Computer Algebra

To gain more insight into the process of teaching and learning mathematics, we experimented during the Fall of 2003 and the spring of 2004 with some calculus chat bots. These bots know an encyclope- dic glossary of mathematics definitions as well as general knowledge background and can solve simple mathematical template problems posed in colloquial language. The bot "Sofia" can also interact with computer algebra systems like Pari or Mathematica to solve simple pre-wired calculus problems.

The use of component architectures to solve the problem of reuse and interoperability in scientific computing has been investigated by various research groups during the last years. Moreover, architectures for Internet accessible math- ematical services have been proposed. In this paper give a brief abstract require- ments analysis with respect to these problems and show that there is an existing

Objectives: In this paper, we present and employ symbolic Maple software algorithm for solving initial value problems (IVPs) of partial differential equations (PDEs). From the literature, the proposed algorithm exhibited a great significant in solving partial differential equation arises in applied sciences and engineering. Results: The implementation include computing partial differential operator (PartialDiffOperator), Greens function (GreensFunction) and exact solution (ExactSolution) of the given IVP. We also present syntax, ApplyPartialDiffOp, to apply the partial differential operator to verify the solution of the given IVP obtained from ExactSolution. Sample computations are presented to illustrate the maple implementation.

This paper describes the recent development of hand-held algebraic calculators and evaluates their significance for secondary education. Sophisticated computer algebra systems (CAS) have been available to mathematicians for some years now but have been too powerful, too sophisticated and too expensive and have required too much access to powerful computers to have had much impact on teaching and learning elementary

1 Introduction
2 Expressions
3 Functions
4 Solutions of Equations
5 Solving a System of Equations for Several Unknowns
6 Solving Dierential Equations
7 Procedures, Variables, and Extending Maple
8 Implementing Packages using Modules
9 Three-dimensional plotting
10 Create a 2-D or 3-D animation on one parameter
11 Maple Help
12 References

Synopsis: Although there are a number of technologies related to school algebra, it is only the personal technology of the graphics calculator that seems likely to be available widely enough to influence curriculum design and implementation on a large scale. The algebra curriculum of the past is overburdened with symbolic manipulation at the expense of understanding for most students. But

If computer algebra systems (CAS) are to be permitted in upper-secondary mathematics teaching, careful consideration should be given to the balance between by-hand and by-CAS procedures. One aspect of this is judging when it is most appropriate for students to use CAS and when they should be encouraged to use by- hand techniques for solving, factoring and differentiating. Twenty-four Australian secondary and tertiary educators with some CAS experience responded to a 49 item questionnaire asking whether they thought a reasonable future goal would be for students to complete particular items by-CAS or by-hand and to estimate the proficiency of current students, measured by time, to complete the items correctly. Current student proficiency is a major determinant of future goals. Almost any complexity in an item increased the probability it would be assigned to CAS. Particular items that demonstrate special features and lead to interesting differences are illustrated.

The book, Orthogonal Designs: Quadratic Forms and Hadamard Matrices, Marcel Dekker, New York-Basel, 1979, by A.V. Geramita and Jennifer Seberry, has now been out of print for almost two decades. Many of the results on weighing matrices presented therein have been greatly improved. Here we review the theory, restate some results which are no longer available and expand on the

Objectives: In this paper, we discuss a Maple package, deaSolve, of the symbolic algorithm for solving an initial value problem for the system of linear differential-algebraic equations with constant coefficients.

Results: Using the proposed Maple package, one can compute the desired Green’s function of a given IVP. Sample computations are presented to illustrate the Maple package.

In this paper we briefly describe a Mathematica program for simulation of quantum circuits and illustrate some of its facilities by simple examples. Unlike other Mathematica-based quantum simulators, our program provides a user-friendly graphical interface for generating quantum circuits and computing the circuit unitary matrices. In addition to standard linear algebra-based tools, our program implements special computer-algebra technique for constructing the multivariate polynomial system that, for a circuit composed from the Toffoli and Hadamard gates, uniquely defines the circuit matrix.

Herein, we use Hardy’s notion of the “false derivative” to obtain exact multiple roots in closed form of the transcendental-algebraic equations representing the generalized LambertW function. In this fashion, we flesh out the generalized Lambert W function by complementing previous developments to produce a more complete and integrated body of work. Finally, we demonstrate the usefulness of this special function with some applications.