## Student Work

#### Senior Seminar Essays

###### Class of 2017

- Bryce Cloke, “Data Clustering Algorithms”
- Joseph Dominic, “Banach Spaces”
- Griffin Dutson, “Linear Programming Problems: A Brief Overview”
- Aaron Lenci, “Benford’s Law”
- Jennifer Ogden, “Proving Napoleon’s Theorem”
- Hunter Rappleye, “Ramsey Theory: Complete Disorder?”
- Sanjay Shrestha, “Discrete Isoperimetric Inequalities on Graphs”
- Sonia Valenzuela, “Lindemann-Weierstrass Theorem With a Bit of “
- Ahsan Zahid, “Lattices, Cryptography, and NTRU: An Introduction to Lattice Theory and the NTRU Cryptosystem”

###### Class of 2016

- Sophia Burille, “Traveling Salesman Problem”
- Colin Buxton, “Brouwer Fixed-Point Theorem”
- Matthew Dami, “Pseudorandom Number Generation”
- Andres Diestra, “The Gamma Function!”
- Arturo Garcia, “On Perfect Numbers”
- Alan Kane, “Functioning in the Complex Plane”
- Alex Lowen, “The Banach-Tarski Paradox”
- Kelly Lynch, “Spherical Trigonometry”
- Ahn Maciag, “A Two-Person Bargaining Problem”
- David Marquis, “Gershgorin’s Circle Theorem for Estimating the Eigenvalues of a Matrix with Known Error Bounds”
- Roshni Mistry, “Circle Packing, Sphere Packing, and Kepler’s Conjecture”
- Rahul Murthy, “Hilbert’s Nullstellensatz”
- Erica Musgrave, “Breaking the Enigma Code”
- Christopher Queen, “Genetic Algorithms Applied to the Knapsack Problem”
- Mike Rambo, “The Conjugate Gradient Method for Solving Linear Systems of Equations”
- Camille Santos, “Shannon’s Coding Theorems”
- Justine Seastres, “Cellular Automata and the Game of Life”
- Elijah Soria, “Matrix Groups and Their Lie Algebras”

#### Research

- Elijah Soria, “Some Properties of Generalized -Pell Sequences”, The Pi Mu Epsilon Journal, Vol. 14, No. 3, pp. 205–217 (2015).
- Sophia Burille, “Bounding Tree Cover Number and Positive Semidefinite Zero Forcing Number”, Saint Mary’s College School of Science Summer Research Program (2014).
- Xiaowei Li and Rachel Phillips, “Minimum Vector Rank and Complement Critical Graphs”, Electronic Journal of Linear Algebra, Vol. 27, Art. 5, pp. 100–121 (2014).
- Brandy Cho, “The Prime Maze”, Saint Mary’s College School of Science Summer Research Program (2012).
- Avineet Pannu, “Prime Numbers Arising from Quadratic Polynomials”, Saint Mary’s College School of Science Summer Research Program (2012).
- Victoria Wang, “Edge Isoperimetric Inequalities for a Family of Graphs on “, Saint Mary’s College School of Science Summer Research Program (2012).
- Stephanie Wang, “Distribution of Digits in the Binary Representation of Prime Numbers”, Saint Mary’s College School of Science Summer Research Program (2008).

## Have you ever considered…

#### Declaring a major or minor in Mathematics?

Graduates of the Department are active in an extraordinarily wide range of careers and graduate programs.

The power of mathematical thinking — pattern recognition, generalization, abstraction, problem solving, careful analysis, and rigorous argument — is an important asset which is highly valued by employers.

For an idea of what you can do with a math major, check out When Will I use Math?

#### Declaring a split major in Mathematics?

Can’t choose between your passion for biology and your love of math? Don’t think you can graduate on time with a double major? Try a split major! With a split major in math and a second field, you’ll complete the lower division requirements of both fields, but only have to complete half of the upper division courses in each major. Speak with your advisor for more information.

#### Completing an honors contract?

Want to learn interesting applications of mathematics? Or explore a topic not covered in your favorite math class? An honors contract in a regular math course might be just what you need to explore. Speak with any math professor for more information.

#### Engaging in summer research at SMC?

Can’t seem to let go of your term project in a math class? Want to experience actual research in mathematics? Apply for the School of Science Summer Research Program! You can spend 10 weeks in close collaboration with a faculty advisor on a self-designed project gaining first-hand experience with genuine mathematical research. Each participant receives a stipend, housing on campus, and a very rewarding experience! Speak with any math professor for more information.

#### Applying for an REU?

Want to experience scientific research at another college or university with students from all over the country? Apply for an REU! Research Experiences for Undergraduates (REU) provides opportunities for undergraduate students to experience hands-on participation in research or related scholarly activity in mathematics and other STEM fields. There are a plethora of REU programs held each summer; check out AMS’s list of 2015 REUs. for more information.

#### Working for the Department?

Looking for part-time employment during the semester? Maybe you should consider becoming a grader or SI leader for the Department or tutor at the STEM Center! These opportunities are especially helpful for future teachers and students wishing to go on to graduate school. For more about these positions, contact Prof. Chris Jones.