Recent Publications

Books

The Geometry of the Octonions,
Tevian Dray and Corinne A. Manogue, World Scientific, Singapore, 2015.
Differential Forms and the Geometry of General Relativity,
Tevian Dray, CRC Press (an A K Peters book), Boca Raton, FL, 2014.
- The Geometry of Differential Forms, Preliminary edition, 2011 (PDF version)
- The Geometry of General Relativity, Preliminary edition, 2011 (PDF version)
The Geometry of Special Relativity,
Tevian Dray, CRC Press (an A K Peters book), Boca Raton, FL, 2012. (Wiki version, PDF version)
The Geometry of Vector Calculus,
Tevian Dray and Corinne A. Manogue, 2009–2015. (online only)

Vector Calculus
Using embedding diagrams to visualize curvature,
Tevian Dray, Amer. Math. Monthly (2020; to appear).
Using differentials to differentiate trigonometric and exponential functions,
Tevian Dray, College Math. J. 44, 17–23 (2013).
Putting differentials back into calculus,
Tevian Dray and Corinne A. Manogue College Math. J. 41, 90–100 (2010).

Octonions

Classifying Linear Operators over the Octonions
Alex Putnam and Tevian Dray, Involve 12, 117–124 (2019).
Subalgebras of the Split Octonions
Lida Bentz and Tevian Dray, Adv. Appl. Clifford Algebras 28, 40 (2018).
E6, the Group: The structure of SL(3,O),
Aaron Wangberg and Tevian Dray, J. Algebra Appl. 14, 1550091 (2015).
The 2×2 Lie group magic square (published abstract)
Tevian Dray, John Huerta, and Joshua Kincaid, Lett. Math. Phys. 104, 1445–1468 (2014).
Division Algebra Representations of SO(4,2), (published abstract)
Joshua Kincaid and Tevian Dray, Mod. Phys. Lett. A29, 1450128 (2014).
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).
Discovering Real Lie Subalgebras of e6 using Cartan Decompositions, (published abstract)
Aaron Wangberg and Tevian Dray, J. Math. Phys. 54, 081703 (2013).

Relativity

Reflections on the Energy of Black Holes,
Tevian Dray and Carlo Rovelli, Int. J. Mod. Phys. D (2019; to appear).
The Geometry of Relativity,
Tevian Dray, Am. J. Phys. 85, 683–691 (2016).
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).
Using Three-Dimensional Spacetime Diagrams in Special Relativity,
Tevian Dray, Am. J. Phys. 81, 593--596 (2013). (enhanced figures)
Covariant Derivatives on Null Submanifolds, (published abstract)
Don Hickethier and Tevian Dray, Gen. Rel. Grav. 44, 225–238 (2012).
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).

Science Education

Interpreting Derivatives,
Tevian Dray, Elizabeth Gire, Corinne A. Manogue, and David Roundy, PRIMUS 29, 830–850 (2019; invited paper).
Thick Derivatives,
Tevian Dray, AMS Blog: On Teaching and Learning Mathematics, May 31, 2016.
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.
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).
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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