SOAR: Information for New & Potential Mathematics Majors

If you have transfer credits coming in, you should review the math courses that you’ve received transfer credit for and make sure that you are satisfied with the equivalencies. If you are not satisfied with the equivalencies or do not agree with them, the New Student page has information on how to go about requesting a reevaluation.

Because your SOAR date is relatively close to the beginning of the semester, we strongly suggest that you work to get all your materials for a reevaluation as soon as possible so that they can be reevaluated in time for the start of the semester. Course reevaluations may affect your course selection for the upcoming semester (and beyond)!

It would be helpful if you could keep copies of your syllabi and unofficial transcripts on hand, in case they are useful in your meeting with a math major advisor.

If you are missing transfer credits (via AP/IB/college coursework) that should be posted to your student record, please review the New Student page (see the AP Scores, Transfer Credit, Reevaluations & More section) for directions on who to contact to get the credits posted.

Students that are unable to receive credit for MATH 221, 222, and/or 234 for whatever reason (they did not take the AP/IB exams, their transfer credit was not reevaluated as such, they took substantial calculus coursework that can’t be transferred to UW-Madison, etc.) are encouraged to review the Calculus Credit by Examination page. If you feel qualified to do so, you can consider registering for one or more of the exams listed. (Note that you can only take a credit exam for a particular course once, but you are welcome to take the associated exam for multiple courses.)

Students can change their course schedule up until add/drop deadlines after a reevaluation decision has been made, or after a credit exam has been passed.

Regardless of your particular plans and goals, there are three things all majors must accomplish on their way to completing the program: The calculus sequence, a course in linear algebra, and a core intermediate experience.

1. The calculus sequence: the calculus sequence is numbered as MATH 221, 222, and 234. If you have not completed this sequence; if you are awaiting transfer credits; or if you plan on taking the calculus credit exam, we STRONGLY suggest enrolling in a calculus course you qualify for. If/when credits post, we can assist you in updating your enrollment.
2. Linear algebra: students enrolling this coming semester have the following linear algebra options: MATH 320, 340, 341, and 375. 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. Here are some details on each:
   1. MATH 320 is a combined linear algebra and differential equations course. It is suitable for all majors, but might be of particular interest to those interested in applications of mathematics to the physical/biological sciences, engineering, and economics. Its prerequisite is MATH 222.
   2. MATH 340 is a standard course in linear algebra and suited for all majors. It may be of particular interest to those interested in mathematics and computer science, data science, or statistics. Its prerequisite is MATH 222.
   3. MATH 341 is an Honors-level (Accelerated Honors) linear algebra course which also serves as a first course in formal mathematical arguments and proofs. (However, it is open to any student that wants to take it, not just Honors students.) This is regarded as a tougher course than the others due to its theoretical component. We suggest this class to anyone who is interested in an accelerated path through our major curriculum or has some experience in linear algebra already (but no credit for such a class), or has some experience constructing formal mathematical arguments and proofs. The prerequisite for the course is MATH 234. Note: If you have credit for MATH 320 or 340 already then you should not enroll in MATH 341.
   4. MATH 375 is the first half of our MATH 375/376 Honors Calculus sequence, a year-long sequence of two courses–MATH 375 and 376–which serves as a more theoretical and advanced alternative to multi-variable calculus (MATH 234), differential equations (MATH 319), and linear algebra (MATH 341). The goal of these courses is to provide highly motivated and well-prepared students with an opportunity to develop a deeper understanding of these fundamental areas of mathematics. This is a rigorous and challenging sequence and is open to students outside of the Honors Program! Please see our MATH 376/376 page for more information on the sequence, enrollment prerequisites, and the enrollment application form. This course is only taught in fall semesters.
3. Core intermediate course: these courses serve as an introduction to the techniques, vocabulary, and methods of thought of advanced-level undergraduate mathematics. Students have three available options: MATH 321/322, 341, 421, and 467. Here are some details:
   1. 1. MATH 321 is the first course in a two semester sequence (MATH 321-322). Taken together, they explore topics in applied analysis: vector and complex analysis, differential equations, tensor calculus, and so on. This sequence is highly recommended for students interested in mathematics and the natural sciences and engineering. The prerequisite is a course in linear algebra OR a course in differential equations, with MATH 320 preferred.
      2. MATH 341 serves double duty as a linear algebra and a core intermediate course, and is described in the linear algebra courses group above. Note: If you have credit for MATH 320 or 340 already then you should not enroll in MATH 341.
      3. MATH 421 is a review of the essential concepts from single variable calculus and an introduction to formal mathematical arguments and proofs. This is our most popular option of the courses listed since students can rely on their knowledge of calculus and focus on its theory. It also serves as a nice segue into our analysis course (MATH 521). Its prerequisite is MATH 234.
      4. MATH 467 is an option which focuses on an introduction to formal mathematical arguments from the point of view of number theory. This course is a nice introduction to some advanced mathematics outside of calculus and serves as more of an algebra-based introduction to the field. The class is a nice segue into our main algebra course (MATH 541). Note: This course is not offered in Spring 2023, but will be offered Fall 2023.

