Description:  This course will examine the field of discrete mathematics, especially the areas of importance in computer science, such as algorithms, combinatorics, logic, and graph theory.  Equal time will be given to theory, computation, and applications.  This course satisfies the functional programming requirement for moderation into the computer science program.
 
Professor: Robert W. McGrail.

Lectures: Monday and Wednesday from 9:00 AM to 10:20 AM in RKC 100.

Text: Computational Discrete Mathematics, by Sriram Pemmaraju and Steven Skiena.  New York:  Cambridge University Press.  2003.  ISBN:  0-521-80686-0.

Meetings:  These course will be a mixture of modern, multimedia presentation, group work, and occasional brief student presentation.  The running theme of this course is the use of computing to solve problems in discrete mathematics.  A general problem will be introduced and students will form groups in order to solve certain aspects of that problem.  All instructor presentations will be made available online as Mathematica presentation notebooks.

Software and Systems:   We will employ version 6.0 of the Mathematica symbolic computing system.  In particular, we will make use of the Combinatorica package.  Our official platform is Mac OS X, as installed on the RKC 100 machines.   An inexpensive student version of Mathematica is available for all platforms.

Homework:  There will be approximately 10 homework assignments.  Each assignment will be electronically submitted to me in the form of a Mathematica notebook or package attached to an email message.  Mathematica notebooks present allow one to mix programming code with formatted text, graphics, and tables.  The opportunities for creating fully "literate programs" is outstanding.  Hence students will be expected to carefully annotate their code.  That is correct:  Writing matters in this course.

The last few homework assignments will constitute one related course project on some area of discrete mathematics.

Exam:  Each student's journey will rely heavily upon the development of several technical skills.  Hence there is a certain amount of technical knowledge that each student must acquire.  My method for determining whether students are sufficiently absorbing such detail include two in-class exams, one at midterm and one at the end of the course.

Grading: The final grade will be computed according to the following breakdown.

• Homework: 30%
  
• Midterm Exam: 30%
• Project: 40%

Discrete Mathematics Topics

Mathematica Programming

• Basic Run Time Environment
• Notebooks and Publishing
• Lists and Matrices
  
• Functions
• Conditionals
• Iteration and Recursion
• Pattern Matching and Translation
• File Input and Output
• Graphics
• Graphical User Interfaces