Fundamentos Matemáticos de la IA

Resumen

The “Mathematical Foundations of AI” course provides a rigorous introduction to the fundamental mathematical concepts behind many algorithms in machine learning and artificial intelligence, including linear algebra, calculus, and optimization theory. Starting with vectors and matrices, the course covers basic operations and geometric interpretations, matrix transformation and inversion, solving systems of linear equations, matrix factorizations such as diagonalization, singular value decomposition (SVD), and Cholesky decomposition.

The course then introduces calculus-based optimization to identify and classify extrema in both univariate and multivariate functions before handling constrained optimization using Lagrange multipliers and the Karush-Kuhn-Tucker (KKT) conditions. Finally, attention turns to iterative optimization methods, which form the computational basis of many modern machine learning models.

By the end of the course, students will be equipped with the mathematical knowledge needed to understand the foundations of machine learning and AI techniques, providing a solid basis for further study in AI-related fields. Enroll now to build the mathematical foundations you need for a career in AI!

Programa

• Comprender y aplicar operaciones de vectores y matrices
• Utilizar transformaciones de matrices (por ejemplo, eliminación de Gauss) y calcular inversas de matrices para resolver sistemas de ecuaciones lineales
• Aplicar diagonalización, descomposición en valores singulares y descomposición de Cholesky para la reducción de dimensiones y la factorización de matrices
• Aplicar conceptos básicos de cálculo para realizar optimización no restringida en funciones univariadas y multivariadas
• Formular y resolver problemas de optimización con restricciones utilizando multiplicadores de Lagrange y las condiciones de Karush-Kuhn-Tucker (KKT)
• Comprender e implementar algoritmos de optimización iterativos

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Materias

Artificial Intelligence