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Ahmad, Faiz – Mathematics and Computer Education, 2011
It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…
Descriptors: Textbooks, Matrices, Mathematics Instruction, College Mathematics
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Flesher, Tatyana; Holder, Eleanor – Mathematics and Computer Education, 2007
One of the main problems in undergraduate research in pure mathematics is that of determining a problem that is, at once, interesting to and capable of solution by a student who has completed only the calculus sequence. It is also desirable that the problem should present something new, since novelty and originality greatly increase the enthusiasm…
Descriptors: Computer Software, Graphs, Calculus, Algebra
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Skurnick, Ronald; Javadi, Mohammad – Mathematics and Computer Education, 2006
The Law of Sines and The Law of Cosines are of paramount importance in the field of trigonometry because these two theorems establish relationships satisfied by the three sides and the three angles of any triangle. In this article, the authors use these two laws to discover a host of other trigonometric relationships that exist within any…
Descriptors: Geometric Concepts, Textbooks, Algebra, Preservice Teacher Education
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Sher, David B. – Mathematics and Computer Education, 1996
Describes the development of a method of generating problems that are easy to present in classroom settings because all the important points to be graphed are single-digit integers. Uses an algorithm that generates intersection problems that fit the criteria. A proof of the algorithm is included. (DDR)
Descriptors: Algebra, Algorithms, Equations (Mathematics), Functions (Mathematics)
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Lambert, Howard B. – Mathematics and Computer Education, 1989
Reviews the underpinnings of synthetic division. Shows how to quickly obtain the coefficients of the Taylor expansion of a polynomial about a point, and a partial fraction decomposition of a polynomial. (MVL)
Descriptors: Algebra, Calculus, College Mathematics, Instructional Materials
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Dence, Joseph B.; Dence, Thomas P. – Mathematics and Computer Education, 1989
Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)
Descriptors: Algebra, College Mathematics, Instructional Materials, Mathematical Concepts
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Schuette, Paul H. – Mathematics and Computer Education, 1998
Discusses the rationale behind the technique of rationalizing the denominator in algebra. Argues that the importance of this technique is greatly exaggerated and is usually unnecessary. Examines an appropriate application of rationalizing the denominator. (ASK)
Descriptors: Algebra, Fractions, Graphing Calculators, Higher Education
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Thrash, Karen R.; Walls, Gary L. – Mathematics and Computer Education, 1991
Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)
Descriptors: Algebra, College Mathematics, Higher Education, Learning Activities
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Klima, Richard E.; Sigmon, Neil P. – Mathematics and Computer Education, 2005
The use of the computer, and specifically the mathematics software package Maple, has played a central role in the authors' abstract algebra course because it provides their students with a way to see realistic examples of the topics they discuss without having to struggle with extensive computations. However, Maple does not provide the computer…
Descriptors: Programming Languages, Computer Science, Algebra, Computer Assisted Design
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Mathews, John H. – Mathematics and Computer Education, 1990
Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)
Descriptors: Algebra, College Mathematics, Computer Assisted Instruction, Computer Uses in Education
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Bosch, William W.; Strickland, Jeff – Mathematics and Computer Education, 1998
The Optimizer in Quattro Pro and the Solver in Excel software programs make solving linear and nonlinear optimization problems feasible for business mathematics students. Proposes ways in which the Optimizer or Solver can be coaxed into solving systems of linear equations. (ASK)
Descriptors: Algebra, Computer Software, Computer Uses in Education, Educational Technology
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Ecker, Michael W. – Mathematics and Computer Education, 2005
In this article, the author proves a theorem about polynomial zeros, but the focus is on how the theorem is integrated into a QuickBASIC computer program, and how that program answers the questions of the theorem--a unification of mathematics and computer programming. For a given polynomial, how can one overcome assorted problems in finding zeros…
Descriptors: Computers, Programming, Intervals, Computer Software
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Anderson, Oliver D. – Mathematics and Computer Education, 1990
Discussed is the use, importance, and availability of programmed algebraic manipulation packages. The general power summation formula is presented and an example using a programed numerical verification package is provided. (KR)
Descriptors: Algebra, College Mathematics, Computation, Computer Assisted Instruction
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Sigmon, Neil P. – Mathematics and Computer Education, 1997
Demonstrates the use of technology to enhance the appreciation of applications involving abstract algebra. The symbolic manipulator Maple can perform computations required for a linear cryptosystem. One major benefit of this process is that students can encipher and decipher messages using a linear cryptosystem without becoming confused and…
Descriptors: Algebra, Coding, College Mathematics, Computer Assisted Instruction
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Fernandez, Eileen; Jones, Michael A. – Mathematics and Computer Education, 2006
"How can this Abstract Algebra course help me to teach Algebra in high school?" To professors of prospective mathematics teachers, this type of question has a resounding familiarity. Because students are unclear as to the relationship between upper division mathematics courses and the high school curriculum, answering the opening question to the…
Descriptors: Teaching Methods, Teaching (Occupation), High Schools, Secondary School Curriculum
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