Successful outcomes for a "Transition Course in Mathematics" have resulted from two unique design features. The first is to run the course as a "survey course" in mathematics, introducing sophomore-level students to a broad set of mathematical fields. In this single mathematics course, undergraduates benefit from an introduction of proof techniques in diverse fields, from abstract algebra and number theory to real analysis and probability. The second is to use one of these fields, mathematical logic, as the foundation upon which to explain the methods of proof. Logic is interesting in its own right as one of the surveyed mathematical fields of study, but it also provides a helpful framework for thinking mathematically, allowing students to progress rapidly to prove results from all the surveyed fields. At one institution, an unexpected benefit that coincided with the establishment of the survey transition course was an increase in the number of majors, fulfilling a long-sought goal for a freshman-sophomore course serving as a "pump" to entice students to become mathematics majors. (Contains 1 figure and 1 table.)