### Department Faculty Size

- We currently have 9 full time faculty members.
- In addition, we have 3 part-time faculty members.

### Approximate Class Sizes

- Introductory Level: 20 - 30 students
- Intermediate Level: 15 - 25 students
- Upper Level: 10 - 20 students

### College Student Selectivity

- Our student body has approximately 2600 students.
- The average combined SAT score is near 1300.
- 71% of incoming students were in the top ten percent of their high school class.

### Math Majors and Minors

- We typically graduate 15-20 math majors and 10 – 12 math minors each year.
- Many of our students are involved in independent research projects under faculty supervision. All math majors are required to do a senior thesis.

### Teaching

- Each faculty member teaches 5 courses per year.
- Faculty members have the opportunity to teach seminar courses, interdisciplinary courses, and team taught courses as part of their regular teaching load.
- College provides support, both financial and otherwise, for new and innovative teaching through the Johnson Center for Creative Teaching and Learning.
- Student assistants conduct help sessions and operate a drop-in tutoring center.
- Calculus courses use free online Open Educational Resources.

### Extracurricular Activities For Our Students

- We participate in the William Lowell Putnam Mathematics Competition and the COMAP Mathematical Contest in Modeling.
- Several students each year give talks at conferences including the Joint Meetings, the MAA sectional conferences, and other regional conferences.
- We host a popular Mathematics Colloquium, featuring speakers from places such as the US Naval Academy, Bucknell University, Haverford College, Courant Institute, Penn State, and the NSA

### Research

- Department supports research-related travel with an annual travel allowance.
- Tenure-track faculty have the opportunity to take a one-semester pre-tenure sabbatical with full pay during their third or fourth year.
- College supports research-related travel and a wide variety of other research activities with several generous internal grant programs.

### Where Some of Our Recent Graduates Have Been Since Graduation

- Graduate programs in mathematics and applied mathematics in schools such as: University of Wisconsin-Madison, North Carolina State University, Wake Forest, Duquesne University, and Cornell.
- Teaching high school mathematics throughout the state of Pennsylvania and the entire region.
- Working with continuing care retirement centers as an actuary.
- Working as an operations research analyst with the Air Force.
- Working at the National Security Agency.
- Teaching mathematics and mentoring at-risk teenagers in Fort Smith, Canada, in the Western Arctic Leadership Program.
- Institutional Consultant at Lord, Abbett Investment Management
- Software developers at various internet companies.

### Technology

- Each faculty member receives a computer with the latest version of appropriate mathematics software.
- Campus has ubiquitous wireless internet access.
- All classrooms include state of the art computer and projection systems.

### Diversity

- Both the college and the Math Department are deeply committed to fostering diversity in all parts of the Gettysburg College community.
- Faculty benefit package includes domestic partner benefits and substantial financial support for H-1 B visa and green card applications.
- Shared faculty appointments are possible.

### About Gettysburg, PA

- The town has a population of 7500 people and is the county seat of Adams County.
- The town is visited by several million tourists annually.
- Many buildings in town are historic landmarks and are over two hundred years old.
- Gettysburg has several fine restaurants and independent coffee houses.
- Town is surrounded by a large National Park, with opportunities for outdoor activities.
- Gettysburg is about an hour from Baltimore and an hour and a half from Washington. Many faculty, particularly dual-career couples, live close to these metropolitan areas.
- Gettysburg is within easy drive from several state parks, the Appalachian Trail, ski resorts, river rafting opportunities, and lakes with beaches.

### Faculty and Selected Publications

### Bela Bajnok

Professor

Ph.D. The Ohio State University (1989)

M.Ed. Eotvos University (1984)

**Research Interests**: Combinatorics, Additive Number Theory, Approximation Theory.

Prior Teaching Experience: Cornell University, Eotvos University, Ohio State University,

Pomona College, University of Houston-Downtown.

