This is the first in a two-course sequence (EN.625.805 and EN.625.806) designed for students in the postmaster’s certificate (PMC) program who wish to work with a faculty advisor to conduct significant, original independent research in the field of applied and computational mathematics. (Each course is one semester.) A sequence may be used to fulfill two courses within the course requirements for the PMC; only one sequence may count toward the certificate. For sequence 625.805 and 625.806, the student is to produce a technical paper for submission to a journal or to a conference with accompanied refereed proceedings. The intent of the research is to expand the body of knowledge in the broad area of applied mathematics, with the research leading to professional-quality documentation. Students with a potential interest in pursuing a doctoral degree at JHU, or another university, should consider enrolling in either this sequence or EN.625.807 and EN.625.808 to gain familiarity with the research process. (Doctoral intentions are not a requirement for enrollment.) Course Note(s): The course EN.625.800 Independent Study may not be used towards the ACM PMC if the student also wishes to count EN.625.805–806 towards the PMC. The student must identify a potential research advisor from the Applied and Computational Mathematics Research Faculty to initiate the approval procedure prior to enrollment in the chosen course sequence; enrollment may only occur after approval. Students may only enroll in 625.805 with the clear intention of also enrolling in 625.806; students seeking only a one-semester research project should register for 625.800. A full description of the guidelines (which includes the list of approved ACM research faculty) and the approval form can be found at https://ep.jhu.edu/current-students/student-forms/.