# Economics & Mathematics

http://economics.barnard.edu/majors/descriptions/economics-mathematics-major

208 LeFrak Center, Barnard Hall

212-854-3454

Department Administrator: Robert O'Connor

## Mission

The Economics and Mathematics major provides the student with a grounding in economic theory comparable to that provided by the general economics major and exposes the student to rigorous and extensive training in mathematics. The program will be particularly useful for students planning to do graduate work in economics, which frequently demands greater mathematical training than that acquired through the minimum requirements of the basic economics degree.

**Economics Department Representative:** Sharon Harrison

**Mathematics Department Representative:** David Bayer

## Requirements for the Major

A major in Economics and Mathematics must complete the following 15 courses or their equivalents:

Code | Title | Points |
---|---|---|

Economics (8 courses) | ||

ECON BC1003 | Introduction to Economic Reasoning | 3 |

ECON BC3018 | Econometrics | 4 |

ECON BC3033 | Intermediate Macroeconomic Theory | 4 |

ECON BC3035 | Intermediate Microeconomic Theory | 4 |

ECON BC3041 | Theoretical Foundations of Political Economy | 3 |

Select one of the following: | 4 | |

Senior Thesis II (two semesters of the Senior Thesis are optional) | ||

Senior Seminar ^{*} | ||

Two economics electives with an intermediate micro- or macroeconomic theory course as prerequisite | ||

Mathematics (7 courses) | ||

MATH UN1102 - MATH UN1201 | Calculus II and Calculus III | 6 |

MATH UN2010 | Linear Algebra | 3 |

MATH UN2500 | Analysis and Optimization ^{**} | 3 |

SIEO W3600 | Introduction to Probability and Statistics (or STAT GU4001) | 4 |

Two electives at or above the 2000 level ^{***} |

* | MATH UN3951 Undergraduate Seminars in Mathematics I, or an equivalent approved by the Chairs of the Mathematics and Economic departments is an acceptable alternative to ECON BC3063 Senior Seminar. |

** | MATH GU4061 Introduction To Modern Analysis I is an acceptable alternative to MATH UN2500 Analysis and Optimization. |

*** | MATH UN2030 Ordinary Differential Equations is an approved Mathematics elective. Also approved is MATH UN3951 Undergraduate Seminars in Mathematics I. |

Students must obtain approval from each department representative before selecting electives. In exceptional cases, these may be from related fields; other courses can be taken with prior approval.

## Cross-Listed Courses

### Economics (Barnard)

**ECON BC3018 Econometrics.** *4 points*.

Prerequisites: ECON BC3033 or ECON BC3035, and ECON BC2411 or STAT W1111 or STAT W1211, or permission of the instructor.

Specification, estimation and evaluation of economic relationships using economic theory, data, and statistical inference; testable implications of economic theories; econometric analysis of topics such as consumption, investment, wages and unemployment, and financial markets.

Fall 2017: ECON BC3018 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ECON 3018 | 001/01690 | M W 11:40am - 12:55pm 903 Altschul Hall |
Anja Tolonen | 4 | 35/45 |

Spring 2018: ECON BC3018 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

ECON 3018 | 001/04759 | T Th 8:40am - 9:55am Room TBA |
Homa Zarghamee | 4 | 45/45 |

**ECON BC3033 Intermediate Macroeconomic Theory.** *4 points*.

Prerequisites: An introductory course in economics and a functioning knowledge of high school algebra and analytical geometry or permission of the instructor.

Systematic exposition of current macroeconomic theories of unemployment, inflation, and international financial adjustments.

Fall 2017: ECON BC3033 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ECON 3033 | 001/06157 | T Th 6:10pm - 7:25pm 504 Diana Center |
Andre Burgstaller | 4 | 19 |

Spring 2018: ECON BC3033 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

ECON 3033 | 001/06157 | M W 1:10pm - 2:25pm Room TBA |
Luis Silva-Yanez | 4 | 31/50 |

**ECON BC3035 Intermediate Microeconomic Theory.** *4 points*.

Prerequisites: An introductory course in microeconomics or a combined macro/micro principles course (ECON BC1003 or ECON W1105, or the equivalent) and one semester of calculus or ECON BC1007, or permission of the instructor.

