Economics-Mathematics

Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors

Economics core courses

All of the core courses must be completed no later than the spring semester of the student’s junior year and must be taken at Columbia. Students who take any core course during the fall semester of their senior year must obtain written permission from the department's director of undergraduate studies.  Unless otherwise specified below all students must complete the following core courses:

1. ECON W1105 Principles of economics
2. ECON W3211 Intermediate microeconomics–it is recommended that this course be completed no later than the fall semester of the junior year
3. ECON W3213 Intermediate macroeconomics–it is recommended that this course be completed no later than the fall semester of the junior year
4. ECON W3412 Introduction to econometrics

Prerequisites

Course prerequisites are strictly enforced. Prerequisites must be taken before the course, not after or concurrently.

Economics courses taken before the completion of any of its prerequisites, even with instructor approval, are not counted toward the major, concentration, or interdepartmental majors. Exemptions from a prerequisite requirement may only be made, in writing, by the department's director of undergraduate studies. Credits from a course taken prior to the completion of its prerequisites are not counted towards the major requirements. As a consequence, students are required to complete additional, specific courses in economics at the direction of the director of undergraduate studies.

The prerequisites for required courses are as follows:

It is strongly recommended that students take ECON W3412 Introduction to econometrics in the semester immediately following the completion of the statistics course.

Grading

No course with a grade of D or lower, including calculus and statistics courses, can count toward the major, concentration, or interdepartmental majors. Economics core courses with a grade of D or F must be retaken and completed with a grade of C- or better.

Students who must retake a core course are permitted to take a higher-level economics course that has that core course as a prerequisite if it is taken concurrently with the retaking of that core course. For example, if a student fails ECON W3211 Intermediate microeconomics, the student must retake it and in the same semester may enroll in an elective course for which it is a prerequisite, provided that all other prerequisites for the elective have been completed.

Only ECON W1105 may be taken for a grade of Pass/D/Fail and the student must receive a grade of P for it to count toward the requirements for the major, concentration, or interdepartmental majors.

The department strictly enforces the rule regarding the grade of UW. In particular a student who has completed substantial work in a class (for example, taken the midterm) is ineligible for the grade of UW. Students who hope to get a UW must contact the instructor of the class in writing before the midterm to request the grade of UW.

Economics electives

Only those courses identified in the Economics Department listings in this bulletin may be taken for elective credit. All 3000-level or higher electives offered by the Economics Department have ECON W3211 and ECON W3213 as prerequisites. However, some electives have additional prerequisites and students should ensure that all prerequisites have been completed. Seminars do not count as electives.

Seminars

Seminars can be taken only after all of the required core courses in economics have been completed and do not count as electives. Each seminar is limited to fifteen students, with priority given to seniors. For ECON W4921 Political economy seminar and ECON W4950 Economics and philosophy seminar, priority is given to economics–political science and economics-philosophy majors, respectively.

Seminars are not available for on-line registration. Students must sign up in person at the Economics Department. Seminar registration is conducted on a first-come, first-served basis at 9 a.m. on the first day of each semester (not the first day the seminar meets). The department registers the first fifteen qualified students. Every seminar requires a research paper and a class presentation.

Please see the department’s website for registration dates and more detailed information.

Mathematics

Students must consult with the Mathematics Department for the appropriate placement in the calculus sequence.

Students must complete one of the following sequences:

1. MATH V1101 and V1201 Calculus I and III
2. MATH V1207 and V1208 Honors mathematics A and B

In addition:

1. Students who receive a grade of D or F in MATH V1201 Calculus III must retake the course but may enroll in ECON W3211 Intermediate microeconomics concurrently.
2. Students who receive a grade of D or F in MATH V1207 Honors mathematics A may either retake the course or take MATH V1201 Calculus III and enroll in ECON W3211 Intermediate microeconomics concurrently.

Statistics

Unless otherwise specified below, all students must take STAT W1211 Introduction to statistics (with calculus), or a higher level course such as SIEO W3600 Introduction to probability and statistics, SIEO W4150 Introduction to probability and statistics, or STAT W4107 Statistical inference.

Barnard courses

A limited number of Barnard economics electives may count toward the major, concentration, and interdepartmental majors. Students should pay careful attention to the limit of Barnard electives indicated in their program’s requirements. Please see the Transfer Credit section below for more information on the number of Barnard electives that may be taken to fulfill major requirements. In addition, students may receive credit for the major, concentration, and interdepartmental majors only for those Barnard economics courses listed in this bulletin. However, students may not receive credit for two courses whose content overlaps. Barnard and Columbia economics electives with overlapping content include but are not limited to:

1. ECON BC3029 Economic development and W4321 Economic development
2. ECON BC3038 International monetary theory and W4505 International money and finance
3. ECON BC3019 Labor economics and W4400 Labor economics
4. ECON BC3047 International trade and W4500 International trade
5. ECON BC3039 Environmental and natural resource economics and W4625 Economics of the Environment
6. ECON BC3041 Theoretical foundations of political economy and G4235 Historical foundations of modern economics

Students should always first consult with an economics adviser to confirm that the Barnard elective they wish to take does not overlap with a Columbia elective that they have already taken or plan to take.  Students may not take the Barnard core economics, math, statistics, or seminar courses for credit towards the completion of the major requirements.

Continuing Education courses

The Department of Economics does not accept any of the courses offered through the School of Continuing Education for credit towards the economics major, concentration, or interdepartmental majors with the exception of the courses offered by the Economics Department during the summer session at Columbia. 

Other department and school courses

Please note that with the exception of the above Barnard courses, no other courses offered through the different departments and schools at Columbia count toward the economics majors or concentration.

Transfer credits

Students who declared in the fall of 2010 and prior to the fall of 2010:

No more than 12 transfer credits are accepted toward the economics major, concentration, or interdepartmental majors including credits toward the calculus and statistics requirements. 

Students who declared in the spring of 2011 and beyond:

Students are required to take a minimum number of courses in the Columbia Economics Department. For all majors and interdepartmental majors other than economics-philosophy major, students must complete a minimum of five lecture courses in the Columbia department. Students in the economics-philosophy major and economics concentration must complete a minimum of four courses. Students may fulfill their remaining requirements for economics lecture courses through AP (or IB) credits, Barnard electives, transfer courses, and study abroad courses (the latter two are subject to the approval of the Economics Department). The following table summarizes the new rules:

1. Lecture courses do not include seminars, which must be taken in the Columbia Economics Department. The lecture course counts are counts of economics courses onlyand do not include math, statistics, or courses in other departments.
2. At least two of the three 3000-level economics core courses must be taken in the department and no corresponding Barnard courses are accepted. ECON V3025 and V3265 are counted as departmental courses regardless of the instructor.
3. Outside courses include AP (or IB) credits, transfer credits, Barnard 2000- and 3000- level elective courses and transfer credits from other universities. In the case where two or more courses taken outside of Columbia are used as the equivalent of ECON W1105 Principles of economics, those courses are counted as one transfer course.

Approval of transfer credits to fulfill economics requirements must be obtained in writing from the Department of Economics (see the departmental website or speak with the advising dean for information regarding applications for transfer credit). Approval is granted only for courses that are considered to be comparable to those offered at Columbia.

Summer courses taken at other institutions must be approved in writing by the department's transfer credit adviser before the course is taken.  Summer courses taken from the department of economics do not need approval.

Instructions on how to request transfer credit approval can be found in the Transfer Credit Information page of the department’s website.

For a Major in Economics

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

The economics major requires a minimum of 32 points in economics, 6 points in mathematics, and 3 points in statistics, for a total of 41 points as follows:

1. Economics core courses (13 points)
2. Mathematics sequence (6 points)
3. Statistics (3 points)
4. Economics electives (15 points)
   • A minimum of five electives, of which no more than one may be taken at the 2000 level (including Barnard courses). 
5. Economics seminar (4 points)
6. Declared in Fall 2010 or prior: no more than three Barnard economics elective courses may be taken for major credit.
7. Declared in Spring 2011 or beyond: students must complete a minimum of five lecture courses in the Columbia Economics Department.
   

For a Concentration in Economics

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

The economics concentration requires a minimum of 22 points in economics, 6 points in mathematics, and 3 points in statistics, for a total of 31 points as follows:

1. Economics core courses (13 points)
2. Mathematics sequence (6 points)
3. Statistics (3 points)
4. Economics electives (9 points)
   
   • A minimum of three electives, of which no more than one may be taken at the 2000 level (including Barnard courses).
5. Declared in Fall 2010 or prior: no more than two Barnard economics elective courses may be taken for major credit.
6. Declared in Spring 2011 or beyond: students must complete a minimum of four lecture courses in the Columbia Economics Department
   

For a Major in Financial Economics

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

Financial markets and institutions play a critical role in shaping the real economy. The department of Economics in collaboration with the Business School is offering the major in financial economics that provides an academic framework in which to explore the role of financial markets and intermediaries in the allocation (and misallocation) of capital. Among the topics studied in financial economics are financial markets, banks and other financial intermediaries, asset valuation, portfolio allocation, regulation and corporate governance.
   The financial economics major requires 23 points in economics, 6 points in mathematics, 3 points in statistics, 3 points in business, and 12 points from a list of selected courses for a total of 47 points as follows:

1. Economics core courses (13 points)
2. Finance core courses (9 points). Students must complete the finance core no later than fall of their senior year.
   • ECON V3025 Financial economics
   • ECON W4280 Corporate Finance
   • BUSI W3013 Financial accounting (or IEOR E2261 Introduction to accounting and finance)
     
3. Mathematics sequence (6 points) see the mathematics requirement for the major
4. Statistics (3 points) see the statistics requirement for the major
5. Electives (12 points)
   
   • Four of the following (of which two must be from the Columbia or Barnard economics departments):
     
     • ECON V3265 Economics of money and banking
     • ECON W4020 Economics of uncertainty and information
     • ECON W4213 Advanced macroeconomics
     • ECON W4251 Industrial organization
     • ECON W4412 Advanced econometrics
       
     • ECON W4415 Game theory
       
     • ECON W4465 Public economics
       
     • 
       
     • ECON W4505 International monetary theory and policy or BC3038 International money and finance
       
     • ECON G4526 Transition reforms, globalization and financial crises
       
     • ECON BC3014 Entrepreneurship
       
     • ECON BC3017 Economics of business organizations
       
     • STAT W4290 Statistical methods in finance
       
     • STAT W4635 Stochastic processes for finance
       
     • STAT W4840 Theory of interest
       
     • MATH V3050 Discrete time models in finance
       
     • MATH W4077 Introduction to the mathematics of finance
       
     • IEOR E3106 Introduction to operations research: stochastic models
       
     • IEOR E4700 Introduction to financial engineering
       
     • BUSI W3021 Marketing management
       
     • BUSI W3701 Strategic behavior/strategy formulation
       
     • BUSI W3703 Leadership in organizations
       
     • BUSI W4412 Managerial negotiations
       
     • POLS W3630 The politics of international economic relations
6. Seminar (4 points)
   
   • The seminar must be chosen from a list of seminars eligible for the financial economics major. The department indicates which seminars are eligible for the major on the Senior Seminars page of the departmental Web site.
     
   • Students must have completed at least one of ECON V3025 or W4280 prior to taking their senior seminar.
7. Declared in spring 2011 or beyond: students must complete a minimum of five lecture courses in the Columbia Economics Department. At least two of the core finance courses must be taken at Columbia University.

For a Major in Economics-Mathematics

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

The major in economics and mathematics provides students with a grounding in economic theory comparable to that provided by the general economics major, while it also exposes students to rigorous and extensive training in mathematics. The program is recommended for any student planning to do graduate work in economics.

The Department of Economics has graduate student advisers that students may consult with on the economics requirements. The Department of Mathematics has an assigned adviser that students may consult with on the mathematics requirements. Please note that the economics adviser can only advise on the economics requirements and the mathematics adviser can only advise on the mathematics requirements.

The economics-mathematics major requires a total of 53 points: 26 points in economics and 27 points in mathematics and statistics as follows:

1. Economics core courses (13 points)
2. Economics electives (9 points)
   • Three electives at the 3000 level or above
3. Mathematics (24 points)
   • One of the following sequences:
     • MATH V1101, V1102, V1201 and V2010 Calculus I, II, III, and Linear algebra
     • MATH V1207 and V1208 Honors math A and B
   • MATH V2500 Analysis and optimization
   • Choose any three electives in mathematics from the following list:
     • MATH E1210 Ordinary differential equations
     • MATH V1202 Calculus IV
     • Any mathematics course at the 3000 level or above
4. Statistics (3 points)
   • One of the following:
     • SIEO W4150 Introduction to probability and statistics
     • STAT W3105 Introduction to statistics: probability models, and STAT W3107 Statistical inference
     • SIEO W4105 Probability and STAT W4107 Statistical inference
5. Economics seminar (4 points)
   
6. Declared in Fall 2010 or prior: no more than two Barnard economics elective courses may be taken for major credit.
7. Declared in Spring 2011 or beyond: students must complete a minimum of five lecture courses in the Columbia Economics Department
   

Notes: (1) Students who fulfill the statistics requirement with STAT W3105 and STAT W3107, or with SIEO W4105 and STAT W4107, may count STAT W3105 or SIEO W4105 as one of the three required mathematics electives.  (2) Students who choose either of the one year sequence (W3105/W3107 or W4105/W4107), must complete the year long sequence prior to taking W3412 Econometrics. Students receive elective credit for the probability course.

For a Major in Economics–Operations Research

The major in economics–operations research is closed to new students beginning in the fall of 2010. Students interested in this major should consider one of the two other quantitative interdepartmental majors (economics-statistics and economics-mathematics) or the new major in financial economics. Students who declared the economics–operations research major prior to the fall of 2010 are allowed to complete the major.

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

The major in economics and operations research provides students with a foundation in economic theory comparable to that provided by the general economics major, while it also introduces students to the field of operations research. The program is recommended for students with strong quantitative skills who are contemplating graduate studies in operations research or business.

The Department of Economics has graduate student advisers that students may consult with on the economics requirements. The Engineering school has an assigned adviser that students may consult with on the operations research requirements. Please note that the economics adviser can only advise on the economics requirements and the operations research adviser can only advise on the operations research requirements.

The economics–operations research major requires a total of 52 points: 23 points in economics, 12 points in mathematics, 14 points in industrial engineering and operations research (IEOR), and 3 points in computer science as follows:

1. Economics core courses (13 points)
2. Economics electives (6 points)
   • Two electives at the 3000 level or above, of which no more than one may be a Barnard course
3. Mathematics (12 points)
   • One of the following sequences:
     • MATH V1101, V1102, V1201 and V2010 Calculus I, II, III, and Linear algebra
     • MATH V1207 and V1208 Honors math A and
4. Industrial engineering and operations research (14 points)
   • IEOR E3600 Introduction to probability and statistics
   • IEOR E3608 Introduction to mathematical programming
   • IEOR E3106 or E4106 Introduction to operations research: stochastic models
   • One elective in operations research or statistics. (See The Fu Foundation School of Engineering and Applied Sciences Bulletin for complete listings)
5. Computer science (3 points)
   • One of the following:
     • COMS W1003 Introduction to computer science and programming in C
     • COMS W1004 (preferred) Introduction to computer science and programming in JAVA
     • COMS W1005 Introduction to computer science and programming in MATLAB
     • COMS W1007 Object-oriented programming and design in JAVA
6. Seminar (4 points)
   • ECON W4918 Seminar in econometrics

For a Major in Economics-Philosophy

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

Economics-philosophy is an interdisciplinary major that, while introducing students to the basic methodologies of economics and philosophy, stresses areas of particular concern to both. These include subjects such as rationality and decision making, justice and efficiency, freedom and collective choice, the logic of empirical theories and their testing. Many of the issues are dealt with historically, and classic texts of Plato, Kant, Mill, Marx, and Smith are reviewed.
   The Department of Economics has graduate student advisers that students may consult with on the economics requirements. The Department of Philosophy has an assigned adviser that students may consult with on the philosophy requirements. Please note that the economics adviser can only advise on the economics requirements and the philosophy adviser can only advise on the philosophy requirements.

The economics-philosophy major requires a total of 44 points: 16 points in economics, 15 points in philosophy, 6 points in mathematics, 3 points in statistics, and 4 points in the interdisciplinary seminar as follows:

1. Economics core courses (10 points)
   • ECON W1105 Principles of economics
   • ECON W3211 Intermediate microeconomics
   • ECON W3213 Intermediate macroeconomics
2. Mathematics sequence (6 points)
   
3. Statistics (3 points)
   
4. Economics electives (6 points)
   • Two of the following:
     • ECON W4020 Economics of uncertainty and information
     • ECON W4080 Globalization, incomes, and inequality
     • ECON W4211 Advanced microeconomics
     • ECON W4213 Advanced macroeconomics
     • ECON W4228 Urban economics
     • ECON G4235 (or BC3041) Historical foundations of modern economics
     • ECON G4301 Economic growth and development
     • ECON W4321 (or BC3029) Economic development
     • ECON W4329 Economics of sustainable development
     • ECON W4345 World economic problems
     • ECON W4370 Political economy
     • ECON W4400 (or BC3019) Labor economy
     • ECON W4415 Game theory
     • ECON W4438 Economics of race in the United States
     • ECON W4465 Public economics
     • ECON W4480 Gender and applied economics
     • ECON W4500 (or BC3047) International trade
     • ECON W4615 Law and economics
     • ECON W4625 (or BC3039) Economics of the environment
     • ECON W4750 Globalization and its risks
     • ECON BC3011 Inequality and poverty
5. Philosophy courses (15 points)
   • PHIL C1010 Methods and problems of philosophical thought
   • PHIL V3411 Symbolic logic
   • PHIL V3701 Moral philosophy (or another adviser-approved course in moral or political philosophy)
   • PHIL W3551 (or another adviser-approved course in epistemology or philosophy of science)
   • One of the following:
     • PHIL G4561 Probability and induction
     • PHIL G4565 Rational choice
6. Seminar (4 points)
   
   • ECPH W4950 Economics and philosophy seminar (or another seminar in philosophy or economics approved by advisers in both departments)
7. Declared in Spring 2011 or beyond: students must complete a minimum of four lecture courses in the Columbia Economics Department.

For a Major in Economics–Political Science

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

Political economy is an interdisciplinary major that introduces students to the methodologies of economics and political science and stresses areas of particular concern to both. This program is particularly beneficial to students planning to do graduate work in schools of public policy and international affairs.

The Department of Economics has graduate student advisers that students may consult with on the economics requirements. The Department of Political Science has an assigned adviser that students may consult with on the political science requirements. Please note that the economics adviser can only advise on the economics requirements and the political science adviser can only advise on the political science requirements.

The economics–political science major requires a total of 54 points: 19 points in economics, 15 points in political science, 6 points in mathematics, 6 points in statistical methods, 4 points in a political science seminar, and 4 points in the interdisciplinary seminar as follows. The political science courses are grouped into three areas: (1) American politics, (2) comparative politics, and (3) international relations. For the political science part of the major, students are required to select one area as a major field and one as a minor field. The corresponding introductory courses in both fields must be taken, plus two electives in the major, and one in the minor field.

1. Economics core courses (13 points)
   • ECON W1105 Principles of economics
   • ECON W3211 Intermediate microeconomics
   • ECON W3213 Intermediate macroeconomics
   • ECON W4370 Political economy
2. Mathematics sequence (6 points)
3. Statistical methods (6 points)
   • One of the following:
     • ECON W3412 Introduction to econometrics and one of the statistics courses listed under Regulations for Economics Majors, Concentrators, and Interdepartmental Majors.
     • POLS W4911 Analysis of political data and one of the statistics course listed under Regulations for Economics Majors, Concentrators, and Interdepartmental Majors or POLS W4910 Principles of quantitative political research.
4. Economics electives (6 points)
   • Two electives at the 3000 level or above
     
5. Political science courses (15 points)
   • Major subfield: 9 points, including the introductory course, all in one of the three subfields of American politics, comparative politics, or international relations, coordinated with the economics electives and approved in advance by the adviser
   • Minor subfield: 6 points of courses, including the introductory course in another subfield, coordinated with the economics electives and approved by the adviser
6. Seminars (8 points)
   
   • A Political Science Department seminar, to be approved in advance by the adviser, in the major subfield.
   • ECON W4921 Seminar in political economy
7. Declared in Fall 2010 or prior: no more than one Barnard economics elective course may be taken for major credit.
   
8. Declared in Spring 2011 or beyond: students must complete a minimum of five lecture courses in the Columbia department.
   
   

Note: POLS W4910 is not equivalent to STAT W1211 and as such cannot be used to fulfill the prerequisite requirements of courses that require STAT W1211 such as ECON W3412, ECON V3025, ECON W4280 and ECON W4020.

For a Major in Economics-Statistics

Please read Regulations for all Economics Majors, Concentrators, and Interdepartmental Majors above.

The major in economics and statistics provides students with a grounding in economic theory comparable to that provided by the general economics major, yet additionally exposes students to a significantly more rigorous and extensive statistics training than is provided by the general major. This program is recommended for students with strong quantitative skills and for those students who are contemplating graduate studies in economics.

The Department of Economics has graduate student advisers that students may consult with on the economics requirements. The Department of Statistics has an assigned adviser that students may consult with on the statistics requirements. Please note that the economics adviser can only advise on the economics requirements and the statistics adviser can only advise on the statistics requirements.

The economics-statistics major requires a total of 53 points: 23 in economics, 15 points in statistics, 12 points in mathematics, and 3 points in computer science as follows:

1. Economics core courses (13 points)
2. Economics electives (6 points)
   • Two electives at the 3000 level or above
3. Mathematics (12 points)
   • One of the following sequences:
     • MATH V1101, V1102, V1201 and V2010 Calculus I, II, III, and Linear algebra
     • MATH V1207 and V1208 Honors math A and B
4. Statistics (15 points)
   • STAT W1211 Introduction to statistics (with calculus)
   • STAT W3105 Introduction to statistics: probability models
   • STAT W3107 Statistical inference
   • STAT W4315 Linear regression models
   • One elective (excluding STAT W1001, W1111, W2110 and SIEO W4150)
5. Computer science (3 points)
   • One of the following:
     • COMS W1003 Introduction to computer science and programming in C
     • COMS W1004 (preferred) Introduction to computer science and programming in JAVA
     • COMS W1005 Introduction to computer science and programming in MATLAB
     • COMS W1007 Object-oriented programming and design in JAVA
6. ECON W4918 Seminar in econometrics (4 points)
7. Declared in Fall 2010 or prior: no more than one Barnard economics elective course may be taken for major credit.
8. Declared in Spring 2011 or beyond: students must complete a minimum of five lecture courses in the Columbia Economics Department.