Publications 2006–2015
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Books
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The Geometry of the Octonions,
Tevian Dray and Corinne A. Manogue, World Scientific, Singapore, 2015.
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Differential Forms and the Geometry of General Relativity,
Tevian Dray,
CRC Press (an A K Peters book), Boca Raton, FL, 2014.
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The Geometry of Special Relativity,
Tevian Dray,
CRC Press (an A K Peters book), Boca Raton, FL, 2012.
(Wiki version,
PDF version)
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The Geometry of Vector Calculus,
Tevian Dray and Corinne A. Manogue, 2009–2015.
(online only)
Vector Calculus
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Using differentials to determine the derivatives
of trigonometric and exponential functions,
Tevian Dray,
College Math. J. 44, 17–23 (2013).
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Putting differentials back into calculus,
Tevian Dray and Corinne A. Manogue
College Math. J. 41, 90–100 (2010).
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Finding Geodesics,
Stuart Boersma, Tevian Dray, and Stan Wagon,
Math Horizons, September 2009, 2.
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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).
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The Geometry of the Dot and Cross Products,
(MathML version;
published version)
Tevian Dray and Corinne A. Manogue,
JOMA 6, June 2006.
Octonions
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E6, the Group: The structure of SL(3,O),
Aaron Wangberg and Tevian Dray,
J. Algebra Appl. 14, 1550091 (2015).
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The 2×2 Lie group magic square
(published abstract)
Tevian Dray, John Huerta, and Joshua Kincaid,
Lett. Math. Phys. 104, 1445–1468 (2014).
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Division Algebra Representations of SO(4,2),
(published abstract)
Joshua Kincaid and Tevian Dray,
Mod. Phys. Lett. A29, 1450128 (2014).
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A Symplectic Representation of E7,
(published abstract)
Tevian Dray, Corinne A. Manogue, and Robert A. Wilson,
in Proceedings of the
3rd Mile High Conference on Nonassociative Mathematics
(Denver 2013),
Comment. Math. Univ. Carolin. 55, 387–399 (2014).
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Discovering Real Lie Subalgebras of e6 using Cartan
Decompositions,
(published abstract)
Aaron Wangberg and Tevian Dray,
J. Math. Phys. 54, 081703 (2013).
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Octonionic Cayley Spinors and E6,
(published abstract)
Tevian Dray and Corinne A. Manogue,
in Proceedings of the
2nd Mile High Conference on Nonassociative Mathematics
(Denver 2009),
Comment. Math. Univ. Carolin. 51, 193–207 (2010).
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Octonions, E6, and Particle Physics,
(published version)
Corinne A. Manogue and Tevian Dray,
in
Quantum Groups, Quantum Foundations, and Quantum Information: a
Festschrift for Tony Sudbery,
J. Phys.: Conf. Ser. 254, 012005 (2010).
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Finding 3×3 Hermitian Matrices over the Octonions with Imaginary
Eigenvalues,
(published abstract)
Henry Gillow-Wiles and Tevian Dray,
Adv. Appl. Clifford Algebras 20, 247–254 (2010).
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Visualizing Lie Subalgebras using Root and Weight Diagrams,
(published version)
Aaron Wangberg and Tevian Dray,
Loci 2, February 2009.
Relativity
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Toy model studies of tuning and typicality with an eye toward
cosmology,
(published abstract)
Aaron Hernley, Andreas Albrecht, and Tevian Dray,
Phys. Rev. D87, 123515 (2013).
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Using Three-Dimensional Spacetime Diagrams
in Special Relativity,
Tevian Dray,
Am. J. Phys. 81, 593--596 (2013).
(enhanced figures)
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Covariant Derivatives on Null Submanifolds,
(published abstract)
Don Hickethier and Tevian Dray,
Gen. Rel. Grav. 44, 225–238 (2012).
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The Effect of Negative-Energy Shells on the
Schwarzschild Black Hole,
(published abstract)
Jeffrey S. Hazboun and Tevian Dray,
Gen. Rel. Grav. 42, 1457–1467 (2010).
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Tensor Generalizations of Affine Symmetry Vectors,
(published abstract)
Samuel A. Cook and Tevian Dray,
J. Math. Phys. 50, 122506 (2009).
Science Education
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An extended theoretical framework for the
concept of derivative,
(published version)
David Roundy, Tevian Dray, Corinne A. Manogue, Joseph F. Wagner, and Eric
Weber,
RUME 18 Conference
(Pittsburgh 2015),
CRUME 18 Proceedings,
eds. Tim Fukawa-Connelly, Nicole Engelke Infante, Karen Keene, Michelle
Zandieh,
MAA, pp. 838–843 (2015).
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Experts' understanding of partial derivatives using the Partial
Derivative Machine,
David Roundy, Eric Weber, Tevian Dray, Rabindra R. Bajaracharya,
Allison Dorko, Emily M. Smith, and Corinne A. Manogue,
Phys. Rev. ST Phys. Educ. Res. 11, 020126 (2015).
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Partial Derivative Games in Thermodynamics:
A Cognitive Task Analysis,
Mary Bridget Kustusch, David Roundy, Tevian Dray, and Corinne A. Manogue,
Phys. Rev. ST Phys. Educ. Res. 10, 010101 (2014).
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Using Non-Euclidean Geometry to Teach Euclidean Geometry to K–12
Teachers,
David Damcke, Tevian Dray, Maria Fung, Dianne Hart, and Lyn Riverstone,
(2008; unpublished).
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Care to Compare: Eliciting Mathematics Discourse in a Professional
Development Geometry Course for K–12 Teachers,
Maria Fung, David Damcke, Dianne Hart, Lyn Riverstone, and Tevian Dray,
in The Role of Mathematics Discourse in Producing Leaders of Discourse,
ed. Libby Knott,
Montana Mathematics Enthusiast Monograph Series in Mathematics Education,
Information Age Publishing, Charlotte, NC, 2009, pp. 199–213.
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Dare to Compare?,
David Damcke, Tevian Dray, Maria Fung, Dianne Hart, and Lyn Riverstone,
The Oregon Mathematics Teacher (TOMT), May/June 2008, 8–10.
Further information
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Publications 1998–2005
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Complete publication list
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Ask arXiv.org for list of preprints:
gr-qc,
hep-th,
math
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Ask MathSciNet for list of reviewed publications
(requires MathSciNet access)
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Ask INSPIRE for list of publications:
by date,
by citations,
metrics
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Ask Google Scholar for list of publications
(includes citation metrics)