The concept and use of proof in mathematics are examined. Uses and purposes of proofs are listed and described. (MP)

The introduction of certain topics in the theory of machines and languages into school and college mathematics courses in place of the more usual discussion of groups and formal logic is proposed. Examples of machines and languages and their interconnections suitable for such courses are outlined. (MP)

A tool to aid elementary calculus students in the computation of unusual limits is reviewed. (MP)

Several BASIC computer programs designed to illustrate concepts in probability are presented. The programs are geared for the Apple II computer, but most samples are adaptable to other systems. (MP)

Two responses to a prior report on significant figures and a discussion on outlining conventions for the accuracy of answers are included in this document. A clarification of the supposed error in the original report is noted at the beginning. (MP)

Presented is a example that shows why a certain technical lemma is necessary for a valid proof of Galois Theory. The usual proof of Galois' Theory is included as well as one using the lemma. (KR)

Presented is an alternate way to derive R from Taylor's Theorem without involving the (n + 1)st derivative of f. Included is the procedure for estimating the bounds of R. (KR)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Describes a course, "Mathematics and the Environment," for liberal arts students. The course is designed to motivate students and to demonstrate that mathematical concepts are necessary to understand global issues. Lists some global issues, information sources, and classroom activities. (YP)

Describes how to measure animals pace, stride, and step angle in degrees. Presents cases of measurements for dinosaur trackways. (YP)

Illustrates how to draw a regular pentagon. Shows the sequence of a succession of regular pentagons formed by extending the sides. Calculates the general formula of the Lucas and Fibonacci sequences. Presents a regular icosahedron as an example of the golden ratio. (YP)

Describes learning difficulties students may have with the basic notions of linear algebra and three phases of abstraction. Discusses results of a program based on the abstraction process. (YP)

Examines aspects of the images and definitions that college students and junior high school teachers have for the concept of function. Provides a seven-item questionnaire. Describes and categorizes the various images and definitions of the concept. (YP)

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)