Mathematica Journal

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  1. https://doi.org/10.3888/tmj.23-3   We present a straightforward implementation of contour integration by setting options for and , taking advantage of powerful results in complex analysis. As such, this article can be viewed as documentation to perform numerical contour integration with the existing built-in tools. We provide examples of how this method can be used when integrating […]
  2. https://doi.org/10.3888/tmj.23-2   Lehmer defined a measure where the may be either integers or rational numbers in a Machin-like formula for . When the are integers, Lehmer’s measure can be used to determine the computational efficiency of the given Machin-like formula for . However, because the computations are complicated, it is unclear if Lehmer’s measure applies […]
  3. https://doi.org/10.3888/tmj.23-1 This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order […]
  4. https://doi.org/10.3888/tmj.22-5 Structural equational modeling is a very popular statistical technique in the social sciences, as it is very flexible and includes factor analysis, path analysis and others as special cases. While usually done with specialized programs, the same can be achieved in Mathematica, which has the benefit of allowing control of any aspect of the […]
  5. https://doi.org/10.3888/tmj.22-4 A method of generating minimally unsatisfiable conjunctive normal forms is introduced. A conjunctive normal form (CNF) is minimally unsatisfiable if it is unsatisfiable and such that removing any one of its clauses results in a satisfiable CNF. Introduction Ivor Spence [1] introduced a method for producing small unsatisfiable formulas of propositional logic that were […]
  6. https://doi.org/10.3888/tmj.22-3 Given a rationally parameterized curve in or , where the and are polynomials, we find the dimension of the smallest linear subset of containing the curve. If all the and are of degree or less, then it is known abstractly that this dimension is or less and rational normal curves play a key role […]
  7. https://doi.org/10.3888/tmj.22-2 The Wolfram Language has numerous knowledge-based built-in functions to support financial computations. This article introduces many built-in and other financial functions that are based on concepts and models covered in undergraduate-level finance courses. Examples are taken from a wide range of finance areas. They emphasize importing and visualization of data from many sources, valuation, […]
  8. https://doi.org/10.3888/tmj.22-1 The metric structure on a Riemannian or pseudo-Riemannian manifold is entirely determined by its metric tensor, which has a matrix representation in any given chart. Encoded in this metric is the sectional curvature, which is often of interest to mathematical physicists, differential geometers and geometric group theorists alike. In this article, we provide a […]
  9. https://doi.org/10.3888/tmj.21-3 We study the distribution of eigenspectra for operators of the form with self-adjoint boundary conditions on both bounded and unbounded interval domains. With integrable potentials , we explore computational methods for calculating spectral density functions involving cases of discrete and continuous spectra where discrete eigenvalue distributions approach a continuous limit as the domain becomes […]
  10. https://doi.org/10.3888/tmj.21-2 H. S. M. Coxeter wrote several geometry film scripts that were produced between 1965 and 1971 [1]. In 1992, Coxeter gave George Beck mimeographs of two scripts that had not been made. Beck wrote Mathematica code for the stills and animations. This material was added to the third edition of Coxeter’s The Real Projective […]
   

   
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