Last updated on November 22, 2016.

You may find some interesting references for Edray Herber Goins on:

Refereed Publications

With Mel Currie, On the Distribution of Fractional Parts.
Internal publication of the National Security Agency. (1997).
With Mel Currie, The Fractional Parts of n/k.
Council for African-American Researchers in the Mathematical Sciences, Vol. III; Contemp. Math. 275 (2001), pgs. 13 - 31.
[PDF]
Artin's Conjecture and Elliptic Curves.
Council for African-American Researchers in the Mathematical Sciences, Vol. III; Contemp. Math. 275 (2001), pgs. 39 - 51.
[arXiv] | [PDF]
A Ternary Algebra with Applications to Binary Quadratic Forms.
Council for African-American Researchers in the Mathematical Sciences, Vol. IV; Contemp. Math. 284 (2001), pgs. 7 - 12.
[arXiv] | [PDF]
Icosahedral Q-curve Extensions.
Mathematical Research Letters, 10 (2003), no. 2-3, pgs. 205-217.
[Journal] | [PDF]
With Davin Maddox, Heron Triangles via Elliptic Curves.
Rocky Mountain Journal of Mathematics, Vol. 36; (2005), no. 5, pgs. 1511 - 1526.
[Journal] | [PDF]
With Alain Togbe, On Pythagorean Quadruplets.
International Journal of Pure and Applied Mathematics, Vol. 35 (2007), no. 3, pgs. 363 - 372.
[Journal] | [PDF]
With Florian Luca and Alain Togbe, On the Diophantine Equation x² + 2^α 5^β 13^γ = yⁿ.
Algorithmic Number Theory Seminar (ANTS-VIII); LCNS 5011 (2008), pgs. 430-442.
[PDF]
Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins.
INTEGERS: The Electronic Journal of Combinatorial Number Theory, Vol. 9 (2009), pgs. 725-734.
[arXiv] | [PDF]
With Talitha Washington, A Tasty Combination: Multivariable Calculus and Differential Forms.
The Pentagon: The Journal of Kappa Mu Epsilon, Fall 2009, pgs. 11-28.
[arXiv] | [Journal] | [PDF]
With Talitha Washington, Sphere-of-Influence Graphs.
Wolfram Demonstrations Project. (February 4, 2010)
[Mathematica CDF]
Semi-Magic Squares and Elliptic Curves.
Missouri Journal of Mathematical Sciences, Vol. 22 (2010), no. 2, pgs. 102 - 107.
[arXiv] | [Journal] | [PDF]
With Kevin Mugo, Points on Hyperbolas at Rational Distance.
International Journal of Number Theory, Vol. 8, No. 4 (2012), pgs. 911-922.
[arXiv] | [Journal] | [PDF]
With Talitha Washington, The Area of the Surface Generated by Revolving a Graph About Any Line.
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Vol. 23, Issue 2 (2013), pgs. 121-132.
[arXiv] | [Journal] | [PDF]
With Jing Ma, Susan Margulies, and Illya V. Hicks, Branch Decomposition Heuristics for Linear Matroids.
Journal of Discrete Optimization. Vol. 10, Issue 2 (May 2013), pgs. 102-119.
[Journal] | [PDF]
With Alejandra Alvarado, Arithmetic Progressions on Conic Sections.
International Journal of Number Theory, Vol. 9, No. 6 (2013), pgs. 1379-1393.
[arXiv] | [PDF]
With Talitha Washington, On the Generalized Climbing Stairs Problem.
Ars Combinatoria, Vol. CXVII (October 2014), pgs. 183-190.
[arXiv] | [PDF]
With Asamoah Nkwanta, Riordan Matrix Representations of Euler's Constant γ and Euler's Number e.
International Journal of Combinatorics, Volume 2016 (2016), Article ID 8324150, 9 pgs.
[arXiv] | [Journal] | [PDF]

Publications In Press

Publications Submitted

With Alejandra Alvarado and Luis Melara. Numerical Approximation of Coefficients of Belyi Maps.
[PDF]. Submitted 2016.
Explicit Descent via 4-Isogeny on an Elliptic Curve, 20 pp.
[arXiv] | [PDF]. Submitted 2016.

