This is the first in a two-course sequence (EN.625.807 and EN.625.808) 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 towards the certificate. For sequence 625.807 and 625.808, the student is to produce a bound hard-copy thesis for submission to the JHU library and an electronic version of the thesis based on standards posted at https://www.library.jhu.edu/library-services/electronic-theses-dissertations/. (The student is also encouraged to write a technical paper for publication based on the thesis.) 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.625.805 and EN.625.806 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.625.807–808 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 625.807 with the clear intention of also enrolling in 625.808; 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/.