Research (or scholarly activities) complement teaching and
vice-versa.
I unequivocally believe that an active
and on-going involvement in scholarly activities and research
can enhance and complement my ability to excel in undergraduate
teaching.
Indeed, one way to motivate students to be enthused with what they
are learning is to
make them aware of the current issues pertaining to the
course contents.
Thus, it is my professional priority to keep my research and
scholarly activities an ongoing endeavor.
I also believe that I should work on research projects that
I am excited or enthusiastic about.
Albeit there is a requirement that faculty must
sustain a viable research program in academia, the bottom line
is that I do research because I enjoy thinking about and
solving problems related to mathematics.
Brief and Precise Description of my research interests
In a nutshell, I am a die-hard, self-avowed and
practising applied mathematician
who is interested in problems related to:
Combinatorial and Discrete Optimization
Network Modeling and Optimization
Mathematical Modeling
Operations Research & Optimization
Linear Algebra and applications
Discrete Mathematics
Applications of Graph Theory
Mathematical Programming
Matroid Theory
Applications of Calculus
In general, my areas of teaching and research interests include, but are not
limited
to, diverse areas in the field of operations research and its applications,
namely, most of the aforementioned areas.
For more information on these topics, try to either take or audit
the following scintillating mathematics courses, namely,
Discrete & Combinatorial Math (Math 3411, or
Math 1760 & 3370 under quarters), and
Operations Research
(Math 3401, or
Math 3270 under quarters).
Notwithstanding common misconceptions about mathematics,
this subject is ubiquitous and very interdisciplinary.
These areas of mathematics have a plethora of
real-world applications.
If you would like to learn more about these research areas,
please feel free to talk to me or take or audit the courses I teach.
For potential undergraduate research students who are interested in
working with me
There are several ways you can work on an undergraduate research
project with me.
Research project for your Math Senior Seminar (Math 4901).
See Policies for Math 4901 for the guidelines.
You do NOT get any funding for doing Math 4901; it counts as a required
course towards your major.
University of Minnesota's
Undergraduate Research Opportunities Program (UROP) provides funding for an undergraduate student to
do independent research work with a faculty advisor. UROP projects are,
by and large, initiated by students and students will need to write a
proposal for their project with support from a faculty.
( N.B. There have been several students who have used part of the
results from their UROP research work as their Math Senior Seminar project.
The only catch here is that the proposal of her/his project has to come way
earlier (sometimes at least 7 months) than the Math Senior Seminar's
required initial dates. The advantage is that students get a head-start on
their research ahead of other math senior seminar students.)
University of Minnesota - Morris'
Morris Academic Partnership (MAP) provides funding for an undergraduate student to work with a faculty member on the latter's research project.
MAP is initiated by a UMM faculty member who would then recommend a
particular student who is, by and large, in her/his 3rd year at UMM.
My own research projects are that funded externally. (Please see
me if you need more information).
I am more than happy to work with any student at any level of
undergraduate research experience level. If you are a novice at
undergraduate research but are willing to learn and are motivated, then please
feel free to approach me; we can discuss further.
If you have been involved with undergraduate research,
and have particular ideas or specific interests in
applied math projects, then we can certainly have a discussion to see if
there is a "fit" somewhere for us.
A Subset of Past and Present Research, including Research with Students. (Updated September 2006 )
( Please note that for copyright reasons, only abstracts can be
printed out here for a few articles. )
Abstract of
Totally Unimodular Directed Hypergraphs, (postscript file); Journal of Linear Algebra and Its Applications,VOL 230, Nov 1995; with C.R. Coullard, Northwestern University.
Copy of Classroom Scheduling Problems: A Discrete Optimization Approach (pdf format);
Journal of Undergraduate Mathematics and its Applications,
Vol 23, No. 1, Winter 2002.
This is joint work with Lora M. Martin (UMM '98); the research is partially
supported by University of Minnesota's
Undergraduate Research Opportunities Program.
The preliminary results were presented at the
Mathematical Association of America's Summer Conference in 1998.
Otter Tail County's Efficient Recycling Management Program .
Joint work with Lisa M. Martin (UMM '98) and
Jessica Rybaski (UMM '97).
Sponsored by MAP and Center for Small Towns.
Scheduling for the Regional Fitness Center , Summer 1999.
Joint work with James R. Johnson (UMM '99), sponsored by the
RFC Board.
Characterization of certain properties of Directed Hypergraphs
at the 10th Society of Industrial and Applied Mathematics (SIAM) Conference
in Discrete Mathematics, 2000.
This is joint work with James R. Johnson (UMM '99).
Sponsored by MAP.
