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Author: FRANCISCO JULIAN ARIZA HERNANDEZ

Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept.

FLOR MONSERRAT RODRIGUEZ VASQUEZ FRANCISCO JULIAN ARIZA HERNANDEZ (2021)

The evaluation of learning in mathematics is a worldwide problem, therefore, new methods are required to assess the understanding of mathematical concepts. In this paper, we propose to use the Item Response Theory to analyze the understanding level of undergraduate students about the real function mathematical concept. The Bayesian approach was used to make inferences about the parameters of interest. We designed a test containing twelve items, to which a reliability analysis and validation test were applied. The experiment consisted in administer our test to 48 undergraduate students (18-20 years old) who are in a math career. We concluded that 25% of the students reached a high level of understanding, 39.6% a medium level of understanding and, 35.4% a low level of understanding.

Article

understanding assessment Mathematics education IRT model validation test HUMANIDADES Y CIENCIAS DE LA CONDUCTA PEDAGOGÍA TEORÍA Y MÉTODOS EDUCATIVOS

Stochastic black-scholes equation with time-fractional derivative on the half-line

Jorge Sánchez Ortiz Martin Patricio Arciga Alejandre Francisco Julian Ariza Hernandez Juan Carlos Hernández Pastrana (2016)

We investigate the pricing of options using a modified Black-Scholes equation with a time-fractional derivative and additive white noise on the half-line. We construct the Green function for the initial-boundary value problem adapting the main ideas of the Fokas method and we prove existence and uniqueness of solutions.

Article

Black-scholes Fokas method Caputo fractional derivative Mittag-Le¿efunction CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS

Bayesian analysis for a fractional population growth model

Francisco Julian Ariza Hernandez Jorge Sánchez Ortiz Martin Patricio Arciga Alejandre Luis Xavier Vivas Cruz (2017)

We implement the Bayesian statistical inversion theory to obtain the solution for an inverse problem of growth data, using a fractional population growth model. We estimate the parameters in the model and we make a comparison between this model and an exponential one, based on an approximation of Bayes factor. A simulation study is carried out to show the performance of the estimators and the Bayes factor. Finally, we present a real data example to illustrate the effectiveness of the method proposed here and the pertinence of using a fractional model.

Article

CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS