Recent Publications

Vector Calculus

• Finding Geodesics,
     Stuart Boersma, Tevian Dray, and Stan Wagon, Math Horizons, September 2009 (to appear).
• Putting differentials back into differential (and integral) calculus,
     Tevian Dray and Corinne A. Manogue College Math. J. , (to appear).
• Why is Ampère's Law So Hard?,    (published abstract)
     Corinne A. Manogue, Kerry Browne, Tevian Dray, and Barbara Edwards, Am. J. Phys. 74, 344-350 (2006).
• The Geometry of the Dot and Cross Products,    (MathML version; published version)
     Tevian Dray and Corinne A. Manogue, JOMA 6, June 2006.
• Using Differentials to Bridge the Vector Calculus Gap,
     Tevian Dray and Corinne A. Manogue, College Math. J. 34, 283-290 (2003).
• The Murder Mystery Method for Determining Whether a Vector Field is Conservative,
     Tevian Dray and Corinne A. Manogue, College Math. J. 34, 238-241 (2003).
• Spherical Coordinates,
     Tevian Dray and Corinne A. Manogue, College Math. J. 34, 168-169 (2003).
• Bridging the Vector (Calculus) Gap,
     Tevian Dray and Corinne A. Manogue, in Pathways to Change: An International Conference on Transforming Math and Science Education in the K16 Continuum, Proceedings (CD-ROM; Arlington 2002) ed. Morton M. Sternheim, 2002.
• Electromagnetic Conic Sections,    (PDF version; published abstract)
     Tevian Dray and Corinne A. Manogue, Am. J. Phys. 70, 1129-1135 (2002).
• The Vector Calculus Gap,
     Tevian Dray and Corinne A. Manogue, PRIMUS 9, 21-28 (1999).
  
  Octonions
  
  
• Finding 3×3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues,
     Henry Gillow-Wiles and Tevian Dray, Adv. Appl. Clifford Algebras, (to appear).
• Visualizing Lie Subalgebras using Root and Weight Diagrams,    (published version)
     Aaron Wangberg and Tevian Dray, Loci 2, February 2009.
• Orthonormal Eigenbases over the Octonions,
     Tevian Dray, Corinne A. Manogue, and Susumu Okubo, Algebras Groups Geom. 19, 163-180 (2002).
• Some Properties of 3×3 Octonionic Hermitian Matrices with Non-Real Eigenvalues,
     Tevian Dray, Jason Janesky, and Corinne A. Manogue, Oregon State University, 2000, 12 pages.
• Octonionic Hermitian Matrices with Non-Real Eigenvalues,
     Tevian Dray, Jason Janesky, and Corinne A. Manogue, Adv. Appl. Clifford Algebras 10, 193-216 (2000).
• Quaternionic Spin,
     Tevian Dray and Corinne A. Manogue, in Clifford Algebras and their Applications in Mathematical Physics (Zihuatenejo 1999), eds. Rafal Ablamowicz and Bertfried Fauser, Birkhäuser, Boston, 2000, pp. 29-46.
• The Exceptional Jordan Eigenvalue Problem, (invited paper)
     Tevian Dray and Corinne A. Manogue, Internat. J. Theoret. Phys. 38, 2901-2916 (1999).
• Octonionic Möbius Transformations,    (published abstract)
     Corinne A. Manogue and Tevian Dray, Mod. Phys. Lett. A14, 1243-1255 (1999).
• Dimensional Reduction, (invited paper)    (published abstract)
     Corinne A. Manogue and Tevian Dray, Mod. Phys. Lett. A14, 99-103 (1999).
  (This essay received Honorable Mention in the 1998 competition of the Gravity Research Foundation.)
• Finding Octonionic Eigenvectors Using Mathematica, (invited paper)
     Tevian Dray and Corinne A. Manogue, Comput. Phys. Comm. 115, 536-547 (1998).
• The Octonionic Eigenvalue Problem,
     Tevian Dray and Corinne A. Manogue, Adv. Appl. Clifford Algebras 8, 341-364 (1998).
  
  Relativity
  
  
• Tensor Generalizations of Affine Symmetry Vectors,
     Samuel A. Cook and Tevian Dray, J. Math. Phys. (submitted).
• The Effect of Negative-Energy Shells on the Schwarzschild Black Hole,
     Jeffery S. Hazboun and Tevian Dray, Gen. Rel. Grav. (submitted).
• The Geometry of Special Relativity, (invited paper)
     Tevian Dray, Physics Teacher (India) 46, 144-150 (2004).
• Note on Signature Change and Colombeau Theory,    (published abstract)
     Tevian Dray, George Ellis, and Charles Hellaby, Gen. Rel. Grav. 33, 1041-1046 (2001).
• Distributional Modes For Scalar Field Quantization,    (published abstract)
     Al Agnew and Tevian Dray, Gen. Rel. Grav. 33, 429-453 (2001).
• Tensor Distributions on Signature-Changing Space-Times,    (published abstract)
     David Hartley, Robin W. Tucker, Philip Tuckey, and Tevian Dray, Gen. Rel. Grav. 32, 491-504 (2000).
• A New Look at the Ashtekar-Magnon Energy Condition,    (published abstract)
     Jim Fischer and Tevian Dray, Gen. Rel. Grav. 31, 511-526 (1999).
  
  Science Education
  
  
• Using Non-Euclidean Geometry to Teach Euclidean Geometry to K–12 Teachers,
     David Damcke, Tevian Dray, Maria Fung, Dianne Hart, and Lyn Riverstone, J. Math. Teacher Educ. (submitted).
• Connections between Representations: Ambiguity Helps!
     Gulden Karakok, Tina Johnston, Corinne A. Manogue, Maggie Niess, and Tevian Dray, MTMS (submitted).
• Dare to Compare?,
     David Damcke, Tevian Dray, Maria Fung, Dianne Hart, and Lyn Riverstone, TOMT (2008; to appear).
• Bridging the Gap between Mathematics and the Physical Sciences ,
     Tevian Dray and Corinne A. Manogue, in: Preparing Future Science and Mathematics Teachers, eds. Diane Smith and Elisabeth Swanson, Montana State University, Bozeman, 2005, pp. 39-41.
• Bridging the Gap between Mathematics and Physics,
     Tevian Dray and Corinne A. Manogue, APS Forum on Education, Spring 2004, pp. 13-14.
  
  Other
  
  
• Taxicab Angles and Trigonometry,
     Kevin Thompson and Tevian Dray, Pi Mu Epsilon Journal 11, 87-96 (2000).    (PDF version)

Further information

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