Date of Award


Document Type


Degree Name

Master of Arts in Mathematics



First Reader/Committee Chair

Dr. Jeffrey Meyer


Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented in practice: image classification, text classification, or face recognition. We start by introducing the process of classification in a mathematical framework, then we interpret the algorithm of SVM using linear algebra, analysis, statistics, and topology. We will prove that SVM is a reliable technique using Lagrange multipliers, inner product spaces, metrics spaces, Slater’s theorem, and the kernel trick.