**He has over 20 refereed publications, including:**

- An Invitation to Abstract Mathematics. Undergraduate Texts in Mathematics, Springer, New York, NY

(2013) xiv+406 pp.; Instructors’ Guide, Springer.com (2013) (with B. Kennedy). - Additive Combinatorics—A Menu of Research Problems. Discrete Mathematics and Its Applications. CRC Press, Boca Raton, FL (2018) xix+390 pp.
- An Invitation to Abstract Mathematics – Second Edition. Undergraduate Texts in Mathematics, Springer Nature, Switzerland (2020) xiv+442 pp.
- On the maximum size of (k, l)-sum-free sets in cyclic groups. Bulletin of the Australian Mathematical

Society 99 (2019), no. 2, 184–194 (with R. Matzke ’15). - Secrets and Quantifiers. Math Horizons 28, no. 3 (2021) (with P. Francis ’21).
- Mathematical Comfort Food. American Mathematical Monthly 128, no. 2 (2021) (with C. Yackel, E. Goins, J. Carpenter, S. Kennedy, J. Shakalli, U. Whitcher, D. Kung, K. Kozak, R. Ghrist, and A. Gelman).
- The AMC – What It Is and Why It Matters. Notices of the American Mathematical Society 68 (2021), no. 7, 1173–1175.
- Open problems about sumsets in finite abelian groups: minimum sizes and critical numbers.
*Combinatorial and**additive number theory. II,*9–23, Springer Proc. Math. Stat., 220,*Springer,*2017. - On asymptotic approximate groups of integers.
*Integers*17 (2017), Paper No. A57. - On two questions about restricted sumsets in finite abelian groups.
*Australas**. J.**Combin**.*68 (2017),

229– 244. (with Samuel Edwards ‘17)

### Beth Campbell Hetrick

Associate Professor; Chairperson

Ph.D. Bryn Mawr College (2006)

M.A. Bryn Mawr College (2002)

B.S. Villanova University (2000)

**Research Interests**: Operator Theory, Functional Analysis.

Prior Teaching Experience: Penn State Harrisburg, Bryn Mawr College

**Publications:**

- Regularization results for inhomogeneous ill-posed problems in Banach space. In: Deines A., Ferrero D., Graham E., Im M., Manore C., Price C. (eds),
*Advances in the Mathematical Sciences*. AWMRS 2017. Association for Women in Mathematics Series, vol 15. Springer, Cham. (2018) - With M. Fury and W. Huddell, Continuous dependence on modeling in Banach space using a logarithmic approximation. In: J. Bélair, A. I. Frigaard, H. Kunze, R. Makarov, R. Melnik and J.R. Spiteri (eds),
*Mathematical and Computational Approaches in Advancing Modern Science and Engineering*, (pp. 653-663). Springer, Cham. (2016) - Quasireversibility for Inhomogeneous Ill-Posed Problems in Hilbert Space, Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations.
*Electron. J. Differential Equations*, Conf. 19 (2010), 37–44. *Continuous dependence on modeling for nonlinear ill-posed problems*, J. Math. Anal. Appl. 349 (2009), 420--435. (with R. Hughes)*Regularization of the backward heat equation via**heatlets*, Electron. J. Differential Equations (2008), 1 -- 8. (with R. Hughes and E. McNabb)- Continuous Dependence Results for Inhomogeneous Ill – Posed Problems in Banach Space,
*Journal of Math. Anal. Appl.*331, (2007) No. 1 (with R. Hughes)

**Sarah Bryant**

Lecturer in Mathematics

Ph.D. Purdue University

B.S. Berea College**Research Interests**: Stochastic Processes, Writing Across the Curriculum, Diversity in STEM fields,

- Mathematics Engagement and Outreach, Mathematical Modeling

Prior Teaching Experience: Dickinson College; Shippensburg University, National Science Foundation GK-12 Fellow/Visiting Mathematician, Purdue University

