Concentration in Mathematics
(2015-2016)
What Can You Do With Math?Concentration in mathematics is an excellent preparation for a career in either pure or applied mathematics, in academia or in industry. Because physics, chemistry, computer science, economics, and even social sciences rely heavily on mathematical methods, a math concentration can provide an invaluable background for many different careers. Concentrators who do not choose to continue in mathematics have often gone on to graduate work in other academic subjects, to actuarial and computer science careers, or to professional training in law, business or medicine. A math concentration is very flexible and has a reasonably small number of requirements, so there are ample opportunities to take electives in related and unrelated fields.
Math concentrators who would like to earn teaching certification to
teach in Massachusetts public schools after graduation may want to
look into the Undergraduate Teachers Education Program (UTEP). More
information about UTEP is available from their web site at
http://www.fas.harvard.edu/
Concentration in mathematics requires a minimum of twelve regular,
letter-graded, half-courses of which eight must be courses labeled as
Mathematics and four may be math courses or ones in related subjects.
(Note that a specially certified Freshman Seminar can be substituted
for one of the eight Mathematics courses.) Concentrators must attain
at least one half-course at the 100-level in each of the three
areas: analysis, algebra, and geometry. Students choosing the
``Mathematics and Teaching'' option haveslightly different course requirements.
In addition to the course requirements, all students are required to
satisfy the Math Expository requirement (see the section below). The
exact description of the requirements and the list of related courses
permitted to count for course requirement are printed in the Handbook for Students.
Each concentrator is required to submit a 5-page expository paper in
Mathematics. The paper should be a coherent, correct and original
exposition in a subject of pure or applied mathematics. The paper
should be written during the sophomore or junior year under the
supervision of a professor or tutor in a tutorial (Math 99r) or a 100-
or a 200-level course that the student is contemporaneously enrolled
in. The paper has to be accepted by both that professor or tutor, as
well as the Director of Undergraduate Studies. The student should be
prepared to discuss the contents of the paper with the professor or
the Director of Undergraduate Studies.
Ordinarily students enrolled in a tutorial (Math 99r) automatically
satisfy the expository requirement as part of the structure of the
tutorial.
The expository requirement has to be met before the last day of the
spring reading period of the junior year. Extensions may only be
granted by the Director of Undergraduate Studies.
A candidate for Honors must, in addition to satisfying the above
mentioned requirements, submit a senior thesis. The thesis may be on
any topic in pure or applied mathematics not directly covered in a
student's course work. It need not be an original piece of
mathematical research, but should be an original exposition of
material culled from several sources. The department strongly urges
concentrators to write a senior thesis; this experience tends to
provide a much better glimpse of mathematical research and graduate
work than taking courses alone. If you think you will write a thesis,
be on the lookout for a thesis topic in your junior year. More about
senior theses can be found in the pamphlet ``Honors in Mathematics'',
available from the Undergraduate Program Coordinator Cindy Jimenez,
room 334. Also, feel free to talk with the Director of Undergraduate Studies, Jacob Lurie,
if you need help deciding on either doing a thesis or
finding a topic or and advisor.
The Department encourages students to take the most advanced courses
for which they are qualified. Nevertheless, students who enter as
freshmen or advanced standing sophomores will not ordinarily be
permitted to count courses taken elsewhere toward the twelve-course
requirement. Transfer students wishing to concentrate in mathematics
should consult the Head Tutor who will review their transcripts and
arrange their concentration requirements.
The Department welcomes students who want to change their
concentration to Mathematics as long as it is plausible that they can
fulfill the requirements within the time remaining. Students
considering Mathematics may also wish to consider Applied Mathematics,
Computer Science, any physical science, or Statistics.
Joint concentrations with other departments are possible to arrange.
Common joint concentrations are with Computer Science, Physics,
Philosophy and Statistics. Joint concentrations are honors
only. If Math is primary, the student must fulfill all of the
requirements for Honors in Math (including a senior thesis in Math)
plus whatever other requirements are called for by the secondary
department. (Consult the secondary department for this information.)
If Math is secondary, the Math requirements are as follows: five,
letter-graded semester courses in Mathematics with a grade of C
The Department offers the AB-AM degree, which allows students who are
Mathematics concentrators to obtain a Masters degree (AM) in
Mathematics, in addition
to their Bachelors degree (AB) during their four years at Harvard.
