## Synopsis, credit and prerequisites

MATH 4310 is a course on linear algebra with a higher degree of abstraction than in introductory matrix theory and linear algebra courses. Linear algebra is a major component in the foundation of many areas of modern mathematics, and has applications across the social and physical sciences and in engineering. You have seen in calculus how to use the derivative to approximate a differentiable function with a linear one. In linear algebra, we analyze linear functions and study their applications. We will study of vector spaces, linear transformations, matrices, and systems of linear equations. Additional topics may include quadratic forms and inner product spaces, canonical forms for various classes of matrices and linear transformations.

MATH 4310 is a 4–credit course. The course catalogue states that the prerequisite is at least one of

 MATH 2210 — Linear Algebra MATH 2230 — Theoretical Linear Algebra and Calculus MATH 2310 — Linear Algebra with Applications MATH 2940 — Linear Algebra for Engineers.
In addition, students will be expected to be comfortable with proofs.  Prior knowledge of group theory is not a prerequisite.

If you have not satisfied the prerequisite, seek permission of the instructor to take the course.

The three other courses offered this semester that satisfy the Mathematics Major Algebra requirement are MATH 3320, MATH 4315, and MATH 4330. If this is your first time taking an algebra course at the 3000- or 4000-level, you may find MATH 3320 an easier transition to the upper-level algebra courses.  MATH 4315 and MATH 4330 both have forbidden overlap with MATH 4310.  MATH 4315 may be a better option for Math minors or students who will only take one algebra course: it will discuss some linear algebra, and some topics in the direction of algebraic geometry.  MATH 4330 is a much faster-paced and more theoretical treatment of advanced linear algebra.

Undergraduates who plan to attend graduate school in mathematics should consider taking higher level courses such as MATH 4330 instead of MATH 4310. Students may not receive credit for both MATH 4310 and MATH 4330.