Publications In Progress

With Lloyd Kilford, Counting Mod l Solutions via Modular Forms.
[PDF]
Extending the Serre-Faltings Method for Q-Curves, 15 pp.
[PDF]
With Garikai Campbell, Heron Triangles, Diophantine Problems, and Elliptic Curves, 15 pp.
[PDF]

Books and Monographs

Editor with Donald King, Gaston N'Guerekata, and Alfred Noel. Council for African American Researchers in the Mathematical Sciences, Vol. V; Contemp. Math. 467 (2008), 152 pgs.
[PDF]

Miscellaneous Lecture Notes and Publications

Research Experiences for Undergraduate Faculty (REUF4)
American Institute of Mathematics / ICERM
[Lecture Notes] | [Dessin d'Enfant Explorer]
Ma 162b: Galois Representations
Department of Mathematics, California Institute of Technology (Winter 2004)
Undergraduate Mini-Course #2: A Survey of Diophantine Equations
2013 Modern Mathematics Workshop, SACNAS National Conference (November 2012)
Galois Representations and L-Series: A Tour Through Mathematics
Claytor-Woodard Lecture, National Association of Mathematicians (NAM) / Joint Mathematical Meetings (January 2011)
Why Should I Care About Elliptic Curves?
David Blackwell Lecture, National Association of Mathematicians (NAM) / MAA MathFest (August 2009)
Where Have All the Black Students Gone?
Professionally Speaking Lecture Series, Minority Student Education, California Institute of Technology (February 2003)
Freshman Summer Institute: Research Lectures
Minority Student Education, California Institute of Technology
Conjectures and Prime Numbers | Recursion Formulas | The Unit Circle | Fourier Analysis | Harmonic Motion to Chaotic Behavior
Elliptic Curves and Icosahedral Galois Representations
Doctoral Thesis, Department of Mathematics, Stanford University (1999)
Ol' Time Religion in a Brave New World
Senior Thesis, Department of History, California Institute of Technology (1994)
History of Caltech's Underrepresented Students
Summer Undergraduate Research Fellowship (SURF), California Institute of Technology (1993)

