Lowell Abrams

Lowell Abrams

Associate Professor of Mathematics
The George Washington University


 


 

Contact Information

Lowell Abrams
c/o Department of Mathematics
The George Washington University
Monroe Hall, Room 240

2115 G Street NW

Washington, DC 20052

 

office: Monroe 271
phone: (202) 994-8119
email: labrams@gwu.edu

Office Hours

Until Fall 2014, be in touch by email.

 

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Teaching Activities

 

From some of my more interesting courses in the past:

 

In Spring 2014 I taught a course called “The Mathematical Experience” under the auspices of the GWU Honors Program. In part, the course was based on the book by Davis and Hersh of that name. But more than that, it was an immersion in mathematical research (we studied intersection graphs of lines, rays, and segments in the plane) combined with philosophical reflection on the process of that research.

 

I was very excited in Fall 2012 to be teaching a special “Extreme” Calculus II course which was open only to first-year students. Here’s the flier.

 

In Fall 2008 I taught a Dean’s Seminar for freshmen entitled “A topologist’s view of digital images.” I introduced the students to the digital topology and topological graph theory necessary to understand the ideas in my papers with Donniell Fishkind.

 

In Fall 2006 and Spring 2007, I taught a special course (in the GWU School of Professional Studies) called “Higher Algebra” for middle-school teachers from various DC schools. Here is a blurb about that course:

 

When thinking algebraically, and even more generally, people routinely make use of a variety of properties of their object of thought, and shift between a variety of perspectives, without even noticing. This ease can be positive, allowing one to operate efficiently, but it can also lead to muddled thinking and poor communication. The purpose of this course is to accustom the students to thinking explicitly and abstractly about the properties and perspectives that they already use, and about the interelationships among those, with the goal of developing a sophistication, clarity of thought, and depth of understanding which they can pass on to their students.

 

In Spring 2005 and Spring 2006, I taught a “Writing in the Disciplines” course entitled “Math as a Language.” Here is a short description:

 

This course will provide students with the specialized language skills they need to work effectively with ideas of mathematics and communicate them to a variety of audience. Writing with multiple review/revision cycles will play a prominent role; the course will involve creating original arguments and producing written records of arguments presented orally, as well as presenting oral explanations of written arguments. The focus will be on concepts, vocabulary, and syntactic constructions which are ubiquitous in mathematics.

 

In Spring 2005 I also taught a graduate course in Topological Graph Theory. We used the text by Gross and Tucker, but I presented the material from the vantage point of algebraic topology. Essentially, this course was part of my work to develop a broader version of the perspective introduced in my work with Daniel Slilaty.

 

In Fall 2005 I taught a dean’s seminar for freshmen entitled "Games: an introduction to mathematical reasoning." It was a slightly altered version of the course I taught in Fall 2004 and Fall 2003. Here is a one-paragraph "blurb" about it:

 

The patterns and methods of mathematical reasoning have a wide range of applicability. In this course, we will apply mathematical reasoning to the analysis of a variety of games by playing them, reflecting on them more abstractly, and writing about them. In this context, we will study such fundamental notions as axiomatic system, specialized notation, symbolic manipulation, proof, rigor, heuristic, refinement of ideas, and effective communication of technical ideas.

 

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Research

I have finally come to the conclusion that I am a low-dimensional combinatorial topologist (think: cellular complexes and topological graph theory) who happens to also spend some of his research time on combinatorial algebra. (Not to be confused with algebraic combinatorics!)

 

 Here are some general things I am thinking about now:

  • The combinatorics of a particular family of recursively generated arrays which arise in combinatorial game theory. (With Dena Morton)
  • Embedding graphs in surfaces. (With Dan Slilaty)
  • Segment intersection graphs in various surfaces.

 

If you are interested in any of these things, send me email at labrams@gwu.edu!

 

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Publications and Preprints

  • A Family of Nim-Like Arrays: The Locator Theorem. Theoretical Science. 535 (2014), 31–37 (co-author: Dena Cowen-Morton)

 

 

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Page last updated 5/9/14.