The presented paper is devoted to the new teaching model of congruences of computer science students within the subject of discrete mathematics at universities. The main goal was to create a new model of teaching congruences on the basis of their connection with Diophantine equations and subsequently to verify the effectiveness and efficiency of…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…

This material contains two units which view applications of computer science. The first of these examines Horner's scheme; and is designed to instruct the user on how to apply both this scheme and related algorithms. The second unit aims for student understanding of standard bisection, secant, and Newton methods of root finding and appreciation of…

It is noted that there are some integrals which cannot be evaluated by determining an antiderivative, and these integrals must be subjected to other techniques. Numerical integration is one such method; it provides a sum that is an approximate value for some integral types. This module's purpose is to introduce methods of numerical integration and…

Forty-eight mathematicians in industry, business, and government replied to a questionnaire on the relative merits of the traditional undergraduate curriculum, advanced topics in pure mathematics, computer programing, additional computer science, and specialized or applied topics. They favored programing and applied mathematics, along with a…

This study concerned conceptual difficulties of college students learning programming and ways the teacher can simplify the process. An analysis of general strategies used in solving problems involving loops is given, with four types of hierarchical strategy categorized. Students had difficulty transforming their algebraic descriptions into…

When problems defy solution, mathematicians can settle for "almost." This branch of mathematics (called computational complexity) encompasses both the number of parts involved in a problem and the intricacy of their interrelatedness. Current research in this area is discussed, considering various computer applications involved. (JN)

A program written in PASCAL designed to find the number of binary trees possible for a given number of nodes is presented. The problem was found to be highly motivating and exciting for the group of introductory computer science students with whom it was used. (MP)

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

The nature of "A Programing Language" (APL) is viewed as unambiguous, consistent, and powerful. It is based on the notion of functions as imperative verbs, and is used by a small but growing number of mathematicians and computer programers. Three areas of mathematical activity are addressed: calculation of arithmetic expressions,…

These modules view aspects of computer use in the problem-solving process, and introduce techniques and ideas that are applicable to other modes of problem solving. The first unit looks at algorithms, flowchart language, and problem-solving steps that apply this knowledge. The second unit describes ways in which computer iteration may be used…

Presented is a way to provide students with a review and an appreciation of the versatility of pointers in data structures by improvising with binary trees. Examples are described using the Pascal programing language. (KR)

Presented is a scheduling algorithm that uses all the busses at each step for any rectangular array. Included are two lemmas, proofs, a theorem, the solution, and variations on this problem. (KR)

Loan and estimated payment problems are featured in this presentation of mathematics-oriented programing tasks designed for the beginning student. (MP)