S. D'Agostino, S. Bryant, M. Craddock Guinn, L. Harris (eds) Celebration of the Impact of the EDGE Program on the Mathematics Community and Beyond. AWMS vol 18. Springer (2019) - L. Bryant, S. Bryant, & D. White “Striking the Right Chord: Math Circles Promote (Joyous)Professional Growth" In: D'Agostino, Bryant, Craddock Guinn, Harris (eds) Celebration of the Impact of the EDGE Program on the Mathematics Community and Beyond. AWMS vol 18 Springer (2019)
- W. Strychalski, S. Bryant, B. Jadamba, E. Kilikian, X. Lai, L. Shahriyari, R. Segal, N. Wei, L. Miller “Fluid Dynamics of Nematocyst Prey Capture" In: Radunskaya A., Segal R., Shtylla B. (eds) Understanding Complex Biological Systems with Mathematics. AWMS vol 14 Springer (2018)
- S. Bryant “Counting and Partition Function Asymptotics for Subordinate Killed Brownian Motion" In: Letzter G. et al. (eds) Advances in the Mathematical Sciences. AWMS vol 6 Springer, Cham (2016)
- S. Bryant & J. Schaefer “Becoming Successful Proof-Writers Through Peer-Review, Journals, and Portfolios" MAA Volume Beyond Lecture: Techniques to Improve Student Proof-Writing Across the Curriculum (2016)
- S. Bryant, N. Lape, & J. Schaefer “Transfer and the Transformation of Writing Pedagogies in a Mathematics Course" The WAC Journal, 25 (2014)

### Ricardo Conceição

Associate Professor

Ph.D. University of Texas at Austin (2009)

M.Sc. Federal University of Pernambuco - Brazil (2003)

Bachelor, State University of Feira de Santana** ** - Brazil (2000)

**Research Interests**: Number Theory, Arithmetic Geometry, Arithmetic of Elliptic Curves, Arithmetic of Curves over Finite Fields, Arithmetic of Function Fields, Value Sets of Polynomials over Finite Fields

Prior Teaching Experience: Oxford College of Emory University, University of Texas at Austin, Federal University of Pernambuco (UFPE), Brazil

**Publications:**

- Conceição, R., Kelly, R. & VanFossen, S. The Markoff equation over polynomial rings.
*Monatsh**Math*(2021). https://doi.org/10.1007/s00605-021-01601-0 - On integral points on isotrivial elliptic curves over function fields.
*Bull**.**Aust. Math. Soc.*102 (2020), no. 2, 177–185. - Borges, Herivelto; Conceição, Ricardo A new family of Castle and Frobenius nonclassical curves.
*J. Pure Appl. Algebra*222 (2018), no. 4, 994–1002. (Reviewer: Arman Shamsi Zargar) 14H25 (11G20 11T06 14G05) - On a Frobenius problem for polynomials (with R. Gondim and M. Rodriguez) To appear on Rocky Mountain Journal of Mathematics,
- Explicit points on the Legendre curve II (with C. Hall and D. Ulmer), Mathematical Research Letters 21 (2014), no. 2, 261 - 280.
- Elliptic curves with a large set of integral points over function fields, Acta Arith. 161 (2013), no. 4, 327 - 349.
- On the characterization of minimal value set polynomials (with H. Borges), Journal of Number Theory 133 (2013), no. 6, 2021 – 2035.

### Darren Glass

Professor

Ph.D. University of Pennsylvania (2002)

B.A. Rice University (1997)

**Research Interests**: Galois Theory, Algebraic Geometry, Cryptography

Prior Teaching Experience: Columbia University, University of Pennsylvania

**Recent Publications**:

- Arithmetical structures on bidents . Discrete Mathematics, 343(7):111850, 2020 (with K. Archer, A. Bishop, A. Diaz-Lopez, L. García Puente, and J. Louwsma).
- Multiparty non-interactive key exchange and more from isogenies on elliptic curves. J. Math. Cryptol., 14(1):5–14, 2020 (with D. Boneh, K. Lauter, et al.).
- Chip Firing Games and Critical Groups . In A Project-Based Guide to Undergraduate Research in Mathematics, 107–152. Birkhäuser Basel, 2020 (with N. Kaplan).
- Arithmetical Structures on Paths With a Doubled Edge . Integers, 20(A68), 2020 (with J. Wagner ‘19).
- Optimal Defensive Strategies in One-Dimensional Risk . Mathematics Magazine, 88(3):217–230, 2015 (with T. Neller).
- Pointless Hyperelliptic Curves ,
*Finite Fields and Their Applications*, Vol. 21 (2013) (With R. Becker ’13) - Quasigeometric Distributions and Extra Innings Baseball Games, Mathematics Magazine Volume 81 (2008), No 3 (with P. Lowry)

