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Articles 1 - 18 of 18
Full-Text Articles in Physical Sciences and Mathematics
Using Composition Techniques To Improve Classroom Instruction And Students’ Understanding Of Proof, Christopher D. Goff
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
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
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
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
Euler's Multiple Solutions To A Diophantine Problem, Christopher D. Goff
Christopher Goff
No abstract provided.
Dynkin Diagrams And Fusion Algebras, Christopher D. Goff
Dynkin Diagrams And Fusion Algebras, Christopher D. Goff
Christopher Goff
No abstract provided.
Is Hollywood Good For Mathematics? (A Brief Discussion)., Christopher D. Goff
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
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
Movie Math: Mathematical Talent = Mental Illness, Christopher D. Goff
Christopher Goff
No abstract provided.
Fusion Algebras & Accidental Trigonometry, Christopher D. Goff
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
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
Fusion Algebras & Accidental Trigonometry, Christopher D. Goff
Christopher Goff
No abstract provided.
Ethnomathematics: Challenging Traditional Notions Of Mathematical Authority, Christopher D. Goff
Ethnomathematics: Challenging Traditional Notions Of Mathematical Authority, Christopher D. Goff
Christopher Goff
No abstract provided.
A Beautiful Mind, Christopher D. Goff
Alan Turing: The Man Behind The Machine, Christopher D. Goff
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
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
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
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.