Workshops in Your District: Exploring Discrete Mathematics


ABOUT THE PROGRAM

Would you like the teachers in your district to become familiar with topics in discrete mathematics and use them in your classrooms? If your answer is "yes", consider hosting a workshop on discrete mathematics in your district. Or you may ask, "What is discrete mathematics, anyway?" An in-service workshop is the perfect way for you and others in your school district to find out. (A brief discussion of discrete mathematics appears below.)

These workshops bring math instructors of all levels together to discuss an increasingly important area of contemporary mathematics with practical applications to a wide range of areas - from computers to policy planning. The workshops offer an exciting way to re-energize teachers and math curricula at all levels, providing new classroom applications and fresh perspectives.

Teachers will receive complete in-service packages which can be used both by workshop participants and, with their assistance, by other teachers in the district. Workshop leaders will be available to advise teachers about implementation. The instructional materials used in the workshops are based on the experiences of workshop leaders using discrete mathematics in their own classrooms.

If you want to know more about hosting a workshop on discrete mathematics in your district, either return the request form for additional information or contact Debby Toti by phone at 732/445-4065 (Fax 732/445-3477) or e-mail at toti@dmac.rutgers.edu. Requests may be made at any time. The number of workshops that can be offered is limited, so early requests are encouraged.

WHAT?

The Leadership Program in Discrete Mathematics will sponsor one or more full-day workshops in your school or district covering contemporary topics in discrete mathematics and offering ways of introducing these concepts into the classroom and into the curriculum.

WHO?

Teachers at all levels should be encouraged to participate in the workshops, since many of the concepts can be introduced to and discussed with students at all levels. See the sample questions in discrete mathematics listed below for examples of problems.

WHERE?

Workshop leaders will conduct workshops in your district or school. Whenever possible, we will schedule a workshop leader from your geographic area to minimize travel expenses whenever possible. Workshop leaders live in or near the following states:

  • Arizona
  • California
  • Colorado
  • Connecticut
  • Delaware
  • District of Columbia
  • Florida
  • Georgia
  • Kentucky
  • Maine
  • Maryland
  • Massachusetts
  • Nevada
  • New Hampshire
  • New Jersey
  • New Mexico
  • New York
  • Ohio
  • Oregon
  • Pennsylvania
  • Rhode Island
  • Tennessee
  • Utah
  • Vermont
  • Virginia
  • Washington
  • West Virginia

For workshops in other states, there will be additional travel expenses.

WHEN?

Workshops will be scheduled on an individual basis at the request of the participating district. Workshops may be scheduled during the school year or during the summer. Every effort will be made to accommodate dates requested by interested districts.

BY WHOM?

The workshops will be conducted by experienced teachers who have participated in the Leadership Program and in a seven-day training program on preparing and presenting such workshops.

SPONSORSHIP?

Workshops in Your District: Exploring Discrete Mathematics is a component of the Leadership Program in Discrete Mathematics. Sponsors include the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) and the Rutgers University Center for Mathematics, Science, and Computer Education (CMSCE). Funding is provided by DIMACS and the National Science Foundation.

Joseph G. Rosenstein, Project Director

WHAT IS DISCRETE MATHEMATICS?

Discrete mathematics is a rapidly growing and increasingly used area of mathematics with many practical and relevant applications. Because it is grounded in real world problems, discrete math lends itself easily to implementing the recommendations of the NCTM Standards.

Discrete math will make mathematical concepts come alive for your students. It's an excellent tool for improving reasoning and problem-solving skills, and is appropriate for students at all levels and all abilities. Teachers have found that discrete mathematics offers a way of motivating unmotivated students and challenging honors students at the same time.

Problems in discrete mathematics are often simply stated and accessible to students with little mathematical background, including those who have not mastered algebra. On the other hand, many problems are complex, leading students to new insights and knowledge. Questions that seem simple give rise to related questions that are quite challenging. As a result, the topics are accessible and interesting both to students that are accustomed to success and already may be contemplating scientific careers, as well as to students who are accustomed to failure and perhaps need a fresh start in mathematics.

Because discrete mathematics deals with complex problem solving, it has widespread uses in a variety of fields. Many current applications to areas such as networking, telecommunications, computer design, cryptanalysis, robotics, social choice theory, and operations research involve discrete mathematics. Students specializing in discrete mathematics will find a wide range of career opportunities open to them.

SOME SAMPLE PROBLEMS IN DISCRETE MATHEMATICS

  • What is the quickest way to sort a list of names alphabetically?
  • Which way of connecting a number of sites into a telephone network requires the least amount of cable?
  • Which version of a lottery gives the best odds?
  • If each voter ranks the candidates for Presidents in order of preference, how can a consensus ranking of the candidates be obtained?
  • What is the best way for a robot to pick up items stored in an automated warehouse?
  • How does a CD player interpret the codes on a CD correctly even if the CD is scratched?
  • How can an estate be divided fairly?
  • How can ice cream stands be placed at various street corners in a town so that at any corner there is a stand which is at most one block away?
  • What is the most efficient way to make collections from MAC machines?
  • How can representatives be apportioned fairly among the states using current census information?

REQUEST FOR ADDITIONAL INFORMATION

For additional information on Workshops in Your District: Exploring Discrete Mathematics, print this form, fill it out, and mail it to us at:

Workshops in Your District
P.O. Box 10867
New Brunswick, NJ 08906-0867

             Name: _________________________________________________

         Position: _________________________________________________

           School: _________________________________________________

   School Address: _________________________________________________

        ____________________________________________________________

        ____________________________________________________________

     School Phone: (______) ______________________________

     Home Address: _________________________________________________

        ____________________________________________________________

        ____________________________________________________________

       Home Phone: (______) ______________________________