Undergraduate Linear Algebra Courses

In order to complete the major in mathematics you must take a course in linear algebra. At UW-Madison we offer several versions of linear algebra. Note that in all versions of the major and certificate, only ONE of the following courses may be used to fulfill any of the requirements. The purpose of this page is to describe the essential differences between the courses.

Math 320 Linear Algebra and Differential Equations

Math 320 covers both some linear algebra and some differential equation theory. As such, students who complete this course can consider themselves as also having some of the content of Math 319 (introduction to differential equations). The difference between this course and taking both 319 and 340 is that one will be able to see how theory and applications unite in a meaningful way. This course also lends itself to the 321-322 applied analysis sequence.

This course is very useful for students interested in the option 2 major focused on traditional applications of mathematics through continuous models. It allows a student to move into intermediate level coursework without having to complete an introduction to differential equations.

Students who have completed Math 320 are STRONGLY encouraged to take either 1) Math 421 or 2) the applied analysis sequence Math 321 and 322 before moving on to the 500 level.

In summary math 320 is:

• Useful for students interested in classical applications of mathematics (i.e., physics, engineering, continuous modeling, etc.)
• Covers material in Math 319 and therefore credit for only one of Math 319 and 320 can be applied to the math major or certificate.
• Not necessarily a good introduction to formal mathematical arguments.
• Good introduction to how theory and applications support each other.
• Is offered with an honors(!) version. This version is suggested for potential math majors and those in the AMEP program.
• Suggested further courses are
  • The applied analysis sequence Math 321 - math 322 which covers more mathematics useful for traditional applications.
  • Dynamical systems Math 415 which includes both continuous and discrete models of changing systems.
  • Theory of Calculus Math 421 for an introduction to more formal mathematical arguments.

Math 340 Elementary Matrix and Linear Algebra

Math 340 a basic linear algebra course which focuses on vectors as ordered sets of real numbers and linear operators as matrices. In this course the focus is typically on computational aspects of the subject with some lighter treatment of the more theoretical points.

Students who complete this course and would also like exposure to differential equations should consider Math 319.

Students who have completed math 340 are STRONGLY encouraged to take Math 421 for an introduction to proofs and proofwriting before moving on to courses above the 500 level.

In summary math 340 is:

• Accepted in both major versions and the certificate.
• Not necessarily a good introduction to proofs and proofwriting.
• Not suggested for majors.
• Ideal for students in other programs who need functional knowledge of basic matrix algebra in particular those looking for applications featuring discrete mathematics (i.e., computer science and possibly statistics).
• Subsequent math courses:
  • Math 421 for those interested in advanced undergradaute math courses above the 500 level.
  • ODE Math 319 for those interested in the applied analysis sequence.

Math 341 Linear Algebra

Math 341 is a linear algebra course which is also meant to be an introduction to proofs and proofwriting. The linear algebra content of the course is more robust than any of the others listed on this page. Students who complete the course should be well prepared to move onto any upper level course, in particular Math 521, 541, or 551.

This course is acceptable to both versions of the major. It is the recommended linear algebra course for most math majors including those in the option 1 path and those in option 2 who may not want to complete the 321-322 sequence.

Students who complete this course and would also like exposure to differential equations should consider Math 319.

In summary math 341 is:

• Accepted in both major versions and the certificate.
• A good introduction to proofs and proofwriting.
• The preferred course for most majors.
• Subsequent courses:
  • Math 421 for another exposure to formal mathematical arguments at the introductory level.
  • Any math course above the 500 level (possibly assuming other prereqs).

Math 375 Topics in Multi-Variable Calculus and Linear Algebra

Math 375 is an Honors course which features the role that linear algebra has in multivariable calculus. Students who have completed Math 234 (Calculus - Functions of Several Variables) may not take this course.

This course is acceptable in both versions of the major.

Students who complete this course are also expected to complete the sequel course: Math 376.

In summary Math 375 is:

• Honors level.
• Not open to students who have completed Math 234.
• Accepted in both major versions and the certificate.
• A good introduction to proofs and proofwriting.