Mathematics for Ai

This course equips students with essential mathematical foundations for understanding and working with artificial intelligence (AI) algorithms. After a brief introduction to the historical and social context that numbers arise in, students will learn about: - Linear Algebra: Matrices, matrix-vector multiplication, linear models, change of basis, dimensionality, spectral decomposition, and principal component analysis (PCA). - Calculus: Rates of change, derivatives, optimization techniques like gradient descent, with a brief touch upon linear approximation. - Probability and Statistics: Mathematically deriving complex probability distributions out of simpler ones, mathematically deriving statistical testing methods - Graph Theory: How graphs are used to find relationships between data as well as being a setting for AI-driven problem solving. - Problem Solving and Algorithms: Applying mathematical concepts to find problem solutions. Students will learn about search methods like uninformed search, informed search with the A* algorithm, and greedy algorithms. - Computational Theory and Automata: Answering questions about what is computable, what is needed in order to compute something, and using this framework to state how much “information” is contained in a mathematical object. By the end of this course, students will possess a strong mathematical toolkit to confidently tackle the complexities of modern AI algorithms.