Mathematica Journal

• Selected Financial Applications

  This article shows how to use some of Mathematica’s built-in financial functions and define new functions useful for the practical analysis of real-world financial data. The main topics covered are linear programming and its application in bond portfolio management, conditional value-at-risk minimization, introductory time-series analysis, simulation, bootstrapping, robust equity portfolio optimization and artificial intelligence. 1. […]

• Mixing Numbers and Unfriendly Colorings of Graphs

  https://doi.org/10.3888/tmj.23-4   Mathematica has many built-in functions for doing research in graph theory. Formerly it was necessary to load the Combinatorica package to access these functions; most are now available within Mathematica itself. This article studies a problem concerning the vertex coloring of graphs using Mathematica by introducing some user-defined functions. Unfriendly Colorings of Graphs […]

• Numerical Contour Integration

  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 […]

• Unconditional Applicability of Lehmer’s Measure to the Two-Term Machin-like Formula for π

  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 […]

• Coverage versus Confidence

  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 […]

• Structural Equation Modeling

  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 […]

• Generating Minimally Unsatisfiable Conjunctive Normal Forms

  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 […]

• Degree versus Dimension for Rational Parametric Curves

  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 […]

• Foundations of Computational Finance

  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, […]

• Sectional Curvature in Riemannian Manifolds

  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 […]