THINKING LIKE A MATHEMATICIAN, cont.

Ray’s text attempts to show how “mathematical knowledge is hard-won,” to give readers a sense for “how many different paths have been tried and abandoned in the process of developing the theories that we have today.”

As he recounted in his recent Faculty Forum presentation, David Hunter has just completed the third edition of his textbook Essentials of Discrete Mathematics, published by Jones & Bartlett. Designed to serve computer science and mathematics majors, the book is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. Much of David’s revisions to the text have sought to Discreet Mathematics textbookemphasize the inquiry-based approaches to learning that now distinguish his courses. Inquiry problems are used to launch each chapter, with the intent of helping students understand the concepts and applications and not just the equations and examples.

The final chapter takes a multidisciplinary perspective and offers case studies that blend the study of mathematics with molecular biology, linguistics, sociology, economics, and music. For instance, he describes how discrete mathematics can help us see patterns in DNA. "Bioinformatics," David observes, " is "now extremely active," and more and more "biology's microscope is being replaced by mathematics." David demonstrates that mathematics is now widely used to“grapple with the gigantic strings of information hidden in nucleotides”—and to study how our minds keep track of complex sentence structures. The book examines how discrete mathematics helps us chart population growth and decline—and helps us describe the twelve-tone compositions of the Viennese school of music, notably the atonal work of Arnold Schoenberg.

Earlier this month Russell Howell gave a colloquium lecture to cadets and faculty at the US Air Force Academy in Colorado Springs. The title was "RAM and Recursion." He offered a prize to any cadet who guessed what the acronym "RAM" designated in his talk. Most all of them guessed the usual meaning: RAM = Random Access Memory. Russ, though, had something else in mind (i.e., "RAM" meant "RAM And Mathematics" so that the title actually illustrated recursion, a self-referential process. Thus, "RAM and Recursion" unwinds to "RAM And Mathematics and Recursion," which in turn becomes "RAM And Mathematics And Mathematics and Recursion," and so forth). As you might expect, no one got it, but he gave a prize anyway to the cadet who at least knew he had missed the mark: "Dr. Howell, Sir, RAM stands for Random Access Memory. I’m guessing, however, that is not what you are looking for. . . ."

It was no doubt easier to keep score at the Air Force-Wyoming football game: the Air Force gave Russ prime seats for a 31-17 victory.