The key word when dealing with computer information systems is “information.” How many people want it? How can they access it? How can they be sure it is accurate? What role does mathematics play?

Millions of people want a variety of information. The greater the number of people who want the information, the more a computer is needed to store and retrieve it quickly, and the greater the chance that mathematics will be used to enable the entire process. It was estimated that in 1998, 100 million people around the world used the Internet. As the number of Internet users increases to one billion by 2005, terms such as Internet, Super Information Highway, the World Wide Web, or e-commerce (electronic commerce) will merely be a reference for the basic notions of computer information systems.

Computer information systems are several subsystems that rely heavily on mathematical processes to manage data or information: database management, software engineering, telecommunications, systems analysis, and decision support systems. Statistics, set theory, Boolean operators,  modular arithmetic, and cryptography are some of the mathematics that assist in dealing with computer information systems.

Statistics

Statistics is a branch of mathematics that involves gathering, summarizing, displaying, and interpreting data to assist in making intelligent decisions.

Examples of the use of statistics in computer information systems include the following:

• gathering data on samples of manufactured products to determine the efficiency of the production process;

• predicting the outcome of presidential elections prior to the total count of votes;

• determining different rates for automobile insurance for male and female teenage drivers; and

• gathering data on automobile accidents that occur while driving using a cellular phone.

Consider the consequences if data are not gathered, summarized, or interpreted properly before decisions are made. For example, there was a major recall on tires produced by a certain manufacturer. Is it possible that data were not gathered under the proper conditions to have an advance warning about the potential for the tire tread separating from the rest of the tire?

Once the data are gathered, statistics is used to look for patterns, determine relationships, and create tables, graphs, and mathematical formulas to report data or predict additional data. The National Highway Traffic Safety Administration (NHTSA), for example, uses data to identify safety issues and monitor trends and the effectiveness of safety regulations.

Statistics is applied to the traffic safety data found with the primary database tools: the Fatal Analysis Reporting System (FARS), the National Sampling System (NASS), and crash reports collected by the states. For example, NHTSA used mathematics to calculate and compare the percentages of the overall 217,651 police-reported crashes in Oklahoma for the period of 1992 to 1994 with the 299 crashes in which cellular telephones were being used.

It was revealed that 17 percent of the cellular phone–related accidents resulted from lack of attention, whereas only 9 percent of all accidents in the state were attributed to that circumstance. This information may influence drivers, lawmakers, and cellular phone manufacturers.

Set Theory and Boolean Operators

How can people access information? First, the location of the data must be determined and then the data must be searched. Masses of data, words, pictures, and sounds have been collected by businesses, libraries, schools, and governments and made available on the Internet. For example, the information on the cellular phones and traffic accidents briefly described above was obtained on the Internet. The mathematics that helps computers to organize and retrieve information in efficient ways is called  set theory and uses the mathematical concept known as Boolean operators.

       To find the information about cellular phones, conduct a web search for “cellular phones.” Entering “cellular phones” in the search window indicates that the set of data related to cellular phones is the data in which the searcher is interested. The web has been programmed by software engineers so that if “cellular phones” is entered as a search, it is understood that the set of web sites desired contain data about both terms—cellular and phones.

Web searches by default use “and” as the linking operator for search terms. Consequently, when “cellular phones” is entered in the search window, the search should return web sites that reference both terms. There is no guarantee that the search will result in the desired hits, but there is a good chance of getting useful information, although it may be intermixed with less useful data. For instance, a search for “cellular phones” may also

yield a web site about  cellular processes in science that were discussed in a phone conference.

 To locate web sites that contain information about cellular phones and auto accidents, the searcher must employ the Boolean operator and. To investigate web sites about auto accidents regardless of whether they include information about cellular phones, the searcher would use the Boolean operator or. The results of the latter search should yield web sites about cellular phones, web sites about auto accidents, and web sites that contain both cellular phones and auto accidents.

In addition to these two rather typical Boolean operators (and and or), there is another seldom used operator: and not. If one wanted to search for web sites that contained information about “cellular” but not “phone,” one could enter a web search for “cellular and not phone.”

Knowing the basics of set theory and Boolean operators that underlie information management can increase the chances of getting a productive web search. In fact, the new web address that appears in the address window after a search will contain some shorthand for these Boolean operators.

A search for “cellular and phone” will be reflected by “cellularphone” in the address window. The shorthand for  and not is a minus sign: “cellularphone.”

Modular Arithmetic

There are at least two other concerns relating to computer information systems. How can the accuracy of the information be determined, and how can it be secured so that others cannot change it or remove it? The latter becomes particularly important when purchases are made on the Internet with credit cards or when private information is requested. But in this discussion only the former question will be addressed.

Information is often encoded in special ways to both ensure accuracy and to provide a quick way of communicating information electronically.

For example, many common items bear special arrangements of vertical barsof various heights to represent such identifiers as zip codes,  Universal Product Codes (UPCs), and International Standard Book Numbers (ISBN). Each of these numbers along with their special symbolic coding can be read quickly by a machine and thus can be quickly processed for computer information systems.

Computer information systems use problem solving, which is a mathematical process, to detect the patterns in the bar codes. Many times, however, a special digit is included in the code merely as a “check digit.” The check digit helps to signal when an error in the code is present.

For example, consider the following ISBN number for a certain book:

0-412-79790-9. The last digit here, 9, is a check digit. Try multiplying the digits of the ISBN number by the counting numbers, counting down from 10 to 1 and finding the sum of each product starting with the left-most digit

If the sum (in this case, 209) can be evenly divided by 11 (with a remainder of 0), then the ISBN number is correct. Now investigate the ISBN of this encyclopedia.

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Reference

Coxford, Arthur F., et al. Contemporary Mathematics in Context: A Unified Approach. (Course 4-Part B). Chicago: Everyday Learning Corporation, 2001.

Currie, Wendy. The Global Information Society. New York: John Wiley & Sons, Ltd 2000.

Iman, Ronald L. A Data-based Approach to Statistics. Belmont, CA: Wadsworth, Inc 1994.