The sequence 1, 1, 2, 3, 5, 8, 13, 21, ..., known as Fibonacci sequence, has a long history and special importance in mathematics. This sequence came about as a solution to the famous rabbits' problem posed by Fibonacci in his landmark book, "Liber abaci" (1202). If the "n"th term of Fibonacci sequence is denoted by [f][subscript n], then it may…

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a…

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

This textbook is designed primarily to follow the third book of the author's series of textbooks of secondary mathematics. Therefore, it presupposes the essentials of high-school algebra, plane and solid geometry, and trigonometry. It aims to combine the work which is commonly covered in separate courses in college algebra and in analytical…

Paper presented at the Annual Convention of the Central Association of Science and Mathematics Teachers, St. Louis, Missouri, November 1968

This study was designed to ascertain the relative effectiveness of two approaches for teaching descriptive geometry by a comparison of the following behavioral variables--(1) performance in the solution of graphical problems, (2) spatial perception, (3) abstract reasoning ability, (4) technical information achievement, and (5) attitude toward…

Studied were the effects of a knowledge of the behaviors associated with mathematical processes on problem-solving ability. Processes defined for the study were those involving: (1) construction of mathematical models, (2) conjecturing, (3) settling conjectures as being true or false, and (4) application of given axioms and theorems to problems. A…

A method is presented for solving the general quartic by using two classical curves: the ellipse and the conchoid of Nichomedes. (MP)

This paper concerns the derivation of a closed form for a function f(x) given closed forms for f(g(x)) and g(x). (SD)

Reasons for using Rolle's Theorem in calculus are discussed, with comparisons to the theorems of Lagrange and Cauchy. (MNS)

University entrance examinations in China are described. Then the 1985 test is presented. (MNS)

Standard calculus textbooks often include a related rates problem involving light cast onto a straight line by a revolving light source. Mathematical aspects to these problems (both in the solution and in the method by which that solution is obtained) are examined. (JN)