Any undergraduate who wishes to apply for this degree must file an
application form for the graduate program in mathematics, just as any
other student files for graduate work at Harvard. Only students with
Advanced Standing are eligible to apply for this four-year program,
and the Department will only accept candidates who have demonstrated
sufficient mastery of undergraduate material. If you are considering
going on to graduate school in mathematics, bear in mind that the
Masters degree will offer you no advantage. The program requires a
large number of additional courses in mathematics. In nearly all
cases, the Department recommends that students should instead take
advantage of the many other academic opportunities that the University
offers. Further details of the requirements are available at the GSAS
website, http://www.gsas.harvard.edu/, under Programs of Study,
and from the Graduate Studies Coordinator.
There are two types of Reading Courses available. Math 60r is designed
to give more time for thesis work to senior honors candidates; Math
91r is for students who want to learn a particular topic not covered
in a regular course or tutorial. Please read the relevant section of
the ``Courses in Mathematics'' pamphlet to learn more about the
requirements and modalities of these courses.
Although tutorials (Math 99r) are not required, students are
encouraged to take a tutorial in the course of their studies. Students
can take as many tutorials as they want, but only one tutorial may
count for the concentration requirements.
Generally one or two tutorials are offered every semester. Typically,
tutorials are directed by graduate students, and have four to eight
students in them. They tend to be less formal and structured than
regular courses, yet require more involvement on the part of the
students, who have to make presentations and write papers. Very
frequently a topic studied in a tutorial leads naturally to a senior
thesis, and the paper submitted for the tutorial will generally
satisfy the Math expository requirement.
A description of offered tutorials is placed into concentrators'
registration envelopes in September, and another is e-mailed in
January. Tutorial descriptions also appear during the first week of
each semester on the undergraduate bulletin boards (one opposite room
320, and one opposite room 503 in the Math Department) and are posted
at Math Department's website http://www.math.harvard.edu/. Often,
tutorials are previewed at Math Table meetings (For more information
on Math Tables, see below). A special organizational meeting for
tutorials is held the first Wednesday of the fall semester. The spring
semester tutorials are organized in the first week of that semester;
see the undergraduate bulletin boards for announcements.
Questions regarding tutorials may be addressed to the Director of
Undergraduate Studies, Jacob Lurie (lurie@math), or
the Undergraduate Program Coordinator, Cindy Jimenez (cindy@math).
Students may cross-register to take a course at M.I.T. It is a
particularly useful option for students interested in logic and
combinatorics. For more information please see the ``Courses in
Mathematics'' pamphlet. You must get advance permission from
the Director of Undergraduate Studies, Jacob Lurie
(lurie@math), to have M.I.T. courses count for concentration
credit.
The department assigns all students a faculty member as their
concentration advisor. If you prefer to change your assignment, please
talk to Cindy Jimenez in room 334 (cindy@math, tel. 495-9116).
Your advisor can help you plan your course-work, and will sign your
study card. How much contact you have with your advisor and how
helpful he or she is will depend almost entirely on your initiative.
Feel welcome to drop by during his or her office hours or during our 4
pm teas (see below), or to invite your advisor to lunch at your House
(students can invite a faculty member for any meal at their House,
courtesy of Harvard - ask the checker in your House's dining hall for
the form). Your advisor can help you plan your courses, choose a
thesis topic, a thesis advisor, learn about mathematical research, and
apply to grad school.
To insure a minimum of advising, the department has
every junior come in for a scheduled 20 minute advising session
with two faculty members in the spring semester;
post-graduate options and senior theses are often discussed.
Juniors will receive a letter by e-mail
in the spring. If you do not receive an appointment letter, please
contact Cindy Jimenez (cindy@math).
Each year a large number of Harvard undergraduates compete in the
William Lowell Putnam Mathematical Competition. It is open only to
regularly enrolled undergraduates in colleges and universities of the
United States and Canada. This is a competitive examination given in
two three-hour sessions in early December. There are substantial
prizes for both individuals and teams, and Harvard students have done
extremely well in the recent past. Sign up to participate in the
Putnam competition in late September on the bulletin board opposite
room 323. Harvard students have also done well in the MAA-SIAM
Mathematical Modeling Contest that occurs in early February.
The Math Department has an undergraduate math club. The club represents the
interests and the views of Math concentrators.
The club also sponsors the Math Table, which meets every Tuesday at
5:30 pm at Mather House Dining Rooms A and B over dinner to hear talks
by faculty and undergraduates. Anyone, at any level of math literacy,
is welcome to come. The talks at the Math Table generally cover topics
which fall outside the scope of regular courses. The talks serve
three purposes: to introduce undergraduates to various fields of
mathematics, to suggest topics for senior thesis research, and to
provide a forum for undergraduates to deliver talks on mathematical
subjects. The Rogers Prizes are awarded each year for the two best
talks delivered by undergraduates. Announcements about the Math Table
talks are posted on the undergraduate bulletin boards (near rm. 320,
rm. 503) and e-mailed to the concentrators' e-mail list.
