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 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. In this event, Multivariable Calculus (MATH 224, the last course in calculus) should be taken in the first year. The basic rule of thumb is that you want to complete the four-course calculus sequence as soon as possible, and most students do so by the end of their sophomore year.
Mathematics Major Requirements
A minimum of 41 credits are required. Twenty-six (26) credits must be from the following mathematics courses: MATH 122, 201, 224, 300, 330, 431, 471, and either 432 or 472. An additional 12 credits must be from MATH or STAT courses at the 300- or 400-level, with at least three of these credits from 400-level MATH or STAT courses. Three additional credits must be from: MATH or STAT courses numbered 207 or above; computer science courses numbered 220 or above (except CPSC 302); physics courses numbered 105 or above (except PHYS 108); PHIL 306. Mathematics majors must meet the department’s computer programming requirement by taking one of the following courses: MATH 351, MATH 421, CPSC 110, CPSC 219, CPSC 220. Courses used to satisfy the programming requirement may also be used elsewhere in the major. At most six credits of directed study (MATH or STAT 491/492) will count for the major. No internship (MATH or STAT 499) credits will count for the major.
See below for further information:
A total of 41 credits is required. 26 credits must be from the following mathematics courses:
- MATH 122 (4 cr.) – Calculus II
- MATH 201 (3 cr.) – Introduction to Discrete Mathematics
- MATH 224 (4 cr.) – Multivariable Calculus
- MATH 300 (3 cr.) – Linear Algebra (this course is a prerequisite for most upper-level courses – you want to take it as early as possible!)
- MATH 330 (3 cr.) – Foundations of Advanced Mathematics
- MATH 431 (3 cr.) – Abstract Algebra I
- MATH 471 (3 cr.) – Real Analysis I
- Either MATH 432 (3 cr.) – Abstract Algebra II or MATH 472 (3 cr.) – Real Analysis II
An additional 12 credits must be from MATH or STAT courses at the 300- or 400-level, with at least three of these credits from 400-level MATH or STAT courses.
Three additional credits must be from: MATH or STAT courses numbered 207 or above; computer science courses numbered 220 or above (except CPSC 302); physics courses numbered 105 or above (except PHYS 108); PHIL 306.
Mathematics majors must meet the department’s computer programming requirement by taking one of the following courses: MATH 351, MATH 421, CPSC 110, CPSC 219, CPSC 220. Courses used to satisfy the programming requirement may also be used elsewhere in the major.
Note that at most six credits of directed study (MATH or STAT 491/492) will count for the major and that no internship (MATH or STAT 499) credits will count for the major.
- MATH 207 – History of Mathematics
- MATH 312 – Differential Equations
- MATH 321 – Number Theory
- MATH 325 – Discrete Mathematics
- MATH 351,352 – Numerical Analysis I,II (satisfying the programming requirement)
- MATH 361 – Topics in Mathematics
- MATH 372 – Modern Geometry
- MATH 411 – Chaotic Dynamical Systems
- MATH 412 – Complex Variables
- MATH 421 – Applied Partial Differential Equations (satisfying the programming requirement)
- MATH 432 – Abstract Algebra II
- MATH 441 – Topology
- MATH 461 – Topics in Mathematics
- MATH 472 – Real Analysis II
- MATH 481 – Theory of Interest
- MATH 491/492 – Directed Study
- STAT 280 – Statistical Methods
- STAT 320 – Applied Regression Analysis
- STAT 361 – Topics in Statistics
- STAT 381,382 – Probability and Statistical Inference
- STAT 461 – Topics in Statistics
- STAT 491/492 – Directed Study
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 I,II, 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 6 through 12 must also take 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.
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.
|Every semester||MATH 122, 201, 207, 224, 300, 312, 330, 431, 432|
|Once per year||MATH 321, 471, 472; STAT 280|
|Alternating years||MATH 351-352, STAT 381-382|
|Sporadically||MATH 325, 372, 411, 412, 421, 441, 481, STAT 320, MATH/STAT 361, 461|
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 (note that the cap of 60 credits for mathematics majors does not include the number of credits from STAT courses; and, so, math majors can pursue more statistics credentials without any potential violations of the 60-credit discipline cap). For example, there are 41 credits required for the mathematics degree. However, many students start their college mathematics courses with MATH 121. This course is not required for the major, but acts as the prerequisite for MATH 122. Therefore, many students accumulate 45 credits in mathematics when working toward their degree. Moreover, many 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.
On a final note, majors are encouraged to fulfill the general education experiential learning requirement by completing URES 197, MATH 361, MATH 491, MATH 492, or MATH 499. Alternatively, majors may meet this requirement by participating in an approved supervised on-campus or off-campus experiential learning activity developed in consultation with the department (such as the UMW Summer Research Program or a similar program at another college or university). To complete the experiential learning requirement through a summer research experience, contact the department chair for more details.