Preferences and demand; production, cost, and supply; behavior of markets in partial equilibrium; resource allocation in general equilibrium; pricing of goods and services under alternative market structures; implications of individual decision-making for labor supply; income distribution, welfare, and public policy. Emphasis on problem solving.

Fall 2017: ECON BC3035 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ECON 3035 | 001/04588 | T Th 4:10pm - 5:25pm 302 Barnard Hall |
Lalith Munasinghe | 4 | 41/60 |

Spring 2018: ECON BC3035 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

ECON 3035 | 001/04588 | T Th 6:10pm - 7:25pm 323 Milbank Hall |
Lalith Munasinghe | 4 | 45/50 |

**ECON BC3041 Theoretical Foundations of Political Economy.** *3 points*.

BC: Fulfillment of General Education Requirement: Reason and Value (REA)., BC: Fulfillment of General Education Requirement: Ethics and Values.

Prerequisites: An introductory course in economics or permission of the instructor.

Intellectual origins of the main schools of thought in political economy. Study of the founding texts in classical political economy, Marxian economics, neoclassicism, and Keynesianism.

Fall 2017: ECON BC3041 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ECON 3041 | 001/07742 | T Th 10:10am - 11:25am 328 Milbank Hall |
David Weiman | 3 | 33/45 |

ECON 3041 | 002/08111 | T Th 8:40am - 9:55am Ll104 Diana Center |
Belinda Archibong | 3 | 35/45 |

Spring 2018: ECON BC3041 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

ECON 3041 | 001/07742 | M W 4:10pm - 5:25pm Room TBA |
Sonia Pereira | 3 | 45/45 |

**ECON BC3061 Senior Thesis I.** *4 points*.

Prerequisites: Permission of the instructor and completion of all courses (except for the senior requirement) required for the economics track, political economy track, or economics and mathematics majors. Exceptions to these prerequisites may be granted by the chair of the department only.

Tutorials and conferences on the research for and writing of the senior thesis. This is the 1st semester of a two-semester course sequence.

Fall 2017: ECON BC3061 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ECON 3061 | 001/03575 | |
Sonia Pereira | 4 | 8 |

ECON 3061 | 002/05329 | Th 2:10pm - 4:00pm 303 Altschul Hall |
Randall Reback | 4 | 6 |

ECON 3061 | 003/04820 | W 9:00am - 10:50am 118 Barnard Hall |
David Weiman | 4 | 1 |

ECON 3061 | 004/04872 | |
0. FACULTY | 4 | 0 |

Spring 2018: ECON BC3061 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

ECON 3061 | 001/04029 | |
4 | 0 |

**ECON BC3062 Senior Thesis II.** *4 points*.

Prerequisites: Permission of the instructor and completion of all courses (except for the senior requirement) required for the economics track, political economy track, or economics and mathematics majors. Exceptions to these prerequisites may be granted by the chair of the department only.

Tutorials and conferences on the research for and writing of the senior thesis. This is the 2nd semester of a two-semester course sequence.

Spring 2018: ECON BC3062 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ECON 3062 | 001/04590 | |
Sonia Pereira | 4 | 6 |

ECON 3062 | 002/03966 | Th 2:10pm - 4:00pm Room TBA |
Randall Reback | 4 | 4 |

ECON 3062 | 003/08224 | |
David Weiman | 4 | 1 |

ECON 3062 | 004/01944 | |
4 | 0 |

**ECON BC3063 Senior Seminar.** *4 points*.

Prerequisites: Permission of the instructor and the completion of all courses (except for the senior requirement) required for the economics track, political economy track, or economics and mathematics majors. Exceptions to these prerequisites may be granted by the chair of the department only. Seminar sections are limited to 15 students.

A topic in economic theory or policy of the instructor’s choice. See department for current topics and for senior requirement preference forms.

