ibl logo  

Mathematics Department - University of Michigan


MATH 217: Linear Algebra & Introduction to Proofs

Content: This course provides a rigorous introduction to linear algebra, as well as an introduction to reading and writing mathematical proofs. It is intended for potential math majors and those interested in theoretical mathematics, and is taught using IBL methods in an interactive classroom. Topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and their subspaces; geometry of Rn linear dependence; bases, dimension, and coordinates; linear transformations; eigenvalues and eigenvectors; diagonalization; inner products and orthogonality. We study not only these concepts and their applications, but also methods of proof and the written communication of mathematics. Students should leave this course prepared to use linear algebra as well as to succeed in further theoretical courses in mathematics.

Prerequisites: Math 215, 255, or 285. Incoming students are not expected to have experience writing proofs, but should have some interest in theory and abstract concepts; those who are more interested in computation, concrete problems, and applications should consider alternative courses such as Math 214 or 417.

Structure: Students learn both content and proof-writing through collaborative in-class problem sessions, instructor coaching, and opportunities for individualized peer-tutoring outside of class. Students are encouraged to write notes, scratch work, and solutions to problems on the dry-erase boards in our classrooms for their peers and instructor to view, question, and discuss. A typical class may consist of a short introductory lecture, a challenging and sometimes open-ended problem set to be worked collaboratively in groups for the majority of the session, and a brief summary of material or explanation of solutions at the end. Grades are determined by in-class quizzes, weekly written homework sets, frequent short web assignments, two midterm exams, and a final exam.

Materials: We have developed materials for the course. Please contact Ralf Spatzier (spatzier@umich.edu) for more information.

Math 351 - Linear Algebra & Introduction to Proofs (link to the "Courses" page)