Dan McQuillan, Professor of Mathematics

Department of Mathematics

Norwich University

Northfield, VT 05663

802 485-2323

dmcquill [at] norwich.edu

There is a menu on the bottom of the above picture of Norwich University. Please explore various pages of this site by clicking on the menu tabs. In addition, several “blogroll” links are on the upper right side of this page, including links to papers in the journal *Discrete Mathematics*, as well as a link to a preprint on ArXiv.org on the Witt Ring and the Witt Cancellation Theorem.

Mathematics is a human activity; as such it is always changing and always exciting. It has a rich history and strong personalities. It is certainly a subject where we continuously learn more by re-examining what was done in the past. We are often looking for another perspective to deepen our understanding. I sincerely hope that you enjoy this article, partly on the Witt Cancellation Theorem, and partly a survey article, but also a tribute to many great mathematical personalities responsible for the birth of the algebraic theory of quadratic forms. We thank and honor a few of the founders, including Ernst Witt, Emmy Noether, and Leonard Dickson. We also celebrate the 75th birthday of a pioneering paper of Witt with a brief overview of recent spectacular work which is still building on his original creation of the the algebraic theory of quadratic forms.

The slides for my talk, “Vertex-magic Graphs,” given during the spring meeting of the Northeastern section of the Mathematical Association of America on June 11, 2011, can be found here. These slides have also been placed on the selected preprints page, found under the “publications” tab on the menu.

Click here for updates on our top performances in the Putnam competition!

A short 9 minute talk has been placed on the Talks on video page, where comments are welcome. I may produce more videos, or refine the current one. This video is about planarity and crossing numbers of graphs, and specifically about drawings of complete graphs, and it is intended as a companion to paper on a parity theorem for drawings of complete graphs and complete bipartite graphs. A direct link to the same talk on youtube is also provided on the blogroll. I’ve also added a link to another fun video by Ján Mináč and Leslie Hallock, entitled, *How Mathematics Could Save Romeo and Juliet*.

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