Prospective Undergraduate Students: MENU
Overview | Curriculum - the first 2 years |
Beyond the second year
Beyond Northwestern |
Admission | Further Information | FAQ | Course Equivalences
Mathematical Experience for Northwestern Undergraduates (MENU) is a special program for entering freshmen with strong mathematical skills who are interested in mathematics, either for its own sake or because of its powerful and broad applications. It offers such students the opportunity to expand their mathematical knowledge while retaining flexibility about their ultimate major. The program offers specially designed MENU courses in addition to a wide range of courses in all areas of modern mathematics. Essential to advanced work in many disciplines is knowing how to formulate questions mathematically; for many jobs, problem-solving experience as part of a team is crucial. The MENU curriculum allows each student to work with a team of similarly talented peers to formulate and solve problems from a variety of fields. MENU is ideal for undergraduates who are considering a major in mathematics, the physical sciences, or economics, although it is by no means limited to them.
The Department of Mathematics at Northwestern University has a long-standing commitment to undergraduate teaching and curricular innovation. MENU classes range from midsize (20 to 25) to small (4 to 6), and faculty are nationally and internationally recognized for their scholarship. The director of MENU is available as an adviser for MENU students during their time at Northwestern, regardless of their major.
Curriculum - the first 2 years
At the foundation of MENU are several specially designed yearlong courses, Mathematics 290, 291, 321, 331 and 360, which provide the basis for advanced work in mathematics and those parts of economics, physics, and other areas that rely on the tools and techniques of modern mathematics.
MENU offers two parallel tracks, one (the 291/321/331 track) for students who are particularly skilled in and passionate about pure mathematics; the second (the 290/360 track) for those more interested in applications. Movement between the two tracks is possible in the initial two weeks of the program. These courses are specially designed for students in the MENU program.
Math 290 MENU: Linear Algebra and Multivariable Calculus includes most of the essential topics typically covered in matrix (linear) algebra and the third through fifth quarters of calculus, chiefly multidimensional calculus. Students gain an understanding of the "how" of mathematics and, just as important, the "why," and see applications to mathematical problems from a variety of disciplines. Math 291 MENU: Accelerated Linear Algebra and Multivariable Calculus covers much of the same material as Math 290, but places greater emphasis on mathematical concepts and rigor. It is available for students who are particularly skilled in and passionate about mathematics and is taken instead of 290 in the first year.
In the second year, the program offers Math 360 MENU: Applied Analysis, intended for students (whether or not they are majoring in math) who are interested in the applications of mathematics. Since differential equations are vital to the applications of mathematics to economics, the physical sciences, and engineering, the first two quarters of Math 360 deal extensively with ordinary and partial differential equations. The third quarter covers a selected topic in analysis such as numerical analysis, complex variables, or Fourier series.
Students who have taken Math 291 in the first year, as well as those who have completed Math 360, can continue into Math 321 MENU: Real Analysis, an accelerated, theoretical course in real analysis, or into Math 331 MENU: Abstract Algebra, an accelerated abstract algebra course. The topics in 331 include group, ring, and Galois theory, which lie at the heart of the solutions to the 3 problems of classical antiquity: squaring the circle, duplicating the cube, and trisecting the angle.
The junior and senior years are the time for MENU students to satisfy the requirements of their chosen major, which might be mathematics, a field in which mathematics is applied, or something entirely unrelated to mathematics. Below we outline some courses of study that have recently proved popular. There are many other possibilities, and an individual program of study should be worked out in consultation with the Director of MENU.
Advanced work in mathematics. MENU students who have completed the 290/360 sequence can continue into any 300-level course offered by the department (such as Probability, Chaotic Dynamical Systems, Topology, Differential Geometry, Theory of Numbers, Real Analysis) to complete a major or minor in Mathematics. (Students who complete the entire 291 sequence in their first year are prepared to take 321 and/or 331 in their second year, whether or not they first take 360).
In the third and fourth years of MENU, students are encouraged to enroll in an undergraduate research-level seminar offered by the department. These seminars are taught by senior members of the department and topics are drawn both from areas of higher mathematics and interdisciplinary fields.
Advanced MENU students can engage in independent study with a faculty member on a project of mutual interest. Such a project can lead to a senior thesis, a key element in graduating with department honors.
Advanced work in Economics. Modern economics is heavily dependent on mathematics and mathematical modeling; solid knowledge of mathematics and mathematical ways of formulating problems are essential for graduate work in economics and for many economics-related jobs with brokerage, consulting, and investment banking firms. Many undergraduates at Northwestern complete double majors in economics and mathematics; MENU offers such students a convenient route to such a double major. Some advanced economics courses can even be counted towards a math major.
