Introduction to Mathematics Research -- 22M:096

A Survey of Applied Mathematics
Fall 2007

The University of Iowa

Introduction to Mathematics Research (22M:096) explores how mathematics is currently being used to interpret and solve real-world problems. The one-semester undergraduate course is composed of five independent modules, each focused on the development, implementation, critique, and analysis of a model relating to a particular area of current research interest. For example, previous topics covered in one semester were: collisions, subsurface fluid flow, traffic flow, epidemiology, and financial option pricing. Despite substantial differences in subject material, each module is approached using the same methodology. A typical three-week module is presented in the following manner:

  1. Motivation for understanding and solving the problem
    1. Determine parameters of importance.
    2. Establish appropriate assumptions.
    3. Agree upon significant output values.
  2. Mathematical formulation
    1. Derive a governing equation.
    2. Introduce a technique for solving the equation.
    3. Develop an implementation plan (create the model).
  3. Model assessment and reassessment
    1. Observe challenges and limitations of the initial model.
    2. Strengthen the existing model.
    3. Discuss current and future research goals in the area.

Successful completion of Calculus II or consent of instructor is required. Grades are based on class participation, homework, mini-projects (with presentation), and a final group project (with presentation). The course is taught by a faculty member and a mathematics graduate student.

Developing the Course

   This course was designed and developed by Ben Galluzzo and me (with the support of the University of Iowa Department of Mathematics VIGRE grant NSF DMS 0602242) in order to provide undergraduates with experience building and analyzing mathematical modules.  During the first offering of this course, we covered five topics: collisions, subsurface fluid flow, traffic flow, epidemiology, and financial option pricing.
   A brief description of each module is available in our module summary (PDF) document.  For a very brief summary of our course goals, results, and plans, see our (one page) course development summary (PDF).  A much more detailed summary (66 pages), including student feedback, is available in our course documentation and evaluation (PDF).

Course materials

The following are samples of materials used throughout the course.

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