Major Requirements

Note: The major requirements outlined in this handbook are accurate for students declared in the Fall 2019 catalog.
Always remember: your major requirements are dictated by the semester in which you declare your major, not the semester in which you entered UMW. Keep this in mind as you read the requirements for any major on campus.

Other than prerequisite restrictions, there are no set-in-stone rules regarding the order in which the more advanced mathematics courses must be taken. There is, however, a standard track of courses leading to these upper-level classes.
Your highest priority is to complete the first two calculus courses as well as MATH 201 or CPSC 284 in your first year at UMW. Many students earn credit for MATH 121 through Advanced Placement, International Baccalaureate, or Cambridge Exams, and therefore start with MATH 122, the second course in calculus. While this is a nice head start, this is not necessary for completing the mathematics degree in four years. As long as you can complete MATH 121, 122, and either 201 or CPSC 284 in the first three semesters, there will be time to finish the degree on schedule. The advice to finish in two semesters would only give you more wiggle room later.
The major in mathematics requires a total of 38 credits, 20 of which must be from the following seven core classes:

• MATH 122: Calculus II (4 credits)
• MATH 224: Multivariable Calculus (4 credits)
• MATH 300: Linear Algebra
• MATH 330: Foundations of Advanced Mathematics
• MATH 431: Abstract Algebra I
• MATH 471: Real Analysis I.

Linear Algebra is a prerequisite for most upper-level courses, so this course should be taken as early as possible; most students take it in their second year. Furthermore, MATH 201 or CPSC 284 is a prerequisite for MATH 300, which is why we suggest you complete it in your first year. MATH 330 is a prerequisite to some upper-level theory courses, some of which are actually required in the degree (MATH 431 and 471). We advise students to take MATH 330 in their sophomore or early-junior year to prepare for these upper-level courses.
Three additional credits must be used to complete a 400-level course sequence. You may meet this requirement by taking one of MATH 432 (Abstract Algebra II) or MATH 472 (Real Analysis II). You may, of course, complete both sequences in algebra and analysis, applying the additional credits to the electives category in the major (described next).
In addition to the sequence requirement, there are 12 credits of upper-level electives required for the mathematics degree. Here you have quite a bit of freedom to choose the courses that interest you the most (internship credits in any discipline do not count toward the major). You may even count up to two independent studies (MATH 491) toward the major in this category. These 12 credits of electives must satisfy the following rules:

• three credits must be at the 400 level, and
• nine credits must be at the 300 or 400 level.

In other words, of these 12 elective credits, at least three of them must be at the 400 level.
So far we have 35 credits accounted for out of the 38 required. The remaining three credits may be earned from any of the following:

• any mathematics course (MATH) numbered 207 or above,
• any computer science course (CPSC) numbered 220 or above (with the exception of CPCS 284 and CPSC 302), or
• any physics course (PHYS) numbered 105 or above (with the exception of PHYS 108).

Note: You may use at most 6 credits of MATH 491/492 towards the major.
You have many options in completing the major electives. You should choose courses that best suit your current academic interests as well as your long-term career goals. Those students interested in working in the private sector are strongly encouraged to pursue courses in applied mathematics and statistics. This includes courses such as Differential Equations, Numerical Analysis, Probability and Statistical Inference, and Chaotic Dynamical Systems.

Students interested in graduate work in mathematics should strongly consider taking Topology and Complex Variables. Finally, students in the UMW Teaching Education Program seeking certification to teach mathematics in grades six through 12 must also take Number Theory (MATH 321) and Modern Geometry (MATH 372). Otherwise, you should take the electives that most intrigue you—any exposure you can gain will benefit you in the long run.
Finally, all math majors must meet the department’s computer programming requirement. We currently have five courses that meet this requirement: MATH 351, 421, and CPSC 110, 219, and 220. If you choose wisely, this course need not be an “additional” class you have to take: if the course you take for the programming requirement is also applicable to the major, you may use it twice. For instance, if you took MATH 351 you could count it toward your 300-level MATH elective requirement in the major, but it would also complete your programming requirement.
We offer a wide range of courses with differing demands and audiences, and as a result not all courses run with the same frequency. You must keep this in mind as you are mapping out your path to graduation. Many of our courses are offered on a regular and predictable basis, and these are described in the table below. However, bear in mind that even this is not 100% certain and offerings may change depending on departmental resource and scheduling issues. When in doubt, contact the department chair.

Course Offerings

Every semester MATH 122, 201, 207, 224, 300, 312, 330, 431, 432, 471
Once per year MATH 253, 321, 472, STAT 280
Alternating years MATH 351–352, STAT 381–382
Sporadically MATH 325, 372, 411, 412, 421, 441, 481, STAT 320,420, MATH/STAT 361, 461

On a final note, there is a limit on the number of credits in any one discipline you may count towards graduation. This cap of 60 credits should be kept in mind when planning for graduation. For example, there are 38 credits required for the mathematics degree. However, many students start their college mathematics studies with MATH 121, which is not in the major, though it counts as a MATH class in the 60-credit cap. Therefore, many students accumulate 41 credits in mathematics when working toward their degree. Moreover, some mathematics majors also take non-required courses such as MATH 115 or STAT 180. Adding in an independent study your senior year brings your total very close to the credit limit. In summary, think ahead, plan carefully, and talk to your advisor.