James J. Alexander

328 Ewing HallDept. of Mathematical Sciences

University of DelawareNewark, DE 19716

Education Ph.D., Mathematics, University of Delaware, Newark, DE, 2016 (Expected)

M.S., Mathematics, Montclair State University, Montclair, NJ, 2012Thesis: Enumeration of independent sets in graphsAdvisor: Professor Jonathan Cutler

B.A., Mathematics, Rutgers University, New Brunswick, NJ, 2010

Research Papers• A new method for enumerating independent sets of a fixed size in general graphs 

with T. Mink, Journal of Graph Theory , submitted• Independent sets in graphs with given minimum degree  with J. Cutler and

T. Mink, Electronic Journal of Combinatorics , 19(3) (2012), #P37

Grants and Research Awards• University of Delaware GEMS Grant , 2013

Award given to fund summer research. Included $6,000 stipend• C.S.A.M. Graduating Masters Research Award , 2012

Award given to one student in the College of Science and Mathematics at MSUnominees from many disciplines, for most outstanding research.

• Outstanding MS Student in Mathematics , 2012Award given to one student graduating with MS in Mathematics from MSU

• The Margaret and Herman Sokol Graduate Research Fellowship, 2011Award given to one graduate student in the College of Science and Mathematicsat MSU, applicants from many disciplines. Included $5,000 stipend.

Talks• Independent sets of a fixed size in graphs with various degree restrictions 

Summer research symposium, University of Delaware, August 2013• Independent sets in graphs with given minimum degree 

Discrete Mathematics Seminar, University of Delaware, March 2013• Independent sets in graphs with given minimum degree 

New York Combinatorics Seminar, CUNY Graduate Center, April 2012• Independent sets in graphs with given minimum degree 

Graduate Student Combinatorics Conference, University of Illinois, April 2012• Independent sets in graphs with given minimum degree 

Spring 2012 Section of MAA meeting, Raritan Valley CC, March 2012• Enumeration of independent sets in graphs  (with Tim Mink)

Department of Mathematical Sciences Seminar, MSU, March 2012

Undergraduate Research• University of Georgia Mathematics REU

Athens, GA, Summer 2008. Included $4,000 stipend.

Experience Teaching• Instructor and lecturer for Math 451:02 (Topology)

Montclair State University, Spring 2011

 

• Lecturer for Math 061 (Basic Skills)Montclair State University, Fall 2010, Spring 2011, Fall 2011

• Substitute Lecturer for Calculus I (3 times), II (4), III (2)Montclair State University, Spring 2011, Fall 2011

• Tutor for SAT and AP Level Test PreperationCambridge Education, Summer 2010, Summer 2011

TA/Grading• TA for Math 230 (Finite mathematics with applications)

University of Delaware, Spring 2013• Grader for Math 222 (Calculus II)

University of Delaware, Fall 2012• TA/Grader for Math 431(Modern Algebra), Math 221 (Calculus II)

Montclair State University, Fall 2010• TA/Grader for Math 451:01 (Topology), Math 221 (Calculus II)

Montclair State University, Spring 2011• TA/Grader for Math 469 (Mathematical Modeling), Math 222 (Calculus III)

Montclair State University, Fall 2011• Peer Mentor/Grader Math 135(Calculus I), Math 136 (Calculus II)

Rutgers University, Spring 2008 - Fall 2010

Languages Proficient in LATEX, Beamer and MapleWorking Knowledge of Matlab and Mathematica

Activities American Mathematical Society, Student Member, 2012-PresentSociety for Industrial and Applied Mathematics, Officer, 2011-2012Tutor for Montclair State University Comprehensive Exam, 2011-2012K.I.P. 501(c)3 Nonprofit, Volunteer, 2002-2010

Coursework Graduate Coursework at UDel:Combinatorics I,II Theory of Probability I,IIFunctional Analysis Numerical DiscretizationVector Spaces Real and Complex Analysis II

Graduate Coursework at MSU:Additive Combinatorics Abstract AlgebraGraph Theory Partial Differential EquationsComplex Variables Measure TheoryDiscrete Mathematics Linear AlgebraOperations Research Applied Industrial Math.Analysis of Real Variables

Undergraduate Coursework:Topology Mathematical LogicAdvanced Calculus I,II Mathematical ReasoningComplex Analysis Ordinary Differential EquationsGraph Theory Partial Differential EquationsSet Theory Applied MathLinear Algeabra Numerical AnalysisAbstract Algebra Linear Optimization

 

Areas of Interest I am particularly interested in extremal graph theory, enumerative combinatorics andprobabilistic graph theory, however, I have really enjoyed all areas of discrete mathe-matics that I’ve encountered. I also enjoy abstract algebra, number theory, and prob-ability theory very much. I am open to doing research in any of these areas.