Fall 2017: ECON BC3063 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

ECON 3063 | 001/03378 | T 4:10pm - 6:00pm 501 Diana Center |
Rajiv Sethi | 4 | 16 |

ECON 3063 | 002/06514 | Th 2:10pm - 4:00pm 203 Diana Center |
Belinda Archibong | 4 | 13 |

Spring 2018: ECON BC3063 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

ECON 3063 | 001/02840 | Th 11:00am - 12:50pm Room TBA |
Homa Zarghamee | 4 | 16 |

ECON 3063 | 002/05970 | T 4:10pm - 6:00pm 117 Barnard Hall |
Lalith Munasinghe | 4 | 7 |

ECON 3063 | 003/02843 | M 2:10pm - 4:00pm Room TBA |
Anja Tolonen | 4 | 13 |

### Mathematics

**MATH UN1101 Calculus I.** *3 points*.

*Prerequisites: (see Courses for First-Year Students).* Functions, limits, derivatives, introduction to integrals, or an understanding of pre-calculus will be assumed.

The Help Room in 333 Milbank Hall (Barnard College) is open during the day, Monday through Friday, to students seeking individual help from the teaching assistants. **(SC)**

Fall 2017: MATH UN1101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1101 | 001/07384 | M W 8:40am - 9:55am 405 Milbank Hall |
Dusa McDuff | 3 | 91/110 |

MATH 1101 | 002/17570 | M W 10:10am - 11:25am 312 Mathematics Building |
Chao Li | 3 | 108/116 |

MATH 1101 | 003/29604 | M W 11:40am - 12:55pm 312 Mathematics Building |
Chao Li | 3 | 116/116 |

MATH 1101 | 004/73071 | M W 2:40pm - 3:55pm 417 Mathematics Building |
Michael Woodbury | 3 | 48/64 |

MATH 1101 | 005/18565 | M W 4:10pm - 5:25pm 417 Mathematics Building |
Michael Woodbury | 3 | 50/64 |

MATH 1101 | 006/73884 | T Th 10:10am - 11:25am 407 Mathematics Building |
Oleksandr Kravets | 3 | 28/35 |

MATH 1101 | 007/26909 | T Th 11:40am - 12:55pm 407 Mathematics Building |
Shuai Wang | 3 | 26/30 |

MATH 1101 | 008/64016 | T Th 1:10pm - 2:25pm 517 Hamilton Hall |
Alexander Perry | 3 | 75/100 |

MATH 1101 | 009/21826 | T Th 4:10pm - 5:25pm 203 Mathematics Building |
Ila Varma | 3 | 80/100 |

MATH 1101 | 010/67061 | T Th 6:10pm - 7:25pm 207 Mathematics Building |
Linh Truong | 3 | 29/100 |

Spring 2018: MATH UN1101 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1101 | 001/67358 | M W 10:10am - 11:25am Room TBA |
Zhi Li | 3 | 30/30 |

MATH 1101 | 002/16721 | M W 4:10pm - 5:25pm Room TBA |
Zhongyi Zhang | 3 | 30/30 |

MATH 1101 | 003/76347 | M W 6:10pm - 7:25pm Room TBA |
Chao Li | 3 | 89/100 |

MATH 1101 | 004/16914 | T Th 11:40am - 12:55pm Room TBA |
Monica Marinescu | 3 | 30/30 |

**MATH UN1102 Calculus II.** *3 points*.

Prerequisites: MATH UN1101 or the equivalent.

Methods of integration, applications of the integral, Taylor's theorem, infinite series. (SC)

Fall 2017: MATH UN1102 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1102 | 001/67192 | M W 10:10am - 11:25am 417 Mathematics Building |
Bin Guo | 3 | 59/64 |

MATH 1102 | 002/70122 | M W 2:40pm - 3:55pm 312 Mathematics Building |
Li-Cheng Tsai | 3 | 50/100 |

MATH 1102 | 003/26180 | M W 4:10pm - 5:25pm 407 Mathematics Building |
Yi Sun | 3 | 29/35 |

MATH 1102 | 004/22286 | T Th 10:10am - 11:25am 203 Mathematics Building |
Vivek Pal | 3 | 86/100 |

MATH 1102 | 005/29410 | T Th 6:10pm - 7:25pm 407 Mathematics Building |
Renata Picciotto | 3 | 21/30 |

