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, Calculus III (Math 223) 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 total of 36 credits is required. 15 credits must be from the following mathematics courses:

- Math 223 – Calculus III
- Math 224 – Multivariable Calculus
- Math 300 – Linear Algebra (this course is a prerequisite for most upper-level courses – you want to take it as early as possible!)
- Math 431 – Abstract Algebra I
- Math 471 – Real Analysis I

an additional 3 credits from completion of one 400-level sequence via:

- Math 432 – Abstract Algebra II or Math 472 – Real Analysis II

an additional 6 credits must be at the 400 level with at most 3 credits of Directed Study (491/492)

an additional 9 credits must be at the 300 or 400 level with at most 3 credits of Directed Study (491/492)

a remaining 3 credits may be selected from the following:

- any mathematics course numbered 207 or above (except Math 499*)
- any computer science course numbered 220 or above (except Cpsc 302 and 499)
- any physics course numbered 105 or above (except Phys 108 and 499)
- Philosophy 306 – Advanced Logic

* Note that internship (499) credits in any discipline do not count toward the major.

### Electives

- Math 207 – History of Mathematics
- Math 280 – Statistical Methods
- Math 312 – Differential Equations
- Math 321 – Number Theory
- Math 325 – Discrete Mathematics
- Math 330 – Foundations of Advanced Mathematics
- Math 351,352 – Numerical Analysis
- Math 372 – Modern Geometry
- Math 381,382 – Probability and Statistical Inference
- Math 411 – Chaotic Dynamical Systems
- Math 412 – Complex Variables
- 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

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 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.

Course Offerings

Every semester | Math 201, 207, 223, 224, 300, 312, 431, 432, 471, 472 |

Once per year | Math 280, 321, 325, 330, 351, 352, 381, 382, 412, 441 |

Sporadically | Math 372, 411, 461, 481 |

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 36 credits required for the mathematics degree. However, many students start their college mathematics courses with Math 121, Math 122, and Math 201. These courses are not required for the major, but act as prerequisites for the more advanced courses. 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 Math 200. 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.