Paul Breiding

Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances.After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety.This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an openaccess book.

Dr. Paul Braden's world gets completely turned upside down when he learns from an inside source that there will be a horrible, apocalyptic viral pandemic beginning in a matter of days. A genetically-altered virus has mutated and will transform the entire population into hordes of psychotic, blood-thirsty, supercharged killing machines that are hard to stop. When he also learns he is one of the very few immune from this virus, along with his family and closest friends, he goes into action to get this unprepared group ready for the unimaginable. He must convince these people to completely forget about their normal lives and commit to securing the group's survival. How can they possibly do everything they need to do in three days? They must form a plan and find someplace where they can survive what appears to be an epidemic of biblical proportion.How can they get enough food, weapons, and ammunition to save themselves?Where can they go to protect their group from this horrible, blood-thirsty, violent army of monsters and hope to survive?How can they do all this and not let others know what kind of awful things are about to happen in the world?Is Dr. Braden ready for the challenge to lead this group and keep his family safe? Yes.