### Caitlin Hult

Assistant Professor

Ph.D., Mathematics, University of North Carolina at Chapel Hill

M.S., Mathematics, University of North Carolina at Chapel Hill

B.A., Mathematics, Hamilton College B.A., English Literature, Hamilton College**Research Interests**: Mathematical modeling of biological systems (agent-based models, multi-scale models, SDE models), immunology, chromatin dynamics, visualization methods**Additional training:** Postdoctoral Research Fellow, jointly appointed in the University of Michigan Medical School and University of Michigan College of Engineering

- C. Hult, J.T. Mattila, H.P. Gideon, J.J. Linderman, D.E. Kirschner. "Neutrophil dynamics affect Mycobacterium tuberculosis granuloma outcomes and dissemination." Frontiers in Immunology. Accepted, August 18, 2021 (to appear).
- M. Renardy, C. Hult, S. Evans, J.J. Linderman, D.E. Kirschner. "Global sensitivity analysis of biological multi-scale models." Current Opinion in Biomedical Engineering. 2019;11:109-116. doi:10.1016/j.cobme.2019.09.012
- B. Walker, D. Taylor, J. Lawrimore, C. Hult, D. Adalsteinsson, K. Bloom, M.G. Forest. "Transient crosslinking kinetics optimize gene cluster interactions." PLOS Computational Biology. 2019;15(8):e1007124. Published 2019 Aug 21. doi:10.1371/journal.pcbi.1007124.
- S. Marino, C. Hult, P. Wolberg, J.J. Linderman, D.E. Kirschner. "The role of dimensionality in understanding granuloma formation." Computation (Basel). 2018;6(4):58. doi:10.3390/computation6040058
- J.M. Cicchese #, S. Evans #, C. Hult #, L.R. Joslyn #, T. Wessler #, J.A. Millar, S. Marino, N.A. Cilfone, J.T. Mattila,
- J.J. Linderman, D.E. Kirschner. "Dynamic balance of pro- and anti-inflammatory signals controls disease and limits pathology." Immunological Reviews. 2018;285(1):147-167. https://doi.org/10.1111/imr.12671

# = co-primary authors

### Benjamin Kennedy

Alumni Professor in Mathematics

Ph.D. Rutgers University (2007)

MST Boston College (2000)

B.A. Swarthmore College (1998)

**Research Interests**: Functional Differential Equations and Dynamical Systems

Prior Teaching Experience: Rutgers University, Boston College

**Recent Publications:**

- A periodic solution with non-simple oscillation for an equation with state-dependent delay and strictly monotonic negative feedback,
*Discrete and Continuous Dynamical Systems-S*13 (1) (2020), 47-66. - (With Y. Mao and E. L. Wendt) A state-dependent delay equation with chaotic solutions,
*Electronic Journal of Qualitative Theory of Differential Equations*(2019), No. 22, 1-20. doi: 10.14232/ejqtde.2019.1.22. - The Poincaré-Bendixson Theorem For a Class of Delay Equations with State-Dependent Delay and Monotonic Feedback
*Journal of Differential Equations*266 (2019), 1865-1898. doi: 10.1016/j.jde.2018.08.012. - Finding Periodic Solutions Without Finding Eigenvalues,
*Elemente**Der**Mathematik*73 (2018), 1-14 - (With Eugen Stumpf) Multiple Slowly Oscillating Periodic Solutions for
*x’(t) = f(x(t-1))*With Negative Feedback,*Annales**Polinici**Mathematici*118 (2016), 113-140. - Stable rapidly oscillating periodic solutions for an equation with state-dependent delay,
*Journal of Dynamics and Differential Equations*28 (2016), 1145-1161. - Symmetric periodic solutions for a class of differential delay equations with distributed delay,
*Electronic Journal of Qualitative Theory of Differential Equations*, No 4 (2014), 1-18. - A state-dependent delay equation with negative feedback and 'mildly unstable' rapidly oscillating periodic solutions,
*Discrete and Continuous Dynamical Systems Series B*, Special Issue on Deterministic and Stochastic Dynamical Systems with Delays (2013), 1633-1650. - Stability and instability for periodic solutions of delay equations with `steplike’ feedback,
*Electronic Journal of Qualitative Theory of Differential Equations*, Proceedings on the 9th Colloquium on the Qualitative Theory of Differential Equations, No. 8, 1—66 (2012)

### Keir Lockridge

Associate Professor

Ph.D. University of Washington (2006)

B.A. Rice University (1999)

**Research Interests**: Ring theory (e.g., homological dimension) of structured ring spectra arising in algebraic topology. Analogues of Freyd's generating hypothesis, a fundamental conjecture in stable homotopy theory, in derived and triangulated categories.

