Hands-On Learning

Problem solving in the Mathematics Learning Lab

Depending on where you want to go after Augustana, the mathematics department will provide hands-on learning experiences through internships, research projects and teaching opportunities.


Collaborate and research with fellow students in state-of-the-art classrooms giving you space to work right next to the open office doors of your professors. Our close-knit community means professors will know you by more than just a number and can help tailor your experience with hands-on learning opportunities that will give you a leg up on the competition after graduation.

Independent Projects

Mathematics majors have the opportunity to pursue independent projects and conduct research.

Some students recently involved:

Andrew Gardner (supervised by Lindsay Erickson, 2016) “Gamification of Nim on graphs via the K_{3,3}.” Andrew worked on solving the arbitrary case of Nim on the K_{2,n} by generating cases through playing games on an online program modeling the K_{3,3}. This led to paper preparation and presentation. Andrew was funded through SD Space Grant Consortium.

Abby Martin (supervised by Lindsay Erickson, 2016) “Visualization of graph theoretic applications using computer programming.” Abby created a program that enabled gamification of Nim on the K_{3,3}. Following this work, she created visualizations via graphs of research collaborations. Abby was funded through the SD Space Grant Consortium.

Bryce Christopherson (supervised by Lindsay Erickson, 2014) “Playing Nim on trees: discovering a complete solution for edge Nim on acyclic graphs.” Bryce worked to find the general solution to the arbitrary weight case of Nim on trees (acyclic graphs) in both the normal and misère form of the game. This led to a paper and numerous presentations. Bryce was funded by the SD Space Grant Consortium.

Kyle Rodgers (supervised by Lindsay Erickson, 2014) “Design and implementation of graph drawing tools.” Kyle created a C++ program to simulate cases of Nim on the complete graph, Petersen graph, and the hypercube. Cases of Nim on the Petersen graph and the hypercube were randomized for both players. Cases for Nim on the complete graph followed a known strategy for the first player confirming the hypothesis that the first player can win for any weight assignment and for any size complete graph. This led to numerous presentations on the topic. Kyle was funded by the SD Space Grant Consortium.

Laura Tinker (supervised by Martha Gregg, 2014). “Finding a Fair Division of Rent: An Application of Sperner's Lemma.” When getting a new apartment with friends, many people experience the problem of dividing rooms and rent so that everyone is happy.  In his paper entitled Rental Harmony: Sperner’s Lemma in Fair Division, Dr. Francis Edward Su tackled this problem using a simple combinatorial lemma, Sperner’s Lemma.  The application of this lemma yields a method for choosing rooms and determining an agreed upon and fair rent share for each participant. Laura gave a general review of fair division, a discussion of Su’s rental harmony application, and discussed how this research can be used in the future projects.

Trent Anderson (Math/Physics/Chemistry, 2011): Trent used modeling software (STELLA) to construct a model of a disease spreading on a college campus. He was able to use the model to quite accurately represent the fall 2009 H1N1 outbreak on the Augustana campus. Trent presented his work at the Augustana Symposium in April 2011. He is currently pursuing graduate studies in chemistry at NDSU.

Nicole Winkler (Math, 2011): Nicole produced mathematical models of swarming in one and two dimensions. Her model is based on behavioral characteristics of the swarming organisms which explain swarming behavior. Nicole traveled to California to present her results in 2010. She is currently employed with a national actuarial science firm.

Research Experiences for Undergraduates (REUs)

Summer 2015

Abby Martin (Augustana University) and Dr. Richard J. Povinelli, Research Mentor (Marquette) "Electric Load Forecasting Using Linear Regression Model Trees."

  • Abstract: Electric load forecasting is essential to the electric generation industry and therefore research into creating more accurate forecasts is of vital importance. The model tree is a type of decision tree that has linear regression models at each leaf that are used for predicting. Model trees are an improvement over other forecasting methods, such as linear regression or possibly even artificial neural networks, because the models are built on a smaller subsection of data and therefore more effectively model instances with specific characteristics.

Rachel Nevin (Augustana University; REU conducted at Iowa State University) "Developing high order numerical methods for solving the Boltmann BGK (model for representing ideal gases)."

  • Abstract: We consider the Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) collision operator, a kinetic model for the dynamics of particles of a gas. Solving this system is difficult because it is a high-dimension PDE. The dimension of this equation can be decreased by a fluid model, but this model assumes thermodynamic equilibrium. We aim to develop an asymptotic-preserving (AP), multiscale method to solve the Boltzmann-BGK equation by combining the specificity and physical accuracy of a kinetic solver with the efficiency and numerical accuracy of a fluid solver. Specifically, we develop a kinetic solver which implements a Semi-Lagrangian Discontinuous Galerkin method and a fluid solver which implements a high-order Runge-Kutta Discontinuous Galerkin method. We present our preliminary multiscale solver.

Nadab Wubshet  (Augustana University; REU conducted at Iowa State University) "Controlling Microfluidic Transformations."

  • Abstract: Obstacles (pillars) are set to deform a fluid flow that propagates through a microchannel. Controlling these deformations has diverse importance including enhancing chemical reactions and heat transfer, fabricating shaped microfibers and other bioassay applications. Thus, a process to control fluid flow transformations is developed. To be able to attain this particular deformation, the genetic algorithm (GA) is used. This method mimics the natural evolutionary process in order to optimize a system. Three major modifications were introduced to enhance the performance of the GA. These include inlet designs in the chromosomes, creating a bound for inlet designs based on the area of the target, and interpreting representation of pillar sequences to real values of pillar locations and diameters.

Facilities 

Located on the second level of the new Froiland Science Complex, the mathematics department provides numerous spaces for research and learning. Study with friends in the Mathematics Learning Lab and enjoy wall to wall chalkboards and write-on glass in addition to being adjacent to your professors' offices. Students will have access to other research and education rooms where they are free to use math programs and databases like MathSciNet and Maple. In addition, the Mikkelsen Library holds more than 17,000 volumes of books and journals on our subject, and we have access to much more material electronically and through interlibrary loan.

The dedicated PC lab in the Froiland Science Complex is open many hours every day.

About research experiences off-campus.