Applied Discrete Structures

Applied Discrete Structures is designed for use in a university course in discrete mathematics spanning up to two semesters. Its original design was for computer science majors to be introduced to the mathematical topics that are useful in computer science. It can also serve the same purpose for mathematics majors, providing a first exposure to many essential topics.

We embarked on this open-source project in 2010, twenty-one years after the publication of the 2nd edition of Applied Discrete Structures for Computer Science in 1989. We had signed a contract for the second edition with Science Research Associates in 1988 but by the time the book was ready to print, SRA had been sold to MacMillan. Soon after, the rights had been passed on to Pearson Education, Inc. In 2010, the long-term future of printed textbooks was uncertain. In the meantime, textbook prices (both printed and e-books) had increased and a growing open source textbook movement had started. One of our objectives in revisiting this text is to make it available to our students in an affordable format. In its original form, the text was peer-reviewed and was adopted for use at several universities throughout the country. For this reason, we see Applied Discrete Structures as not only an inexpensive alternative, but a high quality alternative.

The current version of Applied Discrete Structures has been developed using PreTeXt, a lightweight XML application for authors of scientific articles, textbooks and monographs initiated by Rob Beezer, U. of Puget Sound. When the PreTeXt project was launched, it was the natural next step. The features of PreTeXt make it far more readable, with easy production of web, pdf and print formats.

The current computing landscape is very different from the 1980’s and this accounts for the most significant changes in the text. One of the most common programming languages of the 1980’s was Pascal. We used it to illustrate many of the concepts in the text. Although it isn’t totally dead, Pascal is far from the mainstream of computing in the 21st century. The open source software movement was just starting in the late 1980’s and in 2005, the first version of Sage (later renamed SageMath), an open-source computer algebra system, was first released. In Applied Discrete Structures we have replaced "Pascal Notes" with "SageMath Notes."

Many of the concepts introduced in this text are illustrated using SageMath code. SageMath (sagemath.org¹) is a free, open source, software system for advanced mathematics. Sage can be used either on your own computer, a local server, or on SageMathCloud (https://cloud.sagemath.com).