Department of Mathematical Sciences

The courses for this degree program are offered on campus at Appalachian during the regular academic year. Students are expected to enroll full time in the program; assistantships are available. In exceptional circumstances, students may enroll part-time. Schedule of Planned Graduate Courses

MAT 5610 Analysis I and MAT 5620 Analysis II (6): A sequence in analysis designed to further ground the students in the fundamentals of theory of functions and the calculus

MAT 5860 Mathematical Statistics I and MAT 5865 Mathematical Statistics II (6): A sequence in statistics designed to deepen students understanding of statistical concepts and theory related to topics covered in statistical methods courses

MAT 5415 Seminar in the Pedagogy of Mathematics (3): A one hour seminar in which topics from mathematics and pedagogy are examined, such as research methods, recent advances in mathematics, alternative learning styles, teaching developmental and adult students, and teaching with technology. Students take the seminar for one credit each of three semesters.

MAT 5420 Teaching Apprenticeship (3): An apprenticeship designed to provide a supervised experience in college teaching through direct participation in a classroom situation. Each student will work closely with a faculty mentor teaching an undergraduate course and will be actively engaged in the development of activities and assignments. Students will participate in the apprenticeship three times in different teaching situations.

MAT 5125 History of Mathematics (3): The history of various mathematical concepts is examined, with particular attention paid to topics from geometry, algebra, calculus, linear algebra, differential equations and statistics.

MAT 5210 Abstract Algebra (3): A study of group theory including quotient groups, the fundamental theorem of finite Abelian groups, and the Sylow Theorems. Includes an introduction to rings with emphasis on Euclidean rings and other principal ideal domains.

MAT 5230 Linear Algebra (3): A study of finite dimensional vector spaces. Among the topics covered are matrices, linear transformations, change of basis, eigenvalues, canonical forms, quadratic forms and quasi-inverses.

MAT 5330 Mathematical Models (3): A problems oriented course. The student uses mathematics to model a number of different situations. Among the tools used will be statistics, linear programming, differential equations, and computer simulation.

MAT 5370 Advanced Differential Equations (3) Usual topics include: power series solutions; special functions; methods and theory of systems; existence and uniqueness theorems and continuations of solutions; Sturm theory; nonlinear differential equations; numerical methods.

Students will work with their advisors to determine the appropriate electives. Students may, with permission, take up to 3 hours outside of mathematical sciences. Students interested in community college teaching may consider taking LHE 5440, LHE 5630 or LHE 5890. Students should receive approval prior to enrolling in any elective courses.

LHE 5900 Higher Education Internship (3) and MAT 5600 Directed Research in the Mathematical Sciences (3): This track is for students who wish to pursue immediate entry into teaching at the community college level. Students will teach at a college and will work on a capstone project.

OR

MAT 5600 Directed Research in the Mathematical Sciences (3) and 3 additional hours in mathematical sciences: This track is for students who wish to broaden their mathematics background, taking an additional course in mathematics or statistics and completing a capstone projects.

OR

MAT 5999 Thesis (6): This track is for students who wish to pursue an area of mathematics or statistics in more depth, completing a thesis. Students interested in pursuing additional advanced study in mathematics are encouraged to choose this track.

Demonstrated proficiency in use of technology, subject to the approval of the academic graduate committee in mathematics.