Advanced work in Physics. Classical physics and mathematics have been closely intertwined for hundreds of years: Newton invented the calculus to work out problems of planetary motion; Maxwell's laws of electromagnetism are stated in terms of a linked system of partial differential equations; and Einstein used differential geometry to formulate the special theory of relativity. Thermodynamics, the equations governing the behavior of electromagnetic phenomena, the kinetic theory of gases, and quantum mechanics all are formulated mathematically. MENU offers the chance to approach a physics major with a deeper understanding of its mathematical underpinnings.
Other fields. Applications of mathematics to real world phenomena are not limited to those described above. The list of fields that overlap with mathematics is nearly limitless, including but not limited to Astronomy, Biology, Chemistry, Computer Science, Linguistics, and Psychology. If you have strong mathematical skills and parallel interests in a related field, the Director of MENU can work with the Director of Undergraduate Study in your other field of interest to help design an appropriate advanced course of study for you.
Graduates of MENU have gone on to graduate school in a variety of fields. Others have gone directly into jobs in business, law, social policy, management, and the sciences that use their mathematical talents. A solid background in mathematics is highly valued by job recruiters.
Admission to MENU is limited to students who have demonstrated a solid grasp of the calculus of functions of one variable, including both differentiation and integration, typically by means of a score of 4 or higher on the College Board Advanced Placement Calculus BC exam. Students accepted to Northwestern who received a 4 or higher on the AP Calculus BC exam, or a 5 on the AB exam should receive an invitation to MENU during the summer prior to enrollment.
If you have taken a year of calculus in high school or matriculated outside the USA and were not invited to enroll in MENU, you may contact the Director at the address below for permission to enroll. (At present, the curriculum in the McCormick School of Engineering precludes their students from being in MENU.)
During New Student Week the MENU director, and other members of the department will be available to answer questions and give permission for enrollment in the MENU program.
If you have questions before that time, you contact her by email at
menu
.
Please include your name and netid (if known) in your email.
If you do not have email access, you may phone her at (847) 491-5486 or
(847) 491-3299 for an appointment.
Read our FAQ about MENU.
Prof. Paul Goerss, the Director of MENU, welcomes inquiries by
email at
menu
If you do not have email access, you may phone him at (847) 491-3299
for an appointment.
MENU: Frequently asked questions
Who enrolls in MENU?
We have a well-rounded mix of students. Some chose MENU because
their mathematical strength in high school made them relish further
challenges in college. Others planned careers requiring the mathematical
and analytical skills that MENU helps develop. What they all have in
common is that they enjoy doing math!
What are
the benefits of enrolling in MENU?
Many departments at Northwestern offer courses that use advanced
mathematical concepts and techniques which are only touched upon in
our standard courses. In MENU, the accelerated pace allows such topics
to be covered in depth. Beyond these specific uses, the analytic skills
acquired from a serious study of mathematics will benefit you throughout
your future career.
How will enrolling in MENU affect my other studies at
Northwestern?
Enrolling in MENU requires you neither to take more courses in
mathematics, nor fewer courses from other departments, than you
otherwise might have taken. MENU courses replace some standard courses
and serve as prerequisites for more advanced ones. (See the tables below
for a list of equivalences between MENU courses and the department's
standard courses.) Nor does enrolling in MENU require that you major in
Mathematics. Although most MENU students are in the Weinberg College
of Arts and Sciences (and many do, in fact, pursue a major or a minor
in Mathematics), there are students in the program from almost all the
other undergraduate schools at Northwestern. Students with majors as
diverse as physics and theater are part of MENU.
What first-year courses are offered to MENU students?
There are two year-long sequences open to first year MENU students,
290-1,2,3 (accelerated linear algebra and multivariable calculus),
and 291-1,2,3 (accelerated linear algebra and multivariable calculus,
with an emphasis on theory). Both sequences treat their subject matter
in greater depth than the standard curriculum, and those invited to join
MENU may enroll in either sequence.
How will I know whether to enroll in 290 or 291?
The 291 sequence places greater emphasis on mathematical concepts
and rigor than the 290 sequence. It is designed for students who are
particularly skilled in and passionate about mathematics. Don't be
shy about signing up for 291! This invitation indicates that we think
you would excel in either course. And during the first week of classes,
students are free to move between 290 and 291, while throughout the Fall
quarter, students are free to move from 291 to 290.
When do Math 290 and 291 meet?
Both 290 and 291 meet MTuWF at 12 noon. If you are contemplating enrolling
in MENU and have been assigned to a freshman seminar which overlaps the
12 m - 1 pm hour, please email us immediately; we will work with the
Dean of Freshmen to change your seminar to one which doesn't conflict
with Math 290 or 291.
What courses do MENU students take after the first year?
Open to all 290 and 291 students in their second year is Math 360-1,2,3
(applied analysis, a course in differential equations and mathematical
modeling). Students who complete the entire 291 sequence are also prepared
for Real Analysis (321-1,2,3) and Abstract Algebra (331-1,2,3) in their
second year (without first taking 360 or 300).
