Mathematical Methods for Analyzing Data

Course design and development supported by NSF DUE Award #0942670.

Course Description: A rigorous presentation of topics from linear algebra, discrete mathematics, and statistics for analyzing data. Topics will be taught in the context of modern real-world problems.

(The course description has been kept purposefully brief to allow faculty with research interests at the interface of theory, data, and models to bring their unique perspective into the course.)

Required Prerequistes: Elementary Statistics, Elementary Linear Algebra, and Discrete Mathematics

Rationale: The course connects mathematics to modern real world applications that arise from the massive amounts of data that have become available through a variety of sources. New mathematical methods and novel implementations of well-known methods are being developed to correctly and efficiently analyze large datasets and draw meaningful conclusions. These methods cut across several areas including linear algebra, discrete mathematics, and statistics, but they have much in common and deserve the creation of new course content and pedagogical methods to communicate them. The April, 2012 issue of SIAM News has a front page article on the theme titled Got Data: Now What?. The article identifies the analysis of large data sets to provide understanding, and ultimately knowledge as one of the fundamental intellectual challenges of our time and calls on mathematical scientists to develop novel methods based on their domain expertise, and to see these developments translate into value for society.

To this we add that such a topic also needs a strong civic engagement component. Along with new applications come new ethical issues. Mathematical scientists should not distance themselves from the consequences of their work. As such, a central goal is to connect the mathematics to the pressing real-world issues that did not exist just a decade or two ago. Learning the mathematics in the context of difficult societal problems and thinking about how use it in an advocacy setting creates a much needed awareness of how mathematics applies to society.

Audience: The course serves as a timely senior level/capstone course for majors in mathematics, math education, and computer science.

Learning Objectives:
  • Students develop expertise in a set of techniques for analyzing data;

  • Students learn the mathematics underlying the techniques in a rigorous manner;

  • Students connect mathematics to pressing real-world issues that did not exist just a decade or two ago;

  • Students understand how the data drives the mathematics and vice-versa;

Civic Engagement Objectives:

  • Students engage in a term-project that involves analyzing and making decisions about a societal issue important to them;

  • Student's communicate their analysis to a general audience.


SPRING 2011

In Spring 2011 a pilot version was conducted as an independent study course. At the end of the semester the five students gave presentations at the Brooklyn College Math Club seminar.


SPRING 2012

In Spring 2011 a more formal version of the course was taught. Twelve students enrolled in the course. Student work was showcased in the Undergraduate Student Conference on May 17, 2012.


SPRING 2013

In Spring 2013, the course ran as a special topics course with an emphasis on network science. Eight students enrolled in the course. Their work was presented in the Undergraduate Student Conference, held on May 14, 2013.