Woodstock teaches applied mathematics courses, with an emphasis on how class material is used in everyday life. He specializes in optimization, and how it arises within machine learning tasks. 
His research focuses on two areas, developing new algorithms to solve modern challenges in data science and mathematically proving that these new algorithms are guaranteed to do their job. His work has been used for image reconstruction, audio de-noising and change detection from bitemporal satellite imagery.
 
 A goal of providing these mathematical guarantees is to contribute theoretically-sound alternatives to the theoretically unfounded ad-hoc techniques (e.g., neural network training with ReLU activation and algorithmic differentiation) that are rapidly being adopted in critical infrastructure. 
Woodstock earned a bachelor's degree in mathematics at JMU, a master's degree in applied mathematics at North Carolina State University and a doctorate in mathematics at North Carolina State University. Before joining JMU as faculty, he was a postdoctoral staff scientist at the Interactive Optimization and Learning Laboratory based in Technische Universität Berlin and the Zuse Institute Berlin.