Undergraduate Linear Algebra Courses

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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. The purpose of this page is to describe the functional differences between the courses. This can help you to choose the right course for your current and future interests.

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.

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 completed Math 319 (introduction to differential equations). This course also lends itself to the 321-322 applied analysis sequence.

This course is only available to those who are interested in the option 2 version of the major or certificate. It is very useful in this form of the major since it allows a student to move into intermediate level coursework without having to complete an introduction to differential equations as well.

Students who have completed Math 320 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 320 is:

  • Computational.
  • Nice theory connecting linear algebra and differential equations.
  • Replaces math 319 as an accepted course for the major/certificate.
  • Only acceptable to option 2 majors and the certificate.
  • Not a good introduction to proofs and proofwriting.

Math 340 Elementary Matrix and Linear Algebra

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

This course is accepted in both the option 1 and option 2 form of the major, however in both cases there may be a better choice.

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:

  • Computational.
  • Low theory content.
  • Accepted in both major versions and the certificate.
  • Not a good introduction to proofs and proofwriting.

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. In particular it is the recommended linear algebra course for option 1 students. It is also highly recommended for students 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:

  • Computational.
  • High theory content.
  • Accepted in both major versions and the certificate.
  • A good introduction to proofs and proofwriting.


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 and would also like exposure to differential equations should consider the sequel course: Math 376.

In summary Math 375 is:

  • Computational.
  • High theory content
  • Accepted in both major versions and the certificate.
  • A good introduction to proofs and proofwriting.