This text is intended for the Foundations of Higher Math bridge coursetaken by prospective math majors following completion of themainstream Calculus sequence, and is designed to help studentsdevelop the abstract mathematical thinking skills necessary forsuccess in later upper-level majors math courses. As lower-levelcourses such as Calculus rely more exclusively on computationalproblems to service students in the sciences and engineering, mathmajors increasingly need clearer guidance and more rigorous practicein proof technique to adequately prepare themselves for the advancedmath curriculum.