By Assad Ebrahim and Carol Ouellette, on April 2nd, 2010 (6,161 views)
Topic: Mathematics, Technical
By Assad Ebrahim, on February 25th, 2010 (29,171 views)
Topic: Mathematics, Technical
Updated! February 5, 2017
The value of zero raised to the zero power, , has been discussed since the time of Euler in the 18th century (1700s). There are three reasonable choices: 1,0, or “indeterminate”. Despite consensus amongst mathematicians that the correct answer is one, computing platforms seem to have reached a variety of conclusions: Google, R, Octave, Ruby, and Microsoft Calculator choose 1; Hexelon Max and TI36 calculator choose 0; and Maxima and Excel throw an error (indeterminate). In this article, I’ll explain why, for discrete mathematics, the correct answer cannot be anything other than 0^0=1, for reasons that go beyond consistency with the Binomial Theorem (Knuth’s argument).
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By Assad Ebrahim, on February 22nd, 2010 (39,159 views)
Topic: Toolkit
Maxima is a symbolic computation platform that is free, open source, runs on Windows, Linux, and Mac, and covers a wide range of mathematical functions, including 2D/3D plotting and animation. Capabiities include algebraic simplification, polynomials, methods from calculus, matrix equations, differential equations, number theory, combinatorics, hypergeometric functions, tensors, gravitational physics, PDEs, nonlinear systems. With an active developer base and responsive community, a user gets a secure future lifecycle of the product and plenty of help when dealing with problems. The result: an essential mathematical computing package for students, programmers, engineers, scientists, and mathematicians. This article will help you get started with Maxima.
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By Assad Ebrahim, on February 8th, 2010 (13,447 views)
Topic: Technical
By Assad Ebrahim, on February 8th, 2010 (22,018 views)
Topic: Technical
(Discrete Mathematics Techniques I)
Abstract
We motivate an approach that uses recurrence relations to find closed form solutions to the finitesummationofintegerpowers problem for any individual . The approach is illustrated for small : . Maxima, an opensource (free) software package, is used to demonstrate how a symbolic computation platform can speed up the accurate derivation of messy algebraic expressions.
A recurrence solution to the general case (arbitrary ) is developed in Part 2 along with Maxima source code. A direct (noniterative) matrix method for solving the general case is given in Part 3 along with Maxima and Octave/Matlab source code.
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By Assad Ebrahim, on January 31st, 2010 (4,301 views)
Topic: Education, Phenomenology
Good mathematical technique can bring the solution to certain mathematical questions within reach. By a proper formulation (one that is both tractable and that generalizes readily) and the use of mechanical techniques, one can often pass from a single insight to the solution of a family of problems, and in some cases, to the solution of the general question itself. … Good mathematical technique has built within it the mathematical insight of the best of previous generations.
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