Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majorsand other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved.
Content: The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of R^{n}; linear dependence, bases, and dimension; linear transformations; Eigenvalues and Eigenvectors; diagonalization; inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics.
Alternatives: MATH 214, 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. MATH 513 covers more in a much more sophisticated way.
Subsequent Courses: The intended course to follow MATH 217 is MATH 316 (Differential Equations). MATH 217 is also prerequisite for MATH 312 (Applied Modern Algebra), MATH 412 (Introduction to Modern Algebra) and all more advanced courses in mathematics.