If I join MENU, must I take all of these courses?
Enrolling in the MENU program does not oblige you to take any of
these sequences in its entirety -- it gives you an entitlement, not
an obligation. However, the earlier quarters of these sequences are
prerequisites for the later ones, and each of the 300-level sequences
requires one of the 200-level sequences.
How can I get answers to my additional questions about MENU?
Send email to
menu;
we'll get right back to you! Please include your name and
netid in your email.
I am considering this program, but I am already in the
Integrated Science Program. I believe that in that program I am going
to be taking some sort of accelerated math, so is there any point for
me to enroll in this one as well?
The Integrated Science Program has its own mathematical curriculum;
you would do that curriculum rather than MENU.
Is it possible to be a part of MENU and MMSS at the
same time?
MMSS also has it own math curriculum which you would follow. However,
MMSS does accept applications from freshmen who begin the program as
sophomores. If you did one of the freshman MENU courses (290 or 291)
and were then accepted into MMSS, you would not need to do the first-year
MMSS sequence.
The MENU program seems to offer courses that I'd like to
take, but I do not meet the standard for automatic admission. A scheduling
conflict in my senior year of high school, prevented me from taking BC
calculus. Instead, I took first-year calculus at a local college, and
didn't take the calculus AP exam, since the credit from those classes
seems to be transferable, This leaves me without an AP score! Are other
criteria by which admission to MENU is determined?
Yes, there are alternate criteria for
admission. Contact the Director of MENU at
menu.
I will be in the Medill School of Journalism and was
invited to join the MENU program. Is this possible?
Your invitation means that you are qualified to be in the MENU program,
and we'd very much like to have you. You should check with your adviser
in Medill about whether it will fit into your schedule.
Is there a big difference between the work load in
the MENU courses and standard courses?
The workloads are probably comparable. It's the level of difficulty that
is higher in MENU.
But does a program like this require more time than the ordinary math courses that it replaces?
In general, yes.
Can I withdraw from MENU at anytime?
Admission to the program allows you to take the special MENU courses,
but there is no requirement to do so. You may take as many MENU courses
as you wish, and stop taking them when you wish. No formal withdrawal
from the program is necessary.
Will I receive more attention in this program than in
ordinary calculus classes?
In general, yes. Your class size will be smaller, and you are likely to
have the same professor the whole year.
Are there other benefits to this program, besides the
challenge of more in-depth studies?
You will establish a long-term relationship with the director and your
professor, who will thus be in a better position to advise you and
provide letters of recommendation.
If I am going to medical school, would MENU be
necessary? Would it help me in pursuit of a medical career?
MENU is by no means necessary for a medical career, but developing
your analytical and problem-solving skills (the goal of MENU) should be
useful. Pre-med students tend to have a heavy courseload. Your decision
to join MENU should be based primarily on whether you think you would
enjoy spending extra time learning mathematics and not on career
considerations.
I am thinking of majoring in economics, a subject
for which you must take math courses. Would MENU help me to fulfill the
requirements for that major?
The MENU courses for the most part replace standard courses in the
curriculum. The MENU program is the ideal complement to a major in
economics, especially for those contemplating graduate work in economics
or finance.
I just applied to Northwestern. Is there a separate
application to the MENU program that I must fill out?
Provided that you are accepted to Northwestern and meet the requirements
of the MENU program (a 4 or 5 on the BC AP Calc exam, or a 5 on the
AB exam), you will receive an invitation to join the summer before the
school year starts. There is no separate application for MENU.
I already took multivariable calculus as a high school
student. Can I still be part of MENU?
Yes. Please contact the Director of MENU at
menu
to determine what steps to take next.
How many students are typically enrolled in MENU?
In 2005-2006, a typical year, approximately 115 first-year students
enrolled in MENU (about 50 of them in 291, the rest in 290).
I have accepted the invitation to join MENU.
I am attempting to register for 290 but CAESAR says I need a permission number. How do I get one?
Simply visit the Math Department Office on the second floor of Lunt
Hall. If you have accepted the invitation to join the program, your
name will be on a list, and the Math Department Staff will give you a
permission number.
Here are the precise equivalences between the standard 200-level mathematics sequence and the 290- and 291- sequences taken by MENU students:
| Standard 200-level course | MENU equivalent |
| 220-0, 224-0 | AP exam with high score |
| 230-0 | 290-2 or 291-2 |
| 234-0 | 290-3 or 291-3 |
| 240-0 | 290-1 or 291-1 |
And here are the equivalences between the advanced MENU courses and standard courses in the department:
| MENU course | Standard equivalent |
| 360-1,2,3 | 250-0, 353-0; 325-0 |
| 321-1,2,3 | 320-1,2,3 |
| 331-1,2,3 | 330-1,2,3 |