Prior Teaching Experience: Wake Forest University, Wesleyan University, University of Washington

**Publications:**

- Gaussian binomial coefficients in group theory, field theory, and topology with Sunil Chebolu. To appear,
*Amer. Math. Monthly*. - Fuchs' problem for p-groups with Sunil Chebolu.
*J. Pure Appl. Algebra*223 (2019) 4652–4666. - How many units can a commutative ring have? with Sunil Chebolu. To appear,
*Amer. Math. Monthly.* - Bousfield localization of ghost maps, with Mark Hovey. To appear,
*Homol**.**Homotopy**Appl.* - Fuchs' problem for dihedral groups, with Sunil Chebolu.
*J. Pure Appl. Algebra,*221 (2017), no. 2, 971—982. - Fields with indecomposable multiplicative groups, with Sunil Chebolu.
*Expo. Math.*34 (2016) 237—242 - Fuchs' problem for indecomposable abelian groups, with Sunil Chebolu.
*J. Algebra*438 (2015) 325—336. - Characterizations of Mersenne and 2-rooted primes, with Sunil Chebolu and Gaywalee Yamskulna,
*Finite**Fields**Appl.*35 (2015), 330—351. - Sophie Germain primes and involutions of Z×
*n*, with Karenna Genzlinger.*Involve*8-4 (2015), 653—663. - Homological dimensions of ring spectra, with Mark Hovey. Homol. Homotopy Appl.Vol. 15 (2013), No. 2, 53-71.
- The ghost and weak dimensions of rings and ring spectra, with Mark Hovey. Israel J. Math. 182 (2011), no. 1, 31-46.

### Kimberly Spayd

Associate Professor

Ph.D. University of North Carolina, Raleigh (2012)

M.S. University of North Carolina, Raleigh (2009)

M.S. University of North Carolina, Chapel Hill (2004)

B.S. University of Notre Dame (2001)

**Research Interests**: Analysis and numerical simulation of partial differential equations, flow in porous media

Prior Teaching Experience: North Carolina State University, Wake Technical Community College, University of North Carolina

**Publications**:

- K. Spayd and E. Swanson,
*A Model for Three-Phase Flow in Porous Media with Rate-Dependent Capillary Pressure*, A Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond, eds. S. D'Agostino, S. Bryant, A. Buchmann, M. Craddock Guinn, L. Harris. Springer Association for Women in Mathematics Series 18, pp. 327-338, 2019. - K. Spayd,
*Heat Diffusion*, “9-020-T-HeatDiusion," https://www.simiode.org/resources/6452, 2019 - K. Spayd, M. Reynolds, C. Lansinger, On the Use of Geometric Elements in the Work of Laszlo Moholy-Nagy and Piet Mondrian, submitted.
- K. Spayd, Generalizing the Modified Buckley-Leverett Equation with TCAT Capillary Pressure, European Journal of Applied Mathematics 29 (2), pp.338-351, 2018.
- K. Spayd and J. Puckett, A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics,PRIMUS 26 (10), pp. 938-951, 2016.
- M. Shearer, K. Spayd, E. Swanson, Traveling Waves for Conservation Laws with Cubic Nonlinearity and BBM Type Dispersion, Journal of Differential Equations 259 (7), pp. 3216-3232, 2015.
- K. Spayd, M. Shearer, Z. Hu, Stability of Plane Waves in Two Phase Porous Media Flow, ApplicableAnalysis 91 (2), pp. 295-308, 2012.
- K. Spayd and M. Shearer, The Buckley-Leverett Equation with Dynamic Capillary Pressure, SIAMJournal on Applied Mathematics 71 (4), pp. 1088-1108, 2011.