Linear Algebra Courses

MATH 320 (Differential Equations and Linear Algebra)

Differential equations and linear algebra are crucial for the analysis and control of many dynamical systems such as electrical networks, mechanical structures, chemical and biological networks. Those applications lead to often very large systems of coupled differential equations. The study of the equilibria, stability and control of such systems requires the concepts and tools of differential equations and linear algebra. MATH 320 is a first course in the study of differential equations and linear algebra. As such, students who complete this course can consider themselves as having some of the content of MATH 319 (Techniques in Ordinary Differential Equations) and some of the content of MATH 340 (Elementary Matrix and Linear Algebra). This course lends itself to the MATH 321-322 applied analysis sequence.

Students who have completed MATH 320 will need to complete one of MATH 421; the applied analysis sequence MATH 321-322; or MATH 467 before moving on to 500-level courses that require introductory proofs coursework.

In summary, MATH 320...

• Is useful for students interested in classical applications of mathematics (e.g., physics, engineering, continuous modeling, etc.);
• Covers material in MATH 319 and therefore credit for only one of MATH 319 or 320 can be applied to the math major or certificate;
• Covers material in MATH 340 and therefore credit for only one of MATH 320 or 340 can be applied to the math major or certificate;
• Covers material in MATH 341 and therefore credit for only one of MATH 320 or 341 can be applied to the math major or certificate;
• Covers material in MATH 375 and therefore credit for only one of MATH 320 or 375 can be applied to the math major or certificate;
• Covers material in MATH 376 and therefore credit for only one of MATH 320 or 376 can be applied to the math major or certificate;
• Is not by itself sufficient for taking advanced math courses;
• Is offered with an Accelerated Honors (!) version in some semesters. This version is suggested for students in the AMEP program.

Suggested further courses are...

• The applied analysis sequence MATH 321-322, which covers more mathematics useful for traditional applications;
• MATH 415, which includes both continuous and discrete models of changing systems;
• MATH 421 for an introduction to more formal mathematical arguments; or
• MATH 443 for further study of linear algebra in an applied context.

MATH 340 (Elementary Matrix and Linear Algebra)

MATH 340 is a first course in linear algebra. Linear algebra is of foundational importance to mathematics, computer science, and data science. It also plays an important role in physics and engineering. This course focuses on vectors as ordered sets of real numbers, systems of linear equations, and the fundamental idea of representing linear functions that map vectors of one dimension to vectors of another dimension using matrices. In this course, the emphasis 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 an introduction to differential equations should consider MATH 319.

Students who have completed MATH 340 will need to complete one of MATH 421; the applied analysis sequence MATH 321-322; or MATH 467 before moving on to 500-level courses that require introductory proofs coursework.

In summary, MATH 340…

• Is ideal for students who need comprehensive functional knowledge of basic matrix algebra, and in particular those looking for applications featuring discrete mathematics (i.e., computer science, data science, statistics, and industrial and systems engineering);
• Is not by itself sufficient for enrollment in advanced math courses;
• Covers material in MATH 320 and therefore credit for only one of MATH 320 or 340 can be applied to the math major or certificate;
• Covers material in MATH 341 and therefore credit for only one of MATH 340 or 341 can be applied to the math major or certificate;
• Covers material in MATH 375 and therefore credit for only one of MATH 340 or 375 can be applied to the math major or certificate.

Suggested further courses are…

• MATH 319 for those interested in the applied analysis sequence;
• MATH 421 for those interested in advanced undergraduate math courses above the 500-level; or
• MATH 443 for those interested in seeing further applied aspects of linear algebra.

MATH 341 (Linear Algebra)

MATH 341 is a linear algebra course which is also meant to be an introduction to proofs and proof-writing. The linear algebra content of this course is comparable to that in MATH 340, but at a more accelerated pace because of the devotion of time to proofs and writing proofs. Students who complete the course should be well-prepared to move on to any upper-level course, in particular MATH 521, 541, or 551.

It is the recommended linear algebra course for majors interested in moving to advanced undergraduate courses quickly. Students who prefer to separate their introduction to linear algebra from their introduction to proof should consider MATH 340 for linear algebra and MATH 421 or MATH 467 for introduction to proof.

Due to the more intensive proof-writing nature of the course, students will probably find the course more demanding than MATH 340, and for this reason MATH 341 carries the Accelerated Honors (!) label.

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

In summary, MATH 341...

• Is Honors-level;
• Is accepted in both the major and certificate programs;
• Is a good introduction to proofs and proof-writing;
• Covers material in MATH 320 and therefore credit for only one of MATH 320 or 341 can be applied to the math major or certificate;
• Covers material in MATH 340 and therefore credit for only one of MATH 340 or 341 can be applied to the math major or certificate;
• Covers material in MATH 375 and therefore credit for only one of MATH 341 or 375 can be applied to the math major or certificate;
• Will give students access to advanced-level undergraduate math courses.

Suggested further courses are...

• MATH 421 for another exposure to formal mathematical arguments at the introductory-level;
• Any math course above the 500-level (possibly assuming other prerequisites).

MATH 375 (Topics in Multi-Variable Calculus and Linear Algebra)

MATH 375 is an Accelerated Honors (!) course which features the role that linear algebra has in multivariable calculus. It also provides students with an introduction to proofs and proof-writing. In terms of subsequent coursework, MATH 375 generally fulfills any prerequisite that includes MATH 341.

It is assumed that students who complete this course will move on to complete the sequel course, MATH 376. (Students who complete MATH 375 and not MATH 376 are not considered to have completed the content of MATH 234! By enrolling in MATH 375 in the fall, students should be prepared to enroll in MATH 376 in the spring. Otherwise, they will need to enroll in MATH 234 in order to complete multivariate calculus.)

In summary, MATH 375:

• Is Honors-level;
• Enrollment is by permission only;
• Is accepted in both the major and certificate programs;
• Is not a course you can take if you have credit for one or more of MATH 234, 319, 320, 340, or 341;
• Is a good introduction to proofs and proof-writing;
• Covers material in MATH 320 and therefore credit for only one of MATH 320 or 375 can be applied to the math major or certificate;
• Covers material in MATH 340 and therefore credit for only one of MATH 340 or 375 can be applied to the math major or certificate;
• Covers material in MATH 341 and therefore credit for only one of MATH 341 or 375 can be applied to the math major or certificate;
• Will give students access to a number of advanced-level undergraduate math courses, although some may also require MATH 376.

More information on the MATH 375/376 sequence can be found on our Honors calculus page.