MAT provides a document titled the "MAT Graduate Student Handbook" for incoming students. You can download the 2020-2021 version here (PDF).
Forms to complete that list the requirements necessary for a PhD or MSc degree in the MAT Graduate Program are found on the UCSB General Catalog website:
UCSB General Catalog - Media Arts & Techology.
Various other forms and petitions for UCSB graduate students can be found on this page on the Graduate Division's website: