Mathematics Preparation
Mathematics provides economists with a set of tools that they use for many purposes. First,
mathematics enables economists to prove rigorously the logical connection between
concepts, which is especially crucial in situations where words alone are imprecise or
potentially misleading. Second, mathematics makes it easy to combine several simple
models into a larger model, allowing economists to analyze complex economic systems that
involve interacting parts. For example, macroeconomists study the interactions between
the goods market (involving production and consumption of goods and the setting of prices),
the labor market (involving employment and wages), and the money market (involving
assets, such as cash and bonds, and interest rates). Third, mathematics allows economists
to formulate and test their theories quantitatively. Quantitative testing means that
economic theories must satisfy a demanding standard before they become accepted.
Finally, because economic theories are quantitative, economists can offer quantitative
policy prescriptions.
Because “marginal” conditions hold a central place among economists’ analytical tools,
concentrators are required to demonstrate competence in single-variable calculus by taking
Math 1a or by placing out of it. Single-variable calculus is the prerequisite for the less math
intensive intermediate economic theory courses, Ec 1010a and 1010b.

Although a student can understand virtually all the basic concepts in economics with single
variable calculus, deeper understanding, and understanding of more difficult concepts,
requires more mathematical preparation. And while math beyond the level of first-semester
calculus is not required for the concentration, it is highly recommended. The more-math
intensive intermediate economic theory courses, Ec 1011a and 1011b, require multivariable
calculus at the level of Math 20 or 21a. Math 20 covers multivariable calculus and linear
algebra together, focuses on economic and social science applications, and serves as a last
math course for many economics concentrators. Math 21a covers multivariable calculus as
part of a sequence leading to higher-level math courses, though it can be taken alone.
Students who want to pursue graduate work in economics should take multivariable calculus
(Math 21a), linear algebra (Math 21b), a course that emphasizes writing proofs (Math 101),
and real analysis (Math 112). (Students with very strong math backgrounds may substitute
Math 23ab for 21ab. A student with an extremely strong math background would be
prepared for graduate work in economics after taking Math 25ab or 55ab.)
Ec 10 (formerly Social Analysis 10)
Ideally, students intending to concentrate in Economics spend their first year at Harvard
taking Ec 10, the full-year introduction to current economic issues and to basic economic
principles and methods. (If you did not take Ec 10 as a freshman, you may still concentrate
in economics. You may take all of Ec 10 during the summer at Harvard or take it as a
sophomore. Sit down with one of the concentration advisors to help you plan your courses
so that you will fulfill your concentration requirements without a problem.)
All concentrators are required to either take Ec 10 or demonstrate proficiency at
introductory economics, most typically by a combined score of ten on the Macroeconomics.

and Microeconomics Advanced Placement examinations or a score of 7 on the Higher Level
examination toward the International Baccalaureate. If you meet these requirements, you
may skip Ec 10 and go on to the intermediate theory courses (Ec 1010ab or Ec 1011ab), but
you must replace those credit hours with two other half courses. If you received a five on
one AP economics exam, you may skip that half of Ec 10, but again, must replace it with
one additional half course. Most eligible students who go on to the intermediate theory
courses do very well, but you do not have to skip Ec 10; you may take it if you wish. It is a
personal choice, and we suggest that you speak with one of the concentration advisors to
help you with your decision. (Note that a student who uses macro and/or micro AP exam
scores as part of the basis on which to activate Advanced Standing will not get Harvard
credit for taking Ec 10, or for the semester of Ec 10 represented by the exam taken.)
Ec 10 is taught in sections of 20 students or so, with course-wide lectures on a variety of
topics about 10 times a semester. Unless replaced by course-wide lectures, sections meet
for three one-hour classes each week, on Mondays, Wednesdays, and Fridays. The section
based orientation of the courses is very important because sections teach the principal tools
of economics in an environment in which students can ask questions freely. All sections
cover the same basic course material.
Course-wide lectures are usually given by faculty experts on the specific topic addressed
(e.g., Greg Mankiw on macroeconomics, David Laibson on behavioral economics, Andrei
Shleifer on finance, Richard Freeman on labor). The lectures focus on current economic
problems and policy issues, in coordination with the material being taught in section. Each
lecture is discussed at the following section meeting.
Section leaders are graduate students in Economics, as well as law, business, and public
policy students with strong economics backgrounds and high teaching ratings. Teacher
training sections and videotape reviews of individual sections maintain high pedagogical
standards in the course.

Examinations cover both lecture and section material. There are usually two one-hour
exams and one final each term. One of the hour exams and both finals are course-wide
exams, in which all students taking Ec 10 solve the same problems and write on the same
essay questions. Most sections assign roughly five problem sets per term.
There are no prerequisites for Ec 10. It is not a highly mathematical course. However, it
uses a lot of graphs and some simple algebra. It does not use calculus. Ec 10 cannot be
taken pass/fail by a student intending to concentrate in Economics.
Sophomore Tutorial
Because Economics has so many concentrators, even upper-level courses can be large in
size. But much of what one learns about an analytical subject like economics comes
ultimately from active discovery, which is often better accomplished in a small group
setting. Ec 970, Sophomore Tutorial, is taught in sections of about eight to ten students, and
provides a key opportunity for such active learning. Ec 970 is offered in the spring. As the
name suggests, almost all concentrators take the tutorial during their sophomore year;
however, under certain circumstances (e.g., if you transferred into the department late), it

may be postponed to junior or senior year. To enroll in Ec 970, you must have completed Ec
10, Stat 100 (or its equivalent), and Ec 1010a/1011a. You also must be concurrently enrolled
in (or have already completed) Ec 1010b/1011b. If you do not meet those prerequisites, you
will need to enroll in tutorial in either your junior or senior year. Ec 970 may not be taken
The goals of Ec 970 are to build on the foundations laid in the principles, statistics, and
intermediate theory courses by applying frameworks of economic analysis to specific
subject areas, to help students develop an effective style for writing analytical economics
papers, and to practice the arts of analysis, communication, argument, and listening.
In a typical year, there are 25 to 30 different tutorials to choose from. The vast majority of
students are assigned to one of their top four tutorial choices. Topics vary from year to year.
Recent topics have been behavioral finance, experimental methods and psychology in
economics, economics of professional sports, and law and economics. An overwhelming
majority of tutorials receive high student evaluations, and sophomore tutorial is often one
of a student’s favorite classes in the department.

Intermediate Theory Courses
The Economics Department offers two intermediate microeconomic and macroeconomic
theory course tracks. The Ec 1010 track is intended for students who find mathematical
formulations as much of an obstacle as a help to understanding economics; knowledge of
Math 1a is expected. But many students with higher levels of mathematical preparation
take Ec 1010 courses when they believe that the courses are especially well taught. The Ec
1011 track is intended for students who find mathematical formulations of economic
principles a significant aid in understanding and using them. It uses mathematics at
approximately the level of Math 20/21a. Students who have taken Ec 1010a and 1010b have
sufficient preparation for almost all upper-level undergraduate economics courses. A
handful of upper-level undergraduate economics courses have Ec 1011a or 1011b as a
prerequisite. Students are free to mix and match courses from the different tracks:
combining 1011a with 1010b, or 1010a with 1011b.
Ideally, concentrators should have finished the intermediate micro and macro courses by
the end of their sophomore year. Whether or not a particular upper-level economics course
has Ec 1010 as a formal prerequisite, students who have taken intermediate micro and
macro usually do better and learn more in upper-level courses than students who have not.
Concentrators must demonstrate their command of the basic tools of economic analysis by
receiving a B-/C+ average (that is, a 2.5 grade point average) or better in both intermediate
theory courses. Students who do not meet this standard are required to reinforce their
understanding of macro and micro theory by satisfactorily completing (i.e., receiving at
least a C- in) Ec 975: Tutorial—Theory Review. Ec 975 is not intended as a review for
students who feel weak in their overall economics courses. It is required of, and limited to,
students who receive below a B-/C+ average in the intermediate theory courses. Students
who must take the course are notified by the Undergraduate Office. If you are unsure,
speak to the Undergraduate Program Administrator. Students do not receive economics
course credit for Ec 975.

In the years when 975 is not offered, students who receive below a C+/B- average in the
intermediate series must (unofficially) retake the portion/s of the series in which they got
below a B- and receive at least a B- the second time around. Since such students will not
officially be enrolled in the course, the grade and credit hours will not count for Harvard
credit towards graduation or fulfilling Ec electives in the concentration, nor will it be
factored into your Ec GPA for honors if you choose to pursue them. Students’ fulfillment of
this requirement will be tracked internally by the Economics’ Department and students will
not receive a degree in Economics until this requirement is met.
Statistics and Econometrics
The ability to interpret quantitative data and to understand statistical arguments is
essential to understanding the economy. Statistical methods help economists to summarize
data, to analyze empirical relationships, to test theories, and to make predictions. Because
virtually all research in economics involves at least some statistics, economics
concentrators must take a course in statistics (Stat 100, 104, or 110) before they may take
Ec 970, Sophomore Tutorial. For this reason, most economics concentrators take the course
in statistics in their freshman year or in the fall of their sophomore year.
Stat 100 introduces students to statistical tools like hypothesis testing, parameter
estimation, and regression analysis. The main intent is to enable students to read
contemporary economic literature and to understand how statistical procedures are used to
summarize information. Stat 100 is essential for fully understanding much of the reading in
upper-level Economics courses.
An alternative to Stat 100 is Stat 104, which covers somewhat more material at a faster
pace in a smaller class. Stat 104 is pitched at a slightly higher level and draws on
applications from economics and other social sciences.

Students who have completed multivariable calculus (Math 20 or 21a) and who wish to
understand statistics at a deeper level can fulfill their statistics requirement by taking
(instead of Stat 100 or 104) Stat 110 (often, but not necessarily, followed by Stat 111). Stat
110 covers probability theory, which provides a mathematical foundation for statistics. Stat
111, which requires linear algebra (Math 20 or 21b), builds statistical theory from this
foundation. Stat 111 draws more directly from Stat 110 but has fewer economic applications
and less emphasis on standard econometric methods than Ec 1126.
Stat 101 is not an option. The Economics Department does not give any credit for high
school statistics or the statistics AP exam. Courses taken to meet the Economics
Department’s statistics and econometrics requirements cannot be taken pass/fail by
Economics concentrators.
In addition to a basic course in statistics, the department requires all concentrators to take
Ec 1123 or 1126 (Ec 1127 can also be substituted). These courses are designed to introduce
concentrators to econometrics – the statistical concepts and quantitative methods that are
especially important for economists. Econometrics typically plays a central role in an
economics senior thesis, so students who plan to write a thesis fulfill their econometrics
requirement before senior year.

Ec 1123 provides students with an understanding of econometric techniques and an ability
to apply them using standard software packages. Ec 1123 is less mathematical and more
applied than Ec 1126, covering the essential methods for conducting research in economics.
Ec 1123 provides students with most of the basic tools to write an empirical honors thesis.
Ec 1123 assumes a mathematics preparation at the level of Math 1a.
Ec 1126 goes further into the fundamentals of probability theory and problems of statistical
inference. It is more mathematical and more theoretical than Ec 1123, employing both
multivariable calculus and linear algebra (Math 20 or both Math 21a and 21b). Ec 1126
emphasizes understanding the general framework of econometric theory and covers several
important recent contributions and applications. Like Ec 1123, Ec 1126 provides students
with the basic tools to write an empirical honors thesis, while also providing a rigorous
introduction to econometric methodology. Preparation at the Math 20 level is a prerequisite
for Ec 1126. Students should also have taken, or be taking, the intermediate
microeconomics and macroeconomics courses.