\section{\sc Refereed Publications} \item With Talitha Washington, \href{http://www.combinatorialmath.ca/arscombinatoria/vol117.html}{On the Generalized Climbing Stairs Problem}. Ars Combinatoria, Vol. CXVII (October 2014), pgs. 183-190. \item With Alejandra Alvarado, \href{http://www.worldscientific.com/doi/pdfplus/10.1142/S1793042113500322}{Arithmetic Progressions on Conic Sections}. International Journal of Number Theory. Vol. 9, No. 6 (2013), pgs. 1379-1393. \item With Jing Ma, Susan Margulies, and Illya V. Hicks, \href{http://www.sciencedirect.com/science/article/pii/S157252861200076X}{Branch Decomposition Heuristics for Linear Matroids}. Journal of Discrete Optimization. Vol. 10, Issue 2 (May 2013), pgs. 102 – 119. \item With Talitha Washington, \href{http://www.tandfonline.com/doi/abs/10.1080/10511970.2012.702708}{The Area of the Surface Generated by Revolving a Graph About Any Line}. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Vol. 23, Issue 2 (2013), pgs. 121-132. \item With Kevin Mugo, \href{http://www.worldscinet.com/ijnt/08/preserved-docs/0804/S1793042112500534.pdf}{Points on Hyperbolas at Rational Distance}. International Journal of Number Theory, Vol. 8, No. 4 (2012), pgs. 911-922. \item \href{http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.mjms/1312233140&page=record}{Semi-Magic Squares and Elliptic Curves}. Missouri Journal of Mathematical Sciences, Vol. 22 (2010), no. 2, pgs. 102 - 107. \item With Talitha Washington, Sphere-of-Influence Graphs. Wolfram Demonstrations Project. (February 4, 2010) \url{http://demonstrations.wolfram.com/SphereOfInfluenceGraphs/} \item With Talitha Washington, \href{http://pentagon.kappamuepsilon.org/pentagon/Vol_69_Num_1_Fall_2009.pdf}{A Tasty Combination: Multivariable Calculus and Differential Forms}. The Pentagon: The Journal of Kappa Mu Epsilon, Fall 2009, pgs. 11-28. \item \href{http://www.integers-ejcnt.org/vol9.html}{Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins}. INTEGERS: The Electronic Journal of Combinatorial Number Theory, Vol. 9 (2009), pgs. 725-734. \item With Florian Luca and Alain Togbe, \href{http://link.springer.com/chapter/10.1007%2F978-3-540-79456-1_29#page-1}{On the Diophantine Equation $x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n$}. Algorithmic Number Theory Seminar (ANTS-VIII); LCNS 5011 (2008), pgs. 430-442. \item With Alain Togbe, \href{http://ijpam.eu/contents/2007-35-3/10/10.pdf}{Pythagorean Quadruplets}. International Journal of Pure and Applied Mathematics, Vol. 35 (2007), no. 3, pgs. 363 - 372. \item With Davin Maddox, \href{http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181069379}{Heron Triangles via Elliptic Curves}. Rocky Mountain Journal of Mathematics, Vol. 36; (2005), no. 5, pgs. 1511 - 1526. \item \href{http://intlpress.com/site/pub/files/_fulltext/journals/mrl/2003/0010/0002/MRL-2003-0010-0002-00019947.pdf}{Icosahedral $\mathbb Q$-curve Extensions}. Math Res. Lett. 10 (2003), no. 2-3, pgs. 205-217. \item \href{http://www.ams.org/books/conm/284/}{A Ternary Algebra with Applications to Binary Quadratic Forms}. Council for African-American Researchers in the Mathematical Sciences, Vol. IV; Contemp. Math. 284 (2001), pgs. 7 - 12. \item \href{http://www.ams.org/books/conm/275/}{Artin's Conjecture and Elliptic Curves}. Council for African-American Researchers in the Mathematical Sciences, Vol. III; Contemp. Math. 275 (2001), pgs. 39 - 51. \item With Mel Currie, \href{http://www.ams.org/books/conm/275/}{The Fractional Parts of $\dfrac nk$}. Council for African-American Researchers in the Mathematical Sciences, Vol. III; Contemp. Math. 275 (2001), pgs. 13 - 31. \item With Mel Currie, On the Distribution of Fractional Parts. Internal publication of the National Security Agency. (1997). \section{\sc Publications Submitted} \item With Alejandra Alvarado and Luis Melara. Numerical Approximation of Coefficients of \Belyi Maps. \item With Asamoah Nkwanta, \href{http://arxiv.org/abs/1108.3846}{Riordan Matrix Representations of Euler's Constant $\gamma$ and Euler's Number $e$}, 16 pp. Submitted August 19, 2011. \section{\sc Publications In Progress} \item Explicit Descent via 4-Isogeny on an Elliptic Curve, 20 pp. \item Extending the Serre-Faltings Method for $\mathbb Q$-Curves, 15 pp. \item Heptaoctahedral Galois Representations. \item On the Modularity of Wildly Ramified Galois Representations, I. \item On the Modularity of Wildly Ramified Galois Representations, II. \item Rational Distance Sets on Conic Sections. \item There exist infinitely many rational Diophantine 6-tuples -- almost. \item Why should I care about elliptic curves? \item With Garikai Campbell, Heron Triangles, Diophantine Problems, and Elliptic Curves, 15 pp. \item With Lloyd Kilford, Counting Mod $\ell$ Solutions via Modular Forms. \item With Yu Tsumura, Lutz-Nagell Theorem. Wolfram Demonstrations Project. \item Which Ellipses Go Through Four Points? Wolfram Demonstrations Project. \url{http://demonstrations.wolfram.com/preview.html?draft/26744/000012/WhichEllipsesGoThroughFourPoints} \section{\sc Books and Monographs} \item Editor with Donald King, Gaston N'Gu{\'e}r{\'e}kata, and Alfred No{\"e}l. Council for African American Researchers in the Mathematical Sciences, Vol. V; Contemp. Math. 467 (2008), 152 pgs. \item With Talitha Washington. Ordinary Differential Equations. In progress. \item With Talitha Washington. Ordinary Differential Equations: Worked Examples with Solutions. In progress. \item $y^2 = (1 - x^2) \, (1 - k^2 \, x^2)$. In progress. \item Selmer Groups and Galois Representations. In progress.