This is a student portfolio (to be) completed as part of the course MATH 76.01: Topics in Applied Mathematics at Dartmouth College in the 2024 Summer Term.
Mathematics and AI offers an exploration of the intersection between mathematics and artificial intelligence (AI). Covering state-of-the-art machine learning techniques and their mathematical foundations, this course aims to provide students with both a broad theoretical understanding and practical skills. The syllabus starts with a brief review of the history of AI, and current limits and issues. This is followed by an introduction to statistical learning in a supervised setting and a deeper dive on neural networks and their applications with some references to current mathematical research. The syllabus continues with an overview of unsupervised learning methods and their applications in feature selection. It concludes with student's presentations of their final projects.
Prerequisite courses and skills: Math 13, Math 22 or Math 24, and Math 23, or advanced placement/ instructor override. Familiarity with at least one programming language. (Python preferred.) Students who request an instructor override should have encountered the concepts in the prerequisite concepts checklist in their previous coursework or self study.
Prerequisite concepts: derivative of a function, chain rule, smooth function, optimization, Taylor expansion, differential equation, fixed point, vector, matrix, lines, curves, subspaces, eigenvector, eigenvalue multivariate function, partial derivative, spherical coordinates, probability distribution, conditional probability, joint probability
Github repository: https://github.com/acuschwarze/mathematics-and-ai/
Canvas: https://canvas.dartmouth.edu/courses/66608/
Webpage: https://math.dartmouth.edu/~m76x24/