Information on Student Research Return

Background information

Undertaking a student research project may seems to be a daunting task. The pivotal question for many students is what constitutes undergraduate student research, and how can I get started? As with all research, the answers lie in the topic being investigated itself, and to some extent, the time frame in which the work is to be accomplished. Some topics are relatively deep, requiring substantial background preparation and an extensive time period of study and work in order to be productive. Surprisingly, however there are a large number of interesting problems in mathematics that can be tackled with only a relatively moderate background in the subject. Just as importantly, they can be done in a year, and sometimes in even less time. Examples of this are summer research grants given to faculty and students which is a very tight time deadline, but one which is typically manageable. The purpose of undergraduate student research, however, goes beyond the research study itself. It's intended to provide a growth opportunity for students to learn about how to engage in the process, as well as how to become more productive at producing results.

If you are interested in applied and computational science in the broadest sense, particularly in developing computational methods and algorithms, please contact me to explore opportunities for getting started on a research project. My own interests most recently are in computational algorithms, however I am broadly interested in activities that lie at the interface of mathematics and computer science. My cv can help in determining whether my interests match yours, or feel free to inquire directly.

       

In a way, getting involved with research, doing research, is a bit like watching a movie frame by frame. There is not much to see in any of the frames, it's when the film goes into motion that the scene comes into view. Quality research requires that same flow to create a result, and like good movie, it's immersive, providing you additional insight and a new view of reality.

Some tools

For students writing an Honors or Departmental Thesis, we've put together some packages to help with producing a thesis, including working with symbolic math tools and writing documents, including how to put math into html documents such as the snippet below:      

A polynomial of degree $n$ is a function $p(x)$ of the form \begin{equation} p(x) = a_0 + a_1 x + \ldots + a_n x^n, \end{equation} where the coefficients $a_1$, $a_2, \ldots a_n \in \mathbb{R}$ and $a_n \neq 0$. This is the canonical form of the polynomial with which we are familiar and corresponds to the Taylor series expansion for the function $p(x)$ about the point zero, i.e., \begin{equation} p(x) = p(0) + \frac{p^{\prime} (0) x}{1!} + \frac{p^{\prime \prime} (0) x^2}{2!} + \ldots + \frac{p^{(n)} (0) x^n}{n!}, \end{equation} where $a_i = p^{(i)}(0)/i!$, $i = 0,1,\ldots,n$. Several alternative representations of the polynomial $p(x)$ are useful, of which the Lagrange form: $p(x) = a_0 l_0(x) + a_1 l_1(x) + \ldots + a_n l_n (x),$ where \begin{equation} l_k(x) = \prod_{\stackrel{i=0}{i\neq k}}^n \frac{x-x_i}{x_k - x_i}, \qquad k = 0,1, \ldots n. \end{equation} will be of interest.

 
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Contact: JKolibal@newhaven.edu
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