If you would like to give a talk at the Math Table, please contact the
Math Table coordinator, Professor Noam Elkies (elkies@math).
To facilitate communication with its undergraduates, the department
urges all mathematics concentrators (potential concentrators and those
just interested in math) to forward their e-mail address, together
with their name and year at Harvard to Cindy Jimenez
(cindy@math). Information about events of concern to math
concentrators (for example, job opportunities, math table talks,
tutorials, etc.) will be transmitted as it becomes available.
Additional information is also available on the Math Department
website.
The Math Department hires undergraduates as CA's (i.e. course
assistants). A CA grades homework assignments, leads a section for an
hour a week, has office hours, writes solution sets, and attends the
lectures of his or her class. For more information on CA positions for
the calculus courses (at the level of Math 21 and below), as well as
the 100-level courses, go to http://www.math.harvard.edu/jobs/.
Most hiring for these positions takes place in the
spring.
To help with Science Advising in the fall contact Professor Jacob Lurie
(lurie@math.harvard.edu).
The Office of Career Services can help you arrange to spend a semester
or a year studying abroad. Math concentrators have taken advantage in
the past of a well-regarded ``Budapest Semesters in Mathematics''
program in Hungary. The program allows American students to spend one
or two semesters studying combinatorics, algebra, and discrete math in
small groups with senior Hungarian mathematicians. All classes are
taught in English. Applications for the Fall semester are due at the
end of April, for Spring in mid October. For more information you can
send e-mail to Paul Humke (humke@stolaf.edu) or visit the website
http://www.stolaf.edu/depts/math/budapest.
There are opportunities to do pure or applied math during the summer.
Browse through the undergraduate bulletin boards (near rm. 320, rm. 503)
periodically during the spring semester.
National Science Foundation sponsors a number of Research
Experiences for Undergraduates (REU) programs in mathematics every
year. You may wind up learning something interesting, and making money!
The Weizmann Institute of Science in Rehovot, Israel has an annual
summer research program in science and mathematics for undergraduates.
They match students with researchers and provide a modest stipend.
The program is conducted in English, and the applications are usually
due in late December. More information is available from their website
at http://www.weizmann.ac.il/acadsec/kkiss.html.
Large companies, such as IBM or Bell Labs, often hire undergraduates
to do research (usually somewhat applied math) during the summer. If
you are interested, write directly to the company very early (December
is not too early) and look for advertisements posted on the Division
of Engineering and Applied Sciences' bulletin boards.
Those who register their e-mail accounts with the department (see
``Communications'' above) will periodically receive information about
some of these opportunities. More announcements will appear on the
bulletin boards. You should also regularly check with the Office of
Career Services.
At the beginning of the fall semester Math Department holds a party
for Math concentrators in the Austine and Chilton McDonnell Common Room on the 4th floor of the
Science Center. Please come and meet other math majors and faculty
members. Refreshments provided.
The Birkhoff Mathematics Library on the third floor of Science Center,
holds many mathematical books and journals. All texts used in math courses
during the semester are held on reserve there. It is a noncirculating
library, so its resources may be used only on the premises. The library is
open Monday through Friday 9 to 5 pm.
All Math majors may request the card access to the Math Department
from the Main Office in room 325.
The Austine and Chilton McDonnell Common Room, located on the fourth floor of the Science
Center, is open to all concentrators and friends of the Mathematics
Department. Tea is served Monday through Wednesday (and occasionally
on Thursday) at 4 pm. Cheese, bread, and juice is offered at 4:15 or
so on Fridays. Harvard Math Department prides itself on its informal
atmosphere. Come to these events regularly, and get to know the
faculty and graduate students.
Information about tutorials, jobs, graduate schools, fellowships, and other
matters is posted on the Undergraduate bulletin board opposite room 320.
You can get the pamphlets ``Honors in Mathematics'', ``Beyond
Math 1: Which Math Course is for You?'', ``Mathematical Sciences at
Harvard'', ``Courses in Mathematics'', and ``Graduate Schools and
Fellowships in Mathematics'' from the Undergraduate Program
Coordinator Cindy Jimenez (cindy@math) in room 334.
These pamphlets, as well as some other information is available from
the Math Department homepage at http://www.math.harvard.edu/.
For other information consult the Director of Undergraduate Studies,
Jacob Lurie, room 514 (5-9493), (lurie@math).
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Concentration Requirements
The AB-AM degree program