How to spell the Greek alphabet letters.

A text contained in a 10th century manuscript and that provides a mathematical reason for spelling the Greek alphabet letters in a specific way is published and discussed.

The Von Neumann and Double Slit Paradoxes Lead to a New Schrodinger Wave Mathematics

John von Neumann states a paradox. Why does measuring something disrupt the smooth Schrödinger wave, causing it to collapse for no mathematical reason? This paradox is embedded in the double slit experiment. When a dot appears on the target screen, how does that cause the Schrödinger wave to collapse everywhere else, faster than the speed of light? Von Neumann didn’t follow his mathematics to its logical conclusion. If wave function collapse irreversably changes reality, then the math is telling us that the timing and location of that event cannot be at the target screen. An event fitting that description happens only once: at the gun. A gunshot CAN change history. We propose a new mathematics of Schrödinger waves. Zero energy waves from the target screen pass backwards through the double slits and impinge on the gun prior to the gun firing. A particle randomly chooses one to follow backwards. The particle’s choice of wave is proportional to the amplitude squared of that wave at the gun, determined by the superposition of the two waves moving backwards through the two slits. Why follow a wave of zero energy? Because Schrödinger waves convey amplitudes determining the probability density of that path.

Identificación de procesos matemáticos en la comprensión del concepto de razón en estudiantes universitarios

Resumen: En este artículo se describe y analiza el desarrollo de una experiencia de clasede un curso de cálculo diferencial de primer semestre universitario en la que se abordandistintos conceptos sobre funciones con énfasis en el concepto matemático de razóndesde su aplicación para la resolución de problemas cotidianos. La investigación es denaturaleza cualitativa y se basa en el análisis de los argumentos (verbales o gráficos)dados por los estudiantes en un foro de discusión on line y durante el desarrollo de laclase. Los datos, provienen de grabaciones del episodio de clase y de la interacción enel foro por parte de los estudiantes. Para el análisis de aplicó la técnica de codificaciónteórica, específicamente a la codificación abierta, en la que se identifican los principalesconceptos y sus propiedades contenidos en los datos. Los resultados evidencian algunasdificultades a las que se enfrentan los alumnos en el estudio del cálculo diferencialen relación con concepto de razón, que se considera básico para la comprensión deotras nociones más complejas, como por ejemplo los límites. Las respuestas dadas enla actividad denotan que más allá del manejo algorítmico de las fracciones y de laconversión entre diferentes registros semióticos, como el porcentual o el decimal, noexiste una conciencia suficientemente sólida sobre la naturaleza y aplicabilidad de estoscálculos.Palabras clave: Razón matemática, procesos matemáticos, aprendizaje en el nivel universitario,Enfoque Ontosemiótico (EOS)Abstract: In this article we describe and analyze the development of a class experienceof a course of differential calculus of the first semester of the university in which differentconcepts about functions are approached with emphasis on the mathematical conceptof reason from its application for the resolution of everyday problems. The research isof a qualitative nature and is based on the analysis of the arguments (verbal or graphic)given by the students in an online discussion forum and during the development ofthe class. The data comes from recordings of the class episode and the interactionin the forum by the students. For the analysis, he applied the theoretical coding technique,specifically to open coding, in which the main concepts and their properties containedin the data are identified. The results show some difficulties that students face in thestudy of differential calculus in relation to the concept of reason, which is consideredbasic for the understanding of other more complex notions, such as limits. The answersgiven in the activity denote that beyond the algorithmic management of the fractionsand the conversion between different semiotic registers, such as the percentage or thedecimal, there is not a sufficiently solid awareness about the nature and applicability ofthese calculations.Keywords: mathematical reason, mathematical processes, university-level learning, Ontosemiotic Approach (EOS)

Is There a Correct Stand Density Index? An Alternate Interpretation

Recent authors have asserted that the original form of Reineke's stand density index is flawed, and that an additive version represents the correct form. An examination of the literature provides no historical or mathematical reason why additivity should be required in the original index. Reineke's stand density index, and the additive or area-based stand density index, should be considered as separate indices with different properties. The sensitivity of the area-based index to stand diameter distribution is illustrated with the Weibull distribution. Its sensitivity provides testable hypotheses that could be used in empirical studies to determine the better index. West. J. Appl. For. 18(3):179–184.

RANDOMNESS AND COMPLEXITY IN PURE MATHEMATICS

One normally thinks that everything that is true is true for a reason. I’ve found mathematical truths that are true for no reason at all. These mathematical truths are beyond the power of mathematical reasoning because they are accidental and random. Using software written in Mathematica that runs on an IBM RS/6000 workstation, I constructed a perverse 200-page algebraic equation with a parameter N and 17,000 unknowns: [Formula: see text] For each whole-number value of the parameter N, we ask whether this equation has a finite or an infinite number of whole number solutions. The answers escape the power of mathematical reason because they are completely random and accidental. This work is an extension of the famous results of Gödel and Turing using ideas from a new field called algorithmic information theory.

Infinite non-linear programming

In recent years there has been extensive development in the theory and techniques of mathematical programming in finite spaces. It would be very useful in practice to extend this development to infinite spaces, in order to treat more realistically the problems that arise for example in economic situations involving infinitely divisible processes, and in particular problems involving time as a continuous variable. A more mathematical reason for seeking such generalisation is possibly that of obtaining a unification mathematical programming with other branches of mathematics concerned with extrema, such as the calculus of variations.