A sequential method of sharpening (LP)-relaxations to
the UNcapacitated Fixed Charge Network Flow Problems .
Joint work with Lena Wollan (UMM '01).
Sponsored by the Morris Academic Partnership and the
Undergraduate Research Opportunities Program (UROP).
Worked with Steve Formaneck (UMM '2002) on
"Semidefinite Programming Methods: Improving their algorithms and
implementations".
(This research is supported by UROP-Undergraduate Research Opportunities
Program).
Results were presented at the National Meeting of the
American Mathematical Society and Mathematical Association of America
in San Diego, January 2002.
Project on Optimal Fleet Control and Yield Management
with the Minnesota Department of Transportation (MnDoT) of Stevens County. (Jeanna Schultz (UMM '03) worked on the preliminary data analysis
under the MAP program).
Currently, the optimization modeling is one of my sabbatical projects.
Modeling pollution in the lake systems in
rural Minnesota : Discrete Dynamical Systems Approach.
(Undergraduate research work with Jeanna Schultz (UMM '03); this
research is supported by UROP-Undergraduate Research Opportunities
Program).
Ramsey Numbers: Improving the bounds of R(5,5).
(Undergraduate research work with Curtis Kunkel (UMM '02); this
research is supported by UROP-Undergraduate Research Opportunities
Program).
Project on Minimum sum vertex cover
(Kathryn Sullivan (UMM '05) worked on the preliminary results for special
cases of graphs
under the MAP program).
Project on Prefix permutation problem, aka, Pancake Number
(Kathryn Sullivan (UMM '05); this
research is supported by UROP-Undergraduate Research Opportunities
Program. The results was presented at the 2005
National Meeting of the American Mathematical Society and the
Mathematical Association of America).
Copy of
Designing Efficient Snow Plow Routes: A Service-Learning Project; Book:
Mathematics in Service to the Community : Concepts and Models for Service-Learning in the Mathematical Sciences, Editor: Charles Hadlock,
Publisher: Mathematical Association of America, 2005.
Project on Directed Hypergraphs with balanced or totally
unimodular matrices, (Emily Stout (UMM '07);
(Kathryn Sullivan (UMM '05); this
research is supported by Morris Academic Partnership (MAP).
The results was presented at the 2006
UMM Undergraduate Research Symposium, April 2006.)
(In progress.) Max Flow with Time period constraints .
Joint work with B. Gopalakrishnan, SAS Inc .
Characterization of circuits and basis of the LDH matroids
This is an open problem in the graph theory world; this is
a personal research endeavor.
A list of past and present math senior seminar students I worked with.
Scott Zick (UMM 2000), on
Building Evacuation Problem for the
RFC and PE Centers
Judy Brown (UMM 2001), on
Using mathematical models to describe epidemiology ,
(co-advised with B. McQuarrie).
Lena Wollan (UMM 2001), on
Uncapacitated Fixed Charge Network Flow Problems: A systematic approach to sharpening approximations to optimal solutions
Michael Schwerin (UMM 2001), on
Mathematical Analysis of Western Music
Bessy Rodriguez (UMM 2001), on
Twin Cities Area Congestion & the Hiawatha Light Rail System
Karen Smith (UMM 2001), on
Fuzzy Logic: applications in Career Counseling & Nutritional Diet
Josh Wallestad (UMM 2002), on
Course Scheduling: an application of graph coloring and
integer linear programming problem
Paul Peterson (UMM 2002), on
Modeling mercury's thermal evolution with finite difference methods in a conductive regime
Steve Formaneck (UMM 2002), on
Improving the semidefinite coordinate direction (SCD) and semidefinite stand-and-hit (SSH) methods for detection of necessary linear matrix inequalities
Curtis Kunkel (UMM 2003), on
Ramsey Numbers: Improving the bounds of R(5,5) .
Jeanna Schultz (UMM 2003), on
Modeling pollution in the lake systems in
rural Minnesota : Discrete Dynamical Systems Approach .
Jill McDonald (UMM 2004), on
Game Theory: Much more than playing games
Teri Merkins (UMM 2004), on
Using CPM-PERT for Scheduling Construction , co-advised
with J. Levy
Paul Ting Ho (UMM 2004), on
Art Gallery Problem: Convex Polygons
Uros Martinovic (UMM 2005), on
Studying Time to Default Probability
Beth Schmitz (UMM 2005), on
Emergency Evacuation Routes for Apex International Labs
Kathryn Sullivan (UMM 2005), on
The Pancake Problem: Improving the bounds for Prefix Permutations
Matthew Carlson (UMM 2006), on
Minimum Queried Path on Query Graphs
