Physical Sciences and Mathematics Commons^™

Using Composition Techniques To Improve Classroom Instruction And Students’ Understanding Of Proof, Christopher D. Goff

Christopher Goff

This paper describes an effort to incorporate standard composition exercises into a sophomore-level discrete mathematics class. It provides an example of how peer review can be integrated with a mathematical curriculum through the writing of proofs.

Generalized Twisted Quantum Doubles And The Mckay Correspondence, Christopher D. Goff, Geoffrey Mason

Christopher Goff

We consider a class of quasiHopf algebras which we call generalized twisted quantum doubles. They are abelian extensions H=C[G¯]∗⋈C[G] (G is a finite group, G¯ a homomorphic image, and * denotes the dual algebra), possibly twisted by a 3-cocycle, and are a natural generalization of the twisted quantum double construction of Dijkgraaf, Pasquier and Roche. We show that if G is a subgroup of SU2(C) then H exhibits an orbifold McKay Correspondence: certain fusion rules of H define a graph with connected components indexed by conjugacy classes of G¯, each connected component being an extended affine Diagram of type ADE …

Does Spelling Count? Reflections On Writing In The Mathematics Classroom, Christopher D. Goff

Christopher Goff

The written word is scarce in the stereotypical mathematics course, which instead emphasizes the routine solving of problems. But having students explain their solutions in writing can pave the way to more critical mathematical thinking. This talk will examine the use of writing as a tool to learn mathematics. We will reflect on: reasons to incorporate writing in a mathematics class; which courses lend themselves to writing assignments; what types of assignments to use; samples of student work; and whether using writing can actually improve student learning. Depending on the assignments, writing can also incorporate several “Basic Principles” of AMATYC’s …

Diophantine Geometry, Eulerian Number Theory, And Undergraduates, Christopher D. Goff

Christopher Goff

This talk will tell the story of how a geometry problem of Diophantus led all the way to a paper of Euler on number theory. Then we will describe how translating this work of Euler led ultimately to an undergraduate project in a History of Mathematics course last spring.

Euler's Multiple Solutions To A Diophantine Problem, Christopher D. Goff

Christopher Goff

No abstract provided.

Dynkin Diagrams And Fusion Algebras, Christopher D. Goff

Christopher Goff

No abstract provided.

Is Hollywood Good For Mathematics? (A Brief Discussion)., Christopher D. Goff

Christopher Goff

Mathematics has played a role in many recent films, such as Good Will Hunting, A Beautiful Mind, and Proof. But how exactly is mathematics being portrayed? What ramifications does this portrayal have on our ”students,” broadly defined? In Good Will Hunting, mathematics is Will’s ticket out of his lower-class life and into a prestigious existence. In A Beautiful Mind, mathematical talent and schizophrenia are identified, at least in part. In Proof, mathematics not only links a daughter to her late father, but it also provides a backdrop for much of the story’s conflict. In this discussion, we will begin by …

Euler’S Algebraic Creativity And Undergraduate Math, Christopher D. Goff

Christopher Goff

This talk will describe the author’s work translating a paper of Euler on number theory, and how researching the history of this paper led back to Lagrange, Fermat, and ultimately to a geometry problem of Diophantus. We will investigate Euler’s algebraic creativity and Lagrange’s explanation of his own method, inspired by Fermat. Moreover, we will demonstrate one way in which this paper of Euler’s has been used as part of a project in an undergraduate history of mathematics course. We will even investigate the continuation of Euler’s work.

Movie Math: Mathematical Talent = Mental Illness, Christopher D. Goff

Christopher Goff

No abstract provided.

Fusion Algebras & Accidental Trigonometry, Christopher D. Goff

Christopher Goff

Have you ever been working in one area of math, and another area arises unexpectedly? While working on a problem in 2008, we inadvertently discovered some trigonometric identities. This talk will explain fusion algebras, which are relatively simple algebraic objects that demonstrate nice algebraic applications of linear algebra. Then we will see how trigonometry can arise in even this most algebraic of settings.

How (West) Hollywood Adds Up: A Queer Theoretical View Of Mathematics And Mathematicians In Film, Christopher D. Goff

Christopher Goff

No abstract provided.

Fusion Algebras & Accidental Trigonometry, Christopher D. Goff

Christopher Goff

No abstract provided.

Ethnomathematics: Challenging Traditional Notions Of Mathematical Authority, Christopher D. Goff

Christopher Goff

No abstract provided.

A Beautiful Mind, Christopher D. Goff

Christopher Goff

No abstract provided.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

Christopher Goff

No abstract provided.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

Christopher Goff

No abstract provided.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

Christopher Goff

No abstract provided.

An Isomorphism Between The Fusion Algebras Of Vl+ And Type D(1) Level 2, Michael Cuntz, Christopher D. Goff

Christopher Goff

This talk will show that the fusion algebra of the vertex operator algebra VL+ (where L is a rank 1 even lattice) is isomorphic to the fusion algebra of the affine Kac-Moody Lie algebra of type D(1) at level 2.

English Translation (From Latin) Of "A Solution Of A Most Difficult Problem, In Which The Two Forms Aaxx + Bbyy Et Aayy + Bbxx Must Be Rendered Into Squares" By L. Euler, Christopher Goff

Christopher Goff

English Translation (From Latin) Of “On A Notable Advancement Of Diophantine Analysis,” By L. Euler, Christopher Goff

Christopher Goff

English Translation (From Latin) Of “On Finding Three Or More Numbers, The Sum Of Which Is A Square, While The Sum Of The Squares Is A Fourth Power,” By L. Euler, Christopher Goff

Christopher Goff

Fusion Rules For Abelian Extensions Of Hopf Algebras, Christopher Goff

Christopher Goff

On The Gauge Equivalence Of Twisted Quantum Doubles Of Elementary Abelian And Extra-Special 2-Groups, Christopher Goff, Geoffrey Mason, Siu-Hung Ng

Christopher Goff

To Boldly Go: Current Work And Future Directions In Mathematics And Popular Culture, Christopher Goff, Sarah J. Greenwald

Christopher Goff

No abstract provided.

An Explicit Fusion Algebra Isomorphism For Twisted Quantum Doubles Of Finite Groups, Christopher Goff

Christopher Goff

Benefits Of A Comprehensive Undergraduate Teaching Assistant Program, Christopher Goff, Brigitte Lahme

Christopher Goff

A Family Of Isomorphic Fusion Algebras Of Twisted Quantum Doubles Of Finite Groups, Christopher Goff

Christopher Goff