Mathematical and Statistical Foundations for AI
Description
Essential mathematical concepts including linear algebra, calculus, probability, and statistics that form the backbone of AI algorithms and models.
Learning Objectives
Learners will master fundamental mathematical concepts including linear algebra operations, calculus for optimization, probability distributions, statistical inference, and mathematical modeling techniques essential for understanding and implementing AI algorithms.
Topics (8)
Discrete mathematics concepts including graph theory, trees, combinatorics, logic, and set theory that are fundamental to AI algorithm design and computational complexity analysis.
Comprehensive coverage of linear algebra concepts specifically applied to AI, including vector spaces, matrix operations, decompositions, and transformations used in data representation and model computations.
Study of calculus fundamentals including derivatives, gradients, chain rule, and optimization techniques such as gradient descent that are crucial for training AI models.
Comprehensive study of probability concepts including discrete and continuous distributions, conditional probability, independence, and probabilistic inference methods used in AI systems.
Statistical methods including descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and statistical modeling techniques used in AI data analysis.
Study of information theory concepts including entropy, mutual information, Kullback-Leibler divergence, and their applications in AI for feature selection and uncertainty quantification.
Numerical methods for solving mathematical problems computationally, including numerical integration, differentiation, linear system solving, and optimization algorithms used in AI implementations.
Mathematical modeling techniques for representing complex systems and simulation methods for testing and validating AI models before deployment in real-world scenarios.