Search

In this paper, the author aims to offer an elaboration of simple, yet powerful, mathematical patterns through mathematical games. Mathematical games may serve as colorful instructional tools for teachers and textbooks, and may raise students' motivation and intuition. Patterns are fundamental in mathematics and computer science. In the case of games, they may involve integer properties such as parity, primality, and divisibility, as well as invariant properties of repeated actions. The author presents four simply stated, less familiar mathematical games--Co-primes, Interleaved Parity, Proper Divisors, and Powers of 2--and develops the winning strategy for each of the games. Preliminary novice attempts are mentioned, and then instructive strategy developments are presented, through the illumination of underlying mathematical patterns. The author concludes by reflecting on the illuminated patterns and the way they were reached.

Instructors teaching beginning programming classes are often interested in exercises that involve processing photographs (i.e., files stored as .jpeg). They may wish to offer activities such as color inversion, the color manipulation effects archived with pixel thresholding, or steganography, all of which Stevenson et al. [4] assert are sought by students. However, instructors may not find textual support for these topics since widely used introductory textbooks do not illustrate the needed techniques, and the professional Java literature obscures these straightforward operations in elaborate discussions. This paper presents the code to make image processing accessible through fragments used to hide a text message in a read-in JPEG file, store the image as a PGN file, and extract the message from the stored image.

Teaching is a scholarly activity and a life-long learning process with no single method or pedagogy that is always most effective. Applications of teaching pedagogies properly vary from content-based to discipline-based areas. In this paper, various teaching pedagogies, including scaffolding, concept mapping, constructivism, and learning strategies including problem-based learning, collaborative learning, and active learning, is discussed and their applications in effective teaching of undergraduate Computer Science is demonstrated.

When dealing with a complex problem, solving it by reduction to simpler problems, or problems for which the solution is already known, is a common method in mathematics and other scientific disciplines, as in computer science and, specifically, in the field of computability. However, when teaching computational models (as part of computability) this topic is not usually explicitly emphasized. The authors believe that developing reductive thinking patterns is an important goal in any scientific discipline, and specifically in Computer Science (CS). Problems that deal with computational models can nicely serve to demonstrate and enable practice of such thinking patterns, especially if these problems are carefully chosen, and have a few possible reductive solutions. In this paper, the authors demonstrate this principle using a number of problems for two computational models: The finite automata model (representing finite state machines with no additional memory) and the pushdown automata model (representing finite state machines equipped with an infinite memory, which may be accessed according to the Last-In-First-Out principle.) Although these problems were used for high school students, appropriate problems can be defined that are suitable for college and university courses. (Contains 13 figures.)

Generally, when recursion is introduced to students the concept is illustrated with a toy (Towers of Hanoi) and some abstract mathematical functions (factorial, power, Fibonacci). These illustrate recursion in the same sense that counting to 10 can be used to illustrate a for loop. These are all good illustrations, but do not represent serious applications of recursion. Many of the most important applications of recursion occur on methods of lists, trees and graphs. These data structures are usually presented within the computer science sequences between computer science 2 and algorithms. This paper demonstrates an alternative approach to recursion that combines recursive data with recursive methods. Thus, the recursion will be built into the data structures themselve and the advantages of object-oriented programming will be apparent with this approach to recursion.

This paper describes a "learning community" designed for sophomore computer science majors who are simultaneously studying discrete mathematics. The learning community consists of three courses: Discrete Mathematics, Data Structures and an Integrative Seminar/Lab. The seminar functions as a link that integrates the two disciplines. Participation in the seminar enables students to study and appreciate the mutually beneficial relationship that exists between mathematics and computer science--a relationship that students often fail to see. Through carefully planned experimentation, students investigate how mathematics is used to formalize computer science, and how computer science can be used as a tool to explore mathematics.

The rapid rate of expansion of the disciplines of biotechnology, genomics, and bioinformatics emphasizes the increased interdependency between computer science and biology, with mathematics serving as the bridge between these disciplines. This paper demonstrates this inter-relationship within the context of a computational model for a biological process. We designed and implemented a lesson plan for an interdisciplinary science course that examines the evolutionary process from biological, mathematical, and computer science perspectives. The observations obtained from this lesson can be used to augment studies in mathematics with emphasis on arithmetic functions, probability, and generating series.

Argues that education in computer science in secondary schools has not kept pace with curriculum developments for college programs. Suggests definitions to be agreed upon and ways to close the gap between secondary and college programs. (PK)