Here is the suggested enrollment for your first semester based on your credits:

• If you have credit for MATH 221 and 222…
  • Enroll in MATH 234 and one of (MATH 320 or 340).
• If you have credit for MATH 221, 222, and 234:
  • If you are interested in taking MATH 321/322 sequence (or traditional applied mathematics related to physical sciences and/or engineering) then enroll in MATH 320.
    • Consider adding some programming and/or physics to your first term courses.
  • If you are interested in a more general mathematics major then enroll in:
    • MATH 341 (only if you do not already have credit for neither MATH 320 nor MATH 340) or
    • One of (MATH 320 or 340) and one of (MATH 421 or 467).
• If you have credit for MATH 221, 222, 234, and a linear algebra course:
  • If you have credit for MATH 320 then enroll in MATH 321 OR 421 OR 467.
  • If you have credit for MATH 340 then enroll in (MATH 319 and 321) or 421 or 467.
• Finally, if you are interested in enrolling in more math courses than recommended above, or if you have so much transfer credit that the above categories do not apply to you, then make plans to speak with a major advisor (information below in Step 5). This applies particularly if you have had an introduction to writing formal mathematical proofs that transferred as electives. UW-Madison does not offer a standalone introduction to proofs course, but mathematics major advisors can make exceptions to prerequisites for students who have taken such a course.

• Overview: This page gives some broad information about our major programs, and some general differences between our standard major and our named options programs.
• Getting Started: Here you can find information on major program entrance requirements, general major requirements, early major planning, and course restrictions.
• Major Program Options: We offer a number of named options for our major program, which are listed here.
• Honors in the Major: Students who are interested in our Honors in the Major program should refer to this page for some more information.

The New Student page has some detailed information on the Math Department’s enrollment practices. However, there are a few important things to note:

• In general, we strictly enforce prerequisites on all of our math courses, so students are expected to satisfy the prerequisites or place into a course before enrolling in subsequent courses. 
• Students should not contact individual instructors for enrollment permission (unless the course requisite states that you must do so, such as in the case of MATH 473).
• Students that would like to enroll in a waitlisted section of a course should attempt to enroll in an open section of the course if possible. Otherwise, enrolling on the waitlist is the next best route to take. Note that waitlisting for a course does not guarantee enrollment; the only guarantee to enroll in a course is to enroll in an open section. Students are expected to check their emails daily to check if they have been given permission to enroll off of the waitlist, as waitlist permissions do expire after a certain time.

If you are having issues with math course enrollment despite meeting the prerequisites for courses, you can feel free to reach out to the enrollment coordinator, Kyle Martinez (klmartinez@wisc.edu), for some assistance. You should have a PDF copy of your (un)official transcripts on hand just in case it needs to be reviewed.

If you are having trouble with non-math course enrollment, please contact the appropriate department permission contact.

Once you’ve read through the provided materials and attended SOAR, feel free to reach out to Prof. Mitch Keller (mitch.keller@wisc.edu) via email.