Project Discrete Math

George Novacky, www.cs.pitt.edu/~novacky
Patchrawat Uthaisombut, www.cs.pitt.edu/~utp
Yasir Khalifa,  www.cs.pitt.edu/~khalifa
Department of Computer Science, University of Pittsburgh
 

What is Discrete Mathematics?

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. A typical problem in discrete mathematics is the following

        Q: How many ways to create a 2-person team from a set of 4 people {Adam, Betty, Cindy, Don}.
        A: There are C(4,2) = 4! / (2! (4-2)! ) = 6 ways, namely

                {A,B}, {A,C}, {A,D}, {B,C}, {B,D}, {C,D}.

Why Discrete Mathematics is important?

Discrete mathematics is the foundation for computer science just as calculus is the foundation of engineering. Learning discrete mathematics is essential for success in computer science because the reasoning used in mathematics is the same kind of reasoning used in designing and analyzing algorithms or constructing computer programs. The best predictor for success of a student in a computer science program is the level of mathematical preparation.

Some problems in learning/teaching discrete mathematics

In order to learn discrete mathematics students must solve many homework problems. Mastery of the course material is synonymous with being able to solve homework problems consistently with confidence. It is frustrating for students working on a problem not knowing if he has made a mistake. Furthermore, interaction time between instructor and student is limited to lecture and office hours. Even through email, help is not always instantaneous. These delays cause further frustration.

Our software

We created a prototype for web-based interactive software to help students learn discrete mathematics. One of the main features of the software is the toolbox that allows the user to manipulate various kinds of mathematical objects such as numbers, sets, matrices, functions, relations, etc. The software is capable of generating unlimited number of examples to illustrate concepts and quizzes to test the user’s basic understanding. The software is designed with the learner in mind. It is easy to use and capable of giving corrective feedback when the user makes mistakes.

The various features of the software facilitate learning. The ability of the software to generate as many examples as the students wish helps the students see the problem-solving patterns better. Providing quizzes on demand and instantaneous feedback helps students gain confidence. Furthermore, giving corrective feedback when the student makes mistakes helps clear up any misconception quickly. The ability of the software to perform computations on various mathematical objects enables the student to experiment with different operations on objects, and allow them to focus on higher-order thinking and free them from low-level computation.

The software prototype is made available to students in the Discrete Mathematics course (CS441) at the University of Pittsburgh, and to the public. For more information and download, please visit the “Project Discrete Math” web site at www.cs.pitt.edu/PDM. (DOWNLOAD).
 

Address for this page is www.cs.pitt.edu/~utp/PDM.
Back to Patchrawat "Patch" Uthaisombut's page: www.cs.pitt.edu/~utp.