Mathematics Department

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Please note that this page has not been updated to show the new course Math 215/216.

This section describes the major in mathematics and gives suggestions for choosing elective courses to complement the required ones. It also describes the two options for completing a minor in mathematics and has information that should be useful for anyone who wishes to choose a post-calculus mathematics course. Faculty members in the Department can provide additional details or suggestions.


Requirements for the major

Number of courses.

At least eight units are required for the mathematics major, with at least seven units at the 200- or 300-level. Depending on your future plans, it's often a good idea to take more than the minimum number required.

Required courses

These courses must be completed for the mathematics major. Course descriptions

Major Presentation Requirement

Majors are required to present one classroom talk in either their junior or senior year, usually in one of the courses specially designated as fulfilling this requirement. Usually two such courses are designated each semester. In addition, a limited number of students may be able to fulfill the presentation requirement in other courses. Students need to speak with individual instructors to find out what is possible in a given course.

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Requirements for the minor

The mathematics minor is a good choice when you enjoy learning mathematics and/or think it will be useful to you in your career but your primary interests are in another area. There are two routes to the minor. Each requires 5 courses. Option I specifies a 300-level course and permits one 100-level course to be counted, while Option II has no 300-level requirement but does not count any 100-level courses. Course descriptions

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Honors program

The department offers two options for earning honors: (1) completion of 302, 305, and four 300-level courses, and two written comprehensive examinations or (2) two semesters of thesis work (360 and 370). An oral examination is required for both programs.

Double majors and minors

If you are combining a major or minor in mathematics with one in another department, your advisors in the two departments can help you choose courses that will complement your studies in the other one. You can find some specific suggestions in the following section on planning courses, especially in the course-selection guidelines that follow the course map below.


Planning your required and elective courses

Plan ahead to fulfill the requirements. It's best to complete by the end of your sophomore year 206 or 225 or 214 (i.e. to complete at least one of the three "proof courses" that give entry into 302/305). Take enough courses by the end of your junior year so that you will have several options as a senior. Some 300-level required courses are taught once a year rather than each semester, so you'll need to take that into account when you plan. Moreover, some 300-level electives are taught only every other year. If you are thinking of graduate school, or if you would like to department honors by exam, realize that you will need to take several more courses than are required for the major.

Different pathways through the major/minor

Students often wonder what course they should take next. Generally speaking, there is no single answer, especially after one has completed the basis calculus courses. Whether one just wants to take some math courses, or instead would like to major or minor in mathematics, there are many possible pathways one can take through the array of possible courses. We hope the following course maps will help you visualize the possibilities. As you study these maps, you may wish to consult our "user-friendly" course descriptions. Some course-selection guidelines follow the maps.

Click here for printer-friendly version of course map A.
The map will be displayed in a new window.

A. Courses with at most 100-level prerequisites.

[lower level course map]


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Click here for printer-friendly version of course map B.
The map will be displayed in a new window.

B. Courses with 200-level prerequisites.

 

upper level course map



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Elective courses

It's a good idea to choose your electives according to what you find most interesting and according to your goals. It's also good to take electives that will give you experience in different areas of mathematics, and to take courses from a variety of instructors. Each of us has his or her own perspective on mathematics.

In addition to the courses mentioned below, courses given on changing topics (249, 251, 349) and individual or thesis work (350, 360, 370) offer other ways to complete or extend a mathematics major. You may also wish to take a course at MIT. Remember that at least one of your electives must be at the 300-level.

 

Some guidelines for choosing courses

Here are some suggestions to consider as you choose courses. It is always a good idea to consult with a faculty member, as well. Course descriptions

If you are especially interested in theory in mathematics:
These courses focus on theorems (some concrete, some more abstract) that introduce you to various branches of mathematics: 206, 208, 214, 223, 225, and most 300-level courses. Depending on the topic, you should also consider 249, 348, and 349. The courses may also include applications of these theorems within mathematics or to other fields.

If you are especially interested in applications of mathematics:
These courses focus on mathematical topics and their applications to other fields or within mathematics itself: 210, 212, 220, 251. Depending on the topic, you should also consider 249 and 349. In addition to techniques, the courses usually include some of the theory on which the applications are based.

