Author: Kutlimuratov, Ravshanbek Rozboyevich; Ismailov, Asqar Jaxangirovich

Annotation: Five core directions of applied mathematics were identified: mathematical modeling; numerical methods and computational mathematics; probabilistic and statistical approaches; optimization and data analysis; and hybrid methods combining mathematical and artificial intelligence models. The analysis indicates that increased computing power, big data, and parallel computing are accelerating the integration of these directions. The scientific and practical value of applied mathematics depends not only on model accuracy but also on data quality, algorithmic stability, computational efficiency, and interpretability. Future research should strengthen model verification, uncertainty assessment, and criteria for interdisciplinary implementation.

Keywords: applied mathematics, mathematical modeling, numerical methods, optimization, stochastic processes, data analysis, parallel computing, artificial intelligence, hybrid models.

Pages in journal: 584 - 589