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
- 115 and
116/116Z, Calculus I and II, or the equivalent (120, or
appropriate high school courses)
- 205,
Multivariable Calculus (prerequisite: 116 or 116Z or 120; or
equivalent)
- 206, Linear
Algebra (prerequisite: 205)
- 302,
Elements of Analysis I (prerequisite: 205 and at least one from
206, 225, 214)
- 305, Modern
Algebraic Theory I (prerequisite: 206)
- At least
one elective 300-level course (prerequisite is usually 302 or
305). Independent study units (Math 350, 360, 370) may not be
counted for this requirement.
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
- Option I:
205; 206; either 302 or 305; and two additional units, at least
one of which is at the 200- or 300-level. (Putting it differently:
205, 206, 302 or 305, at least one more 200-or 300-level course,
plus at least one additional course.)
- Option II:
205, 206, and three additional 200- or 300-level units.
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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.
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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.
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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)
- 18.310/11
Principles of Applied Mathematics
- 18.330
Introduction to Numerical Analysis
- 18.385
Nonlinear Dynamics and Chaos
- 18.440
Probability and Random Variables (more advanced than 220)
- 18.441
Statistical Inference
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)
- 18.101
Analysis II (Analysis on Manifolds)
- 18.511
Introduction to Mathematical Logic and Recursion Theory
- 18.950
Differential Geometry
Graduate
level
- 18.125
Measure and Integration
- 18.705
Commutative Algebra
- 18.905
Algebraic Topology
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- Alexia
Sontag asontag@wellesley.edu
- Department
of Mathematics
- Date
Created: October 26, 1994
- Last
Modified: January 22, 2004
- Expires:
June 30, 2004