The Constant Feature: Spanning K–12 Mathematics

2004 ◽  
Vol 97 (3) ◽  
pp. 198-204
Author(s):  
James E. Schultz
Keyword(s):  
Computer Algebra ◽  
Mathematics Learning ◽  
Graphing Calculators ◽  
Computer Algebra Systems ◽  
Teaching Mathematics ◽  
Twelfth Grade ◽  
Constant Feature ◽  
K 12

When I reflect on my many years of teaching mathematics, one of the most enjoyable and fruitful ideas for calculator use came from an article that appeared more than twenty-five years ago (Judd 1976). It gave suggestions for using the constant feature of a simple calculator to enhance mathematics learning. I have used Judd's idea successfully in many classrooms at grades levels ranging from kindergarten through twelfth grade. This article revisits the constant feature for four-function calculators and extends it for use with graphing calculators and computer algebra systems (CASs) for a broad range of topics.

How to Solve Any Triangle: First, Forget the Law of Sines and the Law of Cosines

2003 ◽  
Vol 96 (6) ◽  
pp. 448-449
Author(s):  
Lin McMullin
Keyword(s):  
Computer Algebra ◽  
Newton’S Method ◽  
Newton's Method ◽  
Graphing Calculators ◽  
Computer Algebra Systems ◽  
Mathematics Courses ◽  
Mathematical Problems ◽  
The Law ◽  
Law Of Cosines

Computer algebra systems (CASs) have made, and will continue to make, changes in what is taught in mathematics courses at all levels. Just as scientific calculators made teaching computations with logarithms obsolete, CASs will render obsolete many other topics in the curriculum. Some will be formulas and procedures for computations that are no longer necessary to solve the problems for which they were originally developed. The mathematical problems will remain; we will just use more efficient ways to solve them. A good example is Newton's method for approximating the zeros of an expression. Using Newton's method to find roots by hand has been rendered obsolete by graphing calculators that can either find the roots exactly or do the approximations faster and more accurately.

Soundoff!: A New Breed of Calculators: Do They Change the Way We Teach

1999 ◽  
Vol 92 (2) ◽  
pp. 88-89
Author(s):  
James Podlesni
Keyword(s):  
Advanced Placement ◽  
Computer Algebra ◽  
Graphing Calculators ◽  
Computer Algebra Systems ◽  
New Models ◽  
User Friendly ◽  
New Generation ◽  
The Way

A new generation of graphing calculators—for example, the TI-89 and the Casio 9970—that use computer algebra systems (CAS) are now available. Since they manipulate symbols, one could argue that they represent as big a change as the step from scientific to graphing calculators. A student “asks” the calculator to factor x2 + 5x + 6, and the calculator prints (X + 2)(X + 3). On the Advanced Placement calculus examination, existing graphing calculators allow the student to find the derivative of y = cos x at a specific x-value. In addition, the new models can “tell” the student that the derivative of cos x is −sin x. They can also provide units for numeric answers. They are apparently much more user-friendly than the existing HP-48, thereby assuring widespread use. The TI-89 is essentially a TI-92 in a TI-83 case, without the geometry package but with FLASH™, a feature that allows it to be upgraded electronically.

Soundoff: A Case against Computer Symbolic Manipulation in School Mathematics Today

1992 ◽  
Vol 85 (3) ◽  
pp. 180-183
Author(s):  
Bert K. Waits ◽  
Franklin Demana
Keyword(s):  
Mathematics Education ◽  
Computer Algebra ◽  
Graphing Calculators ◽  
School Mathematics ◽  
Computer Algebra Systems ◽  
National Council ◽  
Symbolic Manipulation ◽  
Symbol Manipulation ◽  
Evaluation Standards ◽  
Exploration Tool

The National Council of Teachers of Mathematics and leaders in mathematics education must move vigorously to build a consensus for acceptance of the Curriculum and Evaluation Standards (NCTM 1989). One important assumption of the Curriculum and Evaluation Standards is that all students should use computers and graphing calculators on a regular basis in school mathematics. The symbol-manipulating ability of such computer algebra systems (CAS) as the IBM Math Exploration Tool Kit, Mathematics™, and Derive™ can be used today in school mathematics to do algebra. However, we take exception to the use of computer symbol manipulation in school mathematics today for two important reasons.

scholarly journals New ideas for handling of loop and angular integrals in D-dimensions in QCD

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Valery E. Lyubovitskij ◽  
Fabian Wunder ◽  
Alexey S. Zhevlakov
Keyword(s):  
Computer Algebra ◽  
Cross Sections ◽  
Orthogonal Basis ◽  
Computer Algebra Systems ◽  
Covariant Formalism ◽  
Linear Combinations ◽  
Recursion Relations ◽  
New Ideas ◽  
Rotational Invariant ◽  
Geometric Picture

Abstract We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori
Keyword(s):  
Automorphism Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Computer Algebra ◽  
Character Table ◽  
Computer Algebra Systems ◽  
Split Extension ◽  
Sporadic Group ◽  
Local Subgroup ◽  
Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

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