VA
Section |
2006 - Present |
|
| |
| Program Chair-Elect, Mathematical Association of America MD/DC/VA
Section |
2005 - 2006 |
|
| |
| Conference Program Co-Director,
Shenandoah Undergraduate Mathematics and Statistics (SUMS) Conference |
2005 - Present |
|
| |
| Carriage House Advisory Board, Mathematical Association of America |
2005 - Present |
|
| |
| Trevor Evans Award Committee, Mathematical Association of America |
2005 - Present |
|
| |
| Editor, JMU Math Department's
Problem of the Week |
2003 - Present |
|
| |
| Editor and Founder,
The Online Journal of Undergraduate Papers in Knot
Theory |
2003 - Present |
|
| |
| Judge, Shenandoah Regional Science Fair (Mathematics, Computer Science,
and Consumer Science categories) |
2003 - Present |
| |
| Proofreading for MATHCOUNTS, Handbook and National and State Competitions |
2002 - Present |
| |
| Pure Math Committee |
2000 - Present |
| |
| Calculus Committee |
2000 - Present |
| |
| Recruitment and Activities Committee |
2005 - Present |
| |
| High School Mathematics Contest Committee (Editor 2003 and 2004) |
2002 - 2004 |
| |
| University of Chicago Alumni Interviewer |
2003 - 2004 |
| |
| Statistics Search Committee |
2003 |
| |
| Calculus Textbook Selection Committee |
2003 |
| |
| Calculus Contest Proofreader |
2001 |
| |
| Ad-hoc Roop Office Assignment Committee |
2006 |
| |
| Ad-hoc Committee for Teacher-Course Evaluations |
2001 |
| MAA Fall MD/DC/VA Sectional Meetings, Hampden-Sydney College and
Longwood University, Farmville, Virginia |
Fall 2006 |
| |
| Shenandoah Undergraduate Mathematics and Statistics Conference (SUMS II)
at James Madison University |
Fall 2006 |
| |
| MathFest Meetings of the MAA, Knoxville, Tennessee |
Summer 2006 |
| |
| MAA Spring MD/DC/VA Sectional Meetings, Loyola College, Maryland |
Spring 2006 |
| |
| Project NExT and MAA Meeting for the Kentucky Section, Centre College |
Spring 2006 |
| |
| Shenandoah Undergraduate Mathematics and Statistics Conference (SUMS I)
at James Madison University |
Fall 2005 |
| |
| MAA Fall MD/DC/VA Sectional Meetings, Montgomery College (Germantown Campus) |
Fall 2005 |
| |
| MathFest Meetings of the MAA, Albuquerque, New Mexico |
Summer 2005 |
| |
| MAA Spring MD/DC/VA Sectional Meetings, University of Virginia |
Spring 2005 |
| |
| MathFest Meetings of the MAA, Providence, Rhode Island |
Summer 2004 |
| |
| Mathematics Workshop Faculty Program, Chicago, Illinois |
Spring 2004 |
| |
| AMS/MAA National Joint Meetings and Project NExT, Phoenix, Arizona |
Spring 2004 |
| |
| Big Sky Discrete Mathematics Conference, University of Montana |
Fall 2003 |
| |
| AMS/MAA National Joint Meetings and Project NExT, Baltimore, MD |
Spring 2003 |
| |
| V2CTM Conference, Harrisonburg High School |
Fall 2002 |
| |
| MAA/PREP Knot Theory Workshop, Wake Forest University |
Summer 2002 |
| |
| AMS/MAA National Joint Meetings and Project NExT, San Diego, California |
Spring 2002 |
| |
| Annapolis Algebraic Geometry Conference, United States Naval Academy |
Fall 2001 |
| |
| Project NExT and MathFest Meetings of the MAA, Madison, Wisconsin |
Summer 2001 |
| |
| Calculus and Precalculus, and Integrative Approach, NSF CHATAQUA short course
at Harvard University |
Summer 2001 |
| |
| National Mathcounts Competition, Washington, D.C. |
Summer 2001 |
| |
| MAA Spring MD/DC/VA Sectional Meetings, Virginia Military Institute |
Spring 2001 |
| |
| MAA Fall MD/DC/VA Sectional Meetings, American University |
Fall 2000 |
| |
| AMS Fall Western Sectional Meetings, San Francisco State University |
Fall 2000 |
| |
| Project NExT and MathFest Meetings of the MAA,
University of California, Los Angeles |
Summer 2000 |
| |
| AMS/MAA National Joint Meetings, Washington, D.C. |
Spring 2000 |
| |
| PCMI Symplectic Geometry and Topology Conference, Park City, Utah |
Summer 1997 |
| |
| Park City Women's Program, Institute for Advanced Study |
Summer 1997 |
| NSF/MAA Grant supporting a Regional Undergraduate
Mathematics Conference (RUMC) |
2005, 2006 |
| NSF Grant DMS-0241090 to partially support the
Shenandoah Undergraduate Mathematics and Statistics (SUMS)
Conference at James Madison University. (Funding for the SUMS Conference is
also provided by the Association for Women in Science, and by the
College of Science and Mathematics,
Department of Mathematics and Statistics, Research Experience for Undergraduates
Program, and Mathematics and Statistics Club at James Madison University.) |
| |
| |
| Texty Award |
2006 |
| Recipient of the 2006 Texty Award in the category of
Mathematics and Statistics, for the textbook Integrated Calculus.
Texty Awards are given annually by the Text and Academic Authors
Association (TAA) to recognize current textbooks and learning materials. |
| |
| |
| Be the Change |
2006 |
One of many James Madison University people whose profiles are featured as
part of the Be the Change campaign.
Be the Change profile
|
| |
| |
| Departmental Distinguished Teacher Award |
2006 |
| This award is given annually by the Department of Mathematics and
Statistics at James Madison University.
|
| |
| |
| Nominee for the College of Science and Mathematics Distinguished
Teacher Award |
2006 |
|
The Department of Mathematics and Statistics nominates one faculty member each year
for the college-wide Distinguished Teacher Award.
|
| |
| |
| Alder Award |
2005 |
| One of three recipients of this national award from the MAA
that recognizes talented young teachers in mathematics whose teaching has
had influence beyond their own classrooms. |
| |
| |
| Trevor Evans Award |
2003 |
| An article I wrote with Eugenie Hunsicker was one
of two articles chosen by the MAA for this award, which honors
authors of exceptional articles that are accessible to undergraduates and published
in Math Horizons. |
| |
| |
| James Madison University Summer Teaching Grant |
2001 |
| Awarded a grant for Summer 2001 to develop a new course sequence that
integrates calculus, precalculus, and algebra. |
| |
| |
| AWM Travel Fellowship |
2000 |
| Fellowship for research conference travel expenses
awarded by the Association for Women in Mathematics. |
| |
| |
| Project NExT Fellow |
2000-2001 |
| Fellowship for new mathematicians and teachers of mathematics,
to attend a series of conferences and professional development workshops. |
| |
| |
| L.P. and Barbara Smith Award for Excellence in Teaching |
1998, 1999 |
| Sole recipient for two years running of the highest graduate
teaching award given by the Duke University Mathematics Department. I was the
first person to win this award twice. |
| |
| |
| Dean's Award for Excellence in Teaching |
1997, 1999 |
| On two occasions, one of two recipients of this
university-wide annual award from the Duke University Graduate School.
Teachers must be nominated by their students (who write essays justifying
the nomination) to be eligible for this award. |
| |
| |
| Duke Mathematics Teaching Award |
1997 |
| Annual award given by the Duke University Mathematics Department
to graduate student teachers. |