## Media

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## Biography

Contact:

Phone: 310.338.5107

Email: Christina.Eubanks-Turner@lmu.edu

Office: University Hall 2714

Dr. Eubanks-Turner's interests are in commutative algebra, graph theory, mathematics education, and broadening participation in the mathematical sciences. Dr. Eubanks-Turner received her Ph.D. and M.S. from the University of Nebraska-Lincoln in 2008 and 2004, respectively, and her B.S. degree from Xavier University of Louisiana in 2002. She joined the LMU faculty in 2013.

## Education (3)

#### University of Nebraska-Lincoln: Ph.D., Mathematics 2008

#### University of Nebraska-Lincoln: M.S., Mathematics 2004

#### Xavier University of Louisiana: B.Sc., Mathematics 2002

## Areas of Expertise (5)

## Industry Expertise (2)

## Accomplishments (2)

#### LA/MS Section NExt Fellow (professional)

2009-03-01

Named the LA/MS Section Next Fellow by the Mathematical Association of America.

#### Project NExT Fellow (professional)

2008-06-01

Named the Project NExT Fellow by the Mathematical Association of America.

## Affiliations (6)

- American Mathematical Society (AMS)
- Association for Women in Mathematics (AWM)
- Mathematical Association of America (MAA)
- National Association of Mathematics (NAM)
- National Council of Teachers of Mathematics (NCTM)
- Association of Mathematics Teacher Educators (AMTE)

## Links (1)

## Media Appearances (1)

#### UL Gets NSF Grant for Math Teacher Training

**UL Today** online

2011-09-09

The National Science Foundation (NSF) has awarded the UL departments of Mathematics, and Curriculum & Instruction, a $127,449 grant for "The Louisiana Noyce Teaching Fellows/Master Teaching Fellows Planning Project" for undergraduate education.

## Event Appearances (4)

#### Graphical Properties of the Bipartite Subgraph of Spec(Z[x])

**Special Session on ALgebraic Structures over Commutative Rings, American Math- ematical Society Fall Sectional Meeting** New Orleans, LA

2012-10-01

#### Prime Ideals in Quotients of Low-Dimensional Mixed Polynomial/Power Series Rings

**The Consortium for Order in Algebra and Logic, University of Florida** Gainseville, FL

2012-03-01

#### Making Myself Useful...

**Mathematics Education Seminar** Lincoln, NE

2011-10-01

#### Error Detection and Correction

**Center for Undergraduate Research in Mathematics Spring Research Conference** Provo, UT

2011-03-01

## Research Grants (2)

#### Research Grant

**National Science Foundation $1,868,895**

2012-07-01

Co-PI: Louisiana Mathematics Masters in the Middle (LaM3). DUE-1240054/

#### Seed Grant

**Mathematical Sciences Research Institute $2,000**

2011-10-01

MSRI Math Circles Seed Grant, Mathematical Sciences Research Institute.

## Articles (5)

**Graphical properties of the bipartite graph of Spec(Z[x])\{0}**

*Journal of Algebra Combinatorics Discrete Structures and Applications*

2015-03-01

Consider $Spec(Z[x])$, the set of prime ideals of $Z[x]$ as a partially ordered set under inclusion. By removing the zero ideal, we denote $G_{Z}=Spec(Z[x])\{0}$ and view it as an infinite bipartite graph with the prime ideals as the vertices and the inclusion relations as the edges.

**Augmented generalized happy functions**

*arXiv*

2014-10-01

An augmented happy function, $S_{[c,b]}$ maps a positive integer to the sum of the squares of its base-$b$ digits and a non-negative integer $c$. A positive integer $u$ is in a cycle of $S_{[c,b]}$ if, for some positive integer $k$, $S_{[c,b]}(u)=u$ and for positive integers $v$ and $w$, $v$ is $w$-attracted for $S_{[c,b]}$ if, for some non-negative integer $\ell$, $S_{[c,b]}^\ell(v)=w$.

**Prime Ideals in Birational Extensions of Two-Dimensional Power Series Rings**

*Communications in Algebra*

2013-02-01

In this article we consider simple birational extensions of power series rings in one variable over one-dimensional Noetherian domains having infinitely many maximal ideals. For these rings we describe the partially ordered sets that arise as prime spectra. We characterize the prime spectra in the case that the coefficient rings are countable Dedekind domains.

**The projective line over the integers**

*The University of Nebraska-Lincoln*

2011-10-01

As a partially ordered set, the prime spectrum of ℤ[x] has been characterized by R. Wiegand [J. Pure Appl. Algebra 40, 209–214 (1986; Zbl 0592.13002)]. This description uses five axioms.

**The McEliece Cryptosystem**

*The University of Nebraska-Lincoln*

2003-09-17

The McEliece cryptosystem is a public key cryptosystem whose security rests on the difficult problem of decoding an unknown error-correcting code. We give two examples of attacks to the cryptosystem, as well as a brief introduction to Goppa codes. One modification to this cryptosystem proposed by Pierre Loidreau increases the security of the system without increasing the key size or length of the code.