First courses in abstract or modern applied algebra are concerned with the investigation of mathematical structures, such as groups and rings, along with certain fundamental properties they, or their associated substructures, possess. Following this...
The term algorithm it self is derived from the name of a ninth century Persian author, Abu Jafar Mohammed ibn Musa a1 Khowarizmi, who wrote a book in which he formulated rules for performing the four basic arithmetic operations of addition,...
A computing system can, in general, be discussed from two points of view: its hardware and its software. In this context, hardware refers first and foremost to the machinery that is used to enter and to store information in the system, to process data...
What accounts for these differences betweeen real and complex differentiable functions? First, when z and f ( z ) are complex, the difference quotient (1) involves subtraction and division of complex rather than real numbers. (We discuss these...
In t he early days of the computer industry, the development of software proceeded ad hoc. As technological advances were made the cost of computer hardware decreased even as its speed and accuracy increased. However, the cost of developing and...
LOGO is a computer language invented by Seymour Papert at the M.I.T. Artificial Intelligence Laboratory in the late sixties. Papert was doing research in the application of technology to elementary education, and needed a language with which children...
In advising students about opportunities for jobs or graduate study in mathematics, I find it helpful to subdivide applied mathematics into four areas: the classical applied mathematics, which developed in tandem with the physical sciences and...
Management science uses the scientific method to develop solutions for management decision problems. For example, a petroleum company manager must decide the quantity of each of many crude oils to blend together to produce the various products a t...
Data base or databasen is a term we hear almost daily in business because business is information based. But the term's use is not limited to business; it refers to any type of data belonging to an organization, company, or individual. These types of...
Cant is an old English word for insincere or meaningless talk used merely from convention or habit. Originally it referred to the singsong chant of street beggars during the Middle Ages. Computer literacy is one of the cant phrases of our age. We hear...
Elementary number theory is the study of the relationships among the integers. These relationships arise from two properties: (1) Under the operations of addition and multiplication, the integers form an integral domain - both operations are...
Number theory is an area of mathematics in which the properties of the positive integers become the focal point of study. Historically, number theory has developed in several directions, one being called analytic number theory. Analytic number theory...
That revived pedagogical entity called discrete mathematics appears surrounded by a mist of uncertainty and some confusion. Three recent articles [5,7,9] have debated the nature, purpose, and relative importance of this subject, but there the experts...
Nearly everyone in college teaching is aware of the tremendous increase in the demand for computer-related courses, and the instructors to teach them, that has taken place in the past 10 years. The same economic forces that are driving the increased...
The primary purpose of this article is to comment on the difference between pure and applied mathematics from the point of view of a mathematician in a diverse high-technology industry. A second purpose is nostalgic: I shall reminisce about...
Poor or imprecise use of language can often confuse a reader or listener. There is particular occasion for such confusion in discussion of growth or decrease, when the speaker or writer may want to impress or even exaggerate. Take a photograph with...
The topic of elliptic curves is an exciting one for a variety of reasons. For one thing, elliptic curves are a meeting ground where ideas from geometry, number theory, topology, group theory, and complex analysis all come together and interact in a...
The red ink informed Jim Washam that he had made a $400 mathematical error. Washam, a bank vice-president, was glad that the mistake was only on a test in his mathematics class, but he wished to improve his mathematical skills so as to avoid such...
Adaptive methods have their foundation in the mathematical field of control theory. The basic idea of an adaptive method is for a computer system to modify the state or condition of the solution procedure to make the algorithm more efficient or...
Once upon a time, there was a country, and the people in this country had strong religious beliefs that influenced their lives in many different ways. They believed that God created the world from nothing, that God did it in six days and then rested on...