Spring 2018: MATH UN1102 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1102 | 001/18873 | M W 11:40am - 12:55pm Room TBA |
Elena Giorgi | 3 | 30/30 |

MATH 1102 | 002/19504 | M W 6:10pm - 7:25pm Room TBA |
Vivek Pal | 3 | 100/100 |

MATH 1102 | 003/21419 | T Th 2:40pm - 3:55pm Room TBA |
Ivan Danilenko | 3 | 30/30 |

**MATH UN1201 Calculus III.** *3 points*.

Prerequisites: MATH UN1101 or the equivalent

Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramer's rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Fall 2017: MATH UN1201 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1201 | 001/27988 | M W 10:10am - 11:25am 203 Mathematics Building |
Joanna Nelson | 3 | 87/105 |

MATH 1201 | 002/15820 | M W 11:40am - 12:55pm 203 Mathematics Building |
Teng Fei | 3 | 51/100 |

MATH 1201 | 003/62151 | M W 1:10pm - 2:25pm 203 Mathematics Building |
Joanna Nelson | 3 | 86/105 |

MATH 1201 | 004/68024 | M W 4:10pm - 5:25pm 312 Mathematics Building |
Jeffrey Kuan | 3 | 100/116 |

MATH 1201 | 005/06129 | T Th 8:40am - 9:55am 304 Barnard Hall |
Daniela De Silva | 3 | 102/110 |

MATH 1201 | 006/63259 | T Th 4:10pm - 5:25pm 312 Mathematics Building |
Akram Alishahi | 3 | 60/100 |

MATH 1201 | 007/27974 | T Th 5:40pm - 6:55pm 312 Mathematics Building |
Akram Alishahi | 3 | 22/100 |

Spring 2018: MATH UN1201 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1201 | 001/05518 | M W 8:40am - 9:55am 304 Barnard Hall |
0. FACULTY | 3 | 66/100 |

MATH 1201 | 002/76403 | M W 10:10am - 11:25am Room TBA |
Igor Krichever | 3 | 100/100 |

MATH 1201 | 003/67090 | M W 11:40am - 12:55pm Room TBA |
Shrenik Shah | 3 | 72/100 |

MATH 1201 | 004/29982 | M W 1:10pm - 2:25pm Room TBA |
Shrenik Shah | 3 | 96/100 |

MATH 1201 | 005/14673 | T Th 6:10pm - 7:25pm Room TBA |
Elliott Stein | 3 | 30/30 |

**MATH UN2010 Linear Algebra.** *3 points*.

Prerequisites: MATH UN1201 or the equivalent.

Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)

Fall 2017: MATH UN2010 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2010 | 001/27023 | M W 4:10pm - 5:25pm 207 Mathematics Building |
Nathan Dowlin | 3 | 99/120 |

MATH 2010 | 002/25355 | M W 1:10pm - 2:25pm 312 Mathematics Building |
Gus Schrader | 3 | 59/100 |

MATH 2010 | 003/03818 | T Th 8:40am - 9:55am 405 Milbank Hall |
David Bayer | 3 | 68/100 |

MATH 2010 | 004/02940 | T Th 10:10am - 11:25am 405 Milbank Hall |
David Bayer | 3 | 77/100 |

MATH 2010 | 005/18445 | T Th 6:10pm - 7:25pm 203 Mathematics Building |
Elliott Stein | 3 | 81/108 |

Spring 2018: MATH UN2010 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 2010 | 001/14202 | M W 8:40am - 9:55am Room TBA |
Gus Schrader | 3 | 65/100 |

MATH 2010 | 002/20875 | M W 10:10am - 11:25am Room TBA |
Guillaume Barraquand | 3 | 100/100 |

MATH 2010 | 003/27803 | M W 1:10pm - 2:25pm Room TBA |
Guillaume Barraquand | 3 | 100/100 |

MATH 2010 | 004/20676 | T Th 8:40am - 9:55am Room TBA |
Teng Fei | 3 | 27/100 |

MATH 2010 | 005/71356 | T Th 10:10am - 11:25am Room TBA |
Teng Fei | 3 | 37/100 |

**MATH UN2030 Ordinary Differential Equations.** *3 points*.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent.

Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.

Fall 2017: MATH UN2030 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2030 | 001/23233 | M W 5:40pm - 6:55pm 203 Mathematics Building |
Hector Chang-Lara | 3 | 28/100 |

MATH 2030 | 002/12064 | T Th 11:40am - 12:55pm 312 Mathematics Building |
Guillaume Barraquand | 3 | 57/100 |

Spring 2018: MATH UN2030 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 2030 | 001/83046 | T Th 1:10pm - 2:25pm Room TBA |
Xin Sun | 3 | 97/100 |

MATH 2030 | 002/15654 | T Th 2:40pm - 3:55pm Room TBA |
3 | 64/100 |

**MATH UN2500 Analysis and Optimization.** *3 points*.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010.

Mathematical methods for economics. Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus of variations and optimal control. (SC)

Fall 2017: MATH UN2500 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2500 | 001/73444 | M W 11:40am - 12:55pm 413 Kent Hall |
Shotaro Makisumi | 3 | 44/100 |

MATH 2500 | 002/26047 | M W 2:40pm - 3:55pm 203 Mathematics Building |
Shotaro Makisumi | 3 | 63/100 |

Spring 2018: MATH UN2500 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 2500 | 001/10629 | T Th 8:40am - 9:55am Room TBA |
3 | 45/100 | |

MATH 2500 | 002/17561 | T Th 10:10am - 11:25am Room TBA |
3 | 61/100 |

**MATH UN3951 Undergraduate Seminars in Mathematics I.** *3 points*.

Prerequisites: Two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.

The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow.

Fall 2017: MATH UN3951 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3951 | 001/02944 | |
Daniela De Silva | 3 | 30/49 |

**MATH GU4061 Introduction To Modern Analysis I.** *3 points*.

Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first.

Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.

Fall 2017: MATH GU4061 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4061 | 001/62851 | M W 8:40am - 9:55am 417 Mathematics Building |
Bin Guo | 3 | 39/64 |

MATH 4061 | 002/73447 | T Th 2:40pm - 3:55pm 417 Mathematics Building |
Patrick Gallagher | 3 | 40/64 |

Spring 2018: MATH GU4061 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 4061 | 001/14621 | M W 1:10pm - 2:25pm Room TBA |
Hui Yu | 3 | 43/64 |

MATH 4061 | 002/67480 | M W 4:10pm - 5:25pm Room TBA |
Hui Yu | 3 | 38/49 |

### Statistics

**SIEO W3600 Introduction to Probability and Statistics.** *4 points*.

Lect: 3. Recit: 1.

Prerequisites: Calculus.

*For undergraduates only. This course is required for undergraduate students majoring in IE, OR:EMS, and OR. This class must be taken during the fourth semester.* Fundamentals of probability and statistics used in engineering and applied science. Probability: random variables, useful distributions, expectations, law of large numbers, central limit theorem. Statistics: point and confidence interval estimation, hypothesis tests, linear regression. SIEO W3600 must be completed by the fourth term. Only students with special academic circumstances may be allowed to take these courses in alternative semesters with the consultation of CSA and Departmental advisors. Recitation section required.

**STAT GU4001 Introduction to Probability and Statistics.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: Calculus through multiple integration and infinite sums.

A calculus-based tour of the fundamentals of probability theory and statistical inference. Probability models, random variables, useful distributions, conditioning, expectations, law of large numbers, central limit theorem, point and confidence interval estimation, hypothesis tests, linear regression. This course replaces SIEO 4150.

Fall 2017: STAT GU4001 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4001 | 001/65735 | Sa 10:10am - 12:55pm 312 Mathematics Building |
Daniel Rabinowitz | 3 | 74/120 |

STAT 4001 | 002/62655 | M W 2:40pm - 3:55pm 614 Schermerhorn Hall |
Mark Brown | 3 | 83/120 |

Spring 2018: STAT GU4001 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4001 | 001/61149 | T Th 1:10pm - 2:25pm Room TBA |
David Rios | 3 | 146/150 |