Burger has written and appeared in hundreds of educational videos, including the 24-lecture video series, "Zero to Infinity: A History of Numbers" and "An Introduction to Number Theory" in "The Great Courses" series through The Teaching Company. He also is the author or co-author of more than 30 research articles and 21 books and CD-ROM texts.
Burger's research interests include algebraic number theory, Diophantine analysis, geometry of numbers, and the theory of continued fractions. He teaches abstract algebra, the art of creating mathematics and Diophantine analysis. His work on fostering and teaching creativity has been recognized in a variety of ways. He is currently a Member of the Board of The Thomas S. Kenan Institute for the Arts at the University of North Carolina School of the Arts.