If you liked calculus or some aspect of calculus:
If you liked the way in which calculus can be applied to understand or model the real world, you'll probably like 210, 212, 220, Partial Differential Equations (a recurring 251 topic), and 307 Knot Theory. If you want to know more about the meaning of limits, continuity, and infinity, or find out how these ideas transfer to other contexts, you can find out in 208/310, 302, 303, 307 (and 248/348). In particular, if you liked the geometry of calculus in two and three dimensions, you can learn more in 212 and 307. If you want to know how differentiation, integration, and the other ideas of calculus change when you allow complex numbers instead of only real numbers, take 208 or 310.

If you liked linear algebra:
If you liked the theory of vector spaces and linear transformations, you'll probably like 305, 306, and 223 Number Theory. If you liked the more computational parts of 206 or the applications of linear algebra you saw in 206, you'll probably like Operations Research (taught in 2002-'03 as Math 251).

If you're thinking about graduate school in theoretical or applied mathematics:
Take as many mathematics courses, and especially as many 300-level courses, as you can. (It is not unusual for a beginning graduate student in mathematics to have taken as many as 16 undergraduate mathematics courses.) Your 300-level courses should include Math 303 and 306, and if possible 307 and 310 as well. Consider taking an independent study course (350) and/or writing an honors thesis (360/370). If at all feasible, take one or more courses at MIT. A strong background in theoretical courses is excellent preparation for graduate work in either theoretical or applied mathematics, and writing an honors thesis is a great way to learn what research in mathematics is like. For graduate school, it's also helpful to acquire the ability to read mathematics written in French, German, and/or Russian. You may not have time to do it all, so discuss your situation with members of the department.

If you're thinking about careers in statistics or actuarial work:
Take 220 and a statistics course such as Statistical Quality Control (sometimes taught as 251), Economics 200 (Econometrics), or MIT 18.441. You might also take Mathematical Modeling, which is sometimes taught as Math 251. To become an actuary you need to pass a series of exams offered by the actuarial profession. You can take the first two exams as an undergraduate. These cover calculus, linear algebra, probability, and statistics. Many insurance companies offer summer jobs for students interested in actuarial work. You can find more information about actuaries and actuarial mathematics by perusing the career materials in the Department office.

If you're thinking about a career in computer science:
Take 225 and/or 305. Wellesley's Computer Science major requires that you take at least one of these mathematics courses. You might also consider Graph Theory (taught in Spring 2003 as Math 349B) or Numerical Analysis (sometimes taught as Math 251 or Math 349).

If you're thinking about medical school:
Most medical schools require one or more semesters of college calculus. (See the pre-medical advisor for more specific information.) Mathematics courses that may be particularly helpful in medical research and practice are 210, 220, and some versions of 251.

If you're thinking about graduate school in economics or business school:
Courses 203, 205, 206, 210, and 220 have applications to various areas of economics and management, as do Operations Research (taught in Spring 2003 as Math 251) and some other versions of 251. If you wish to take a 300-level course, consider 302 and 303. One way to find more information about careers that use mathematics in management is to peruse the career materials in the Department office.

If you're thinking about teaching at the K-12 level:
Talk to faculty members in the Education Department about education courses, student teaching, and certification. If you wish to be certified as a public school teacher, you'll need to plan your mathematics courses to allow time for the required education courses and student teaching. Some faculty members in Mathematics have also taught in high schools, and it's a good idea to talk to them as well. Some private schools use undergraduates as assistants for summer enrichment programs, and these programs provide a good opportunity to get some experience teaching or tutoring. Being a Wellesley math TA, reader, or tutor is also a good way to get some early experience.

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Courses at MIT

Consider taking an MIT course that Wellesley doesn't offer. You can follow up a Wellesley course with more advanced work, or just take a mathematics course in a university environment. Taking a beginning graduate course will give you a flavor of what graduate school will be like, although most students should take at least one undergraduate MIT course first. Be prepared for a very different experience!

Here are some suggested courses at MIT. Talk to a faculty member who knows MIT to get more details (Prof. Bernstein, for instance) and check the
MIT mathematics course catalog (will open in a new window).

200-level

(rough equivalents: 18.02=205, 18.03=210, 18.04=208, 18.05=220, 18.314=225, 18.700=206, 18.781=223)

300-level

(rough equivalents: 18.100=302, 18.103=303, 18.112=310, 18.510=309, 18.701=305, 18.702=306, 18.901 perhaps = 307)

Graduate level

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