Operations Research (BS)
The operations research program is one of several applied science programs offered at the School. At the undergraduate level, it offers basic courses in probability, statistics, applied mathematics, simulation, and optimization as well as more professionally oriented operations research courses. The curriculum is well suited for students with an aptitude for mathematics applications.
It prepares graduates for professional employment as operations research analysts, e.g., with management consultant and financial service organizations, as well as for graduate studies in operations research or business. It is flexible enough to be adapted to the needs of future medical and law students.
Operations Research: Analytics
The analytics concentration within the operations research program seeks to train students to leverage advanced quantitative models, algorithms, and data for making actionable decisions to improve business operations. Examples include staffing and scheduling at hospitals, ride matching and pricing for on-demand car services, personalized promotions in online retail, and smarter energy consumption. Students are provided with a rigorous exposure to optimization and stochastic modeling, as well as machine learning and data analysis tools for predictive modeling and prescriptive analytics. Electives in the areas of healthcare, marketing, transportation, deep learning, and many others further enrich students with domain expertise, and provide many opportunities to work directly with data on real-world problems.
Operations Research: Engineering Management Systems
This operations research option is designed to provide students with an understanding of contemporary technology and management. It is for students who are interested in a technical-management background rather than one in a traditional engineering field. It consists of required courses in industrial engineering and operations research, economics, business, and computer science, intended to provide a foundation for dealing with engineering and management systems problems. Elective courses are generally intended to provide a substantive core in at least one technology area and at least one management area.
Due to the flexibility of this option, it can incorporate the varied educational needs of preprofessional students interested in law, medicine, business, and finance. In addition, most students are encouraged to add a minor in economics or computer science to their standard course schedules.
Operations Research: Financial Engineering
The operations research concentration in financial engineering is designed to provide students with an understanding of the application of engineering methodologies and quantitative methods to finance. Financial engineering is a multidisciplinary field integrating financial theory with economics, methods of engineering, tools of mathematics, and practice of programming. Students graduating with this concentration are prepared to enter careers in securities, banking, financial management, and consulting industries, and fill quantitative roles in corporate treasury and finance departments of general manufacturing and service firms.
Students who are interested in pursuing the rigorous concentration in financial engineering must demonstrate proficiency in calculus, computer programming, linear algebra, ordinary differential equations, probability, and statistics.
Operations Research Program
Students must complete a total of 128 points to graduate. An overview of the degree track in PDF format can be found here.
First and Second Year Degree Track: All IEOR Degree Programs
| First Year | ||
|---|---|---|
| Semester I | ||
| MATH UN1101 | CALCULUS I | |
| Choose one of the following Physics courses depending on track: | ||
| INTRO TO MECHANICS ＆ THERMO | ||
| PHYSICS I:MECHANICS/RELATIVITY | ||
| ACCELERATED PHYSICS I | ||
| Choose one of the following Chemistry courses (taken Semester l or ll): | ||
| GENERAL CHEMISTRY I-LECTURES | ||
| GENERAL CHEMISTRY II-LECTURES | ||
| 2ND TERM GEN CHEM (INTENSIVE) | ||
| INTENSVE ORGANIC CHEMISTRY | ||
| ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
| ECON UN1105 - ECON UN1155 (taken Semester l or ll) | PRINCIPLES OF ECONOMICS | |
| ENGI E1006 (taken Semester l or ll)2 | INTRO TO COMP FOR ENG/APP SCI | |
| PHED UN1001 | ||
| ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
| Semester II | ||
| MATH UN1102 | CALCULUS II | |
| Choose one of the following Physics courses depending on track: | ||
| INTRO ELEC/MAGNETSM ＆ OPTCS | ||
| PHYSICS II: THERMO, ELEC ＆ MAG | ||
| ACCELERATED PHYSICS II | ||
| Choose one of the following Chemistry courses (taken Semester l or ll): | ||
| GENERAL CHEMISTRY I-LECTURES | ||
| GENERAL CHEMISTRY II-LECTURES | ||
| 2ND TERM GEN CHEM (INTENSIVE) | ||
| INTENSVE ORGANIC CHEMISTRY | ||
| ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
| ECON UN1105 - ECON UN1155 (taken Semester l or ll) | PRINCIPLES OF ECONOMICS | |
| ENGI E1006 (taken Semester l or ll)2 | INTRO TO COMP FOR ENG/APP SCI | |
| PHED UN1002 | ||
| ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
| Second Year | ||
| Semester III | ||
| APMA E2000 - APMA E2001 | MULTV. CALC. FOR ENGI ＆ APP SCI | |
| Choose one of the following Chemistry or Physics labs: | ||
| INTRO TO EXPERIMENTAL PHYS-LAB | ||
| INTERMEDIATE LABORATORY WORK | ||
| GENERAL CHEMISTRY LABORATORY | ||
| INTENSVE GENERAL CHEMISTRY-LAB | ||
| PHYSICL-ANALYTICL LABORATORY I | ||
| Choose one of the following Required Nontechnical Electives: | ||
| EURPN LIT-PHILOS MASTERPIECS I | ||
| CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
| HUMA UN1121 or UN1123 (taken Semester lll or lV) | MASTERPIECES OF WESTERN ART | |
| IEOR E3658 (taken Semester lll or lV) | PROBABILITY FOR ENGINEERS | |
| Semester IV | ||
| Linear algebra1 | ||
| Choose one of the following Required Nontechnical Electives: | ||
| EURPN LIT-PHILOS MASTRPIECS II | ||
| CONTEMP WESTRN CIVILIZATION II | ||
Global Core (3–4) | ||
| HUMA UN1121 or UN1123 (taken Semester lll or lV) | MASTERPIECES OF WESTERN ART | |
| IEOR E3658 (taken Semester lll or lV) | PROBABILITY FOR ENGINEERS | |
| IEOR E20003 | Data Engineering with Python | |
- 1
The linear algebra requirement may be filled by either MATH UN2010 LINEAR ALGEBRA or APMA E3101 APPLIED MATH I: LINEAR ALGEBRA or COMS W3251 COMPUTATIONAL LINEAR ALGEBRA.
- 2
ENGI E1006 INTRO TO COMP FOR ENG/APP SCI can be replaced by COMS W1004 Introduction to Computer Science and Programming in Java.
- 3
IEOR E2000 Data Engineering with Python can be replaced by COMS W3134 Data Structures in Java and COMS W4111 INTRODUCTION TO DATABASES. Students cannot get credit for IEOR E2000 Data Engineering with Python if IEOR E2000 Data Engineering with Python is taken after COMS W3134 Data Structures in Java and COMS W4111 INTRODUCTION TO DATABASES.
Third and Fourth Year Degree Track: Operations Research
| Third Year | ||
|---|---|---|
| Semester V | ||
| Required courses:1 | ||
| STOCHASTIC SYSTEMS AND APPLICATIONS | ||
| FOUNDATIONS OF OPTIMIZATION | ||
| STATISTICS AND DATA ANALYSIS | ||
| Nontech Electives: (Students must complete the 27-point requirement. Please refer to https://bulletin-next.columbia.edu/columbia-engineering/undergraduate-studies/undergraduate-programs/first-year-sophomore-program/) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Semester VI | ||
| Required courses:1 | ||
| PRODUCTN-INVENTORY PLAN-CONTRL | ||
| SIMULATION MODELING AND ANALYSIS | ||
| ADVANCED OPTIMIZATION | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Fourth Year | ||
| Semester VII | ||
| Required courses:4 | ||
| GAME THEOR MODELS OF OPERATION | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
| Semester VIII | ||
| Required courses:4 | ||
| PRODUCTION SCHEDULING | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
- 1
Taking required courses later than the prescribed semester is not permitted.
- 2
15 points total. At least 6 points need to be at least 3000 level with the prefix IEOR, ORCS, or CSOR. The complete list is available at ieor.columbia.edu/undergraduate/electives.
- 3
3 points total. Cannot double-count non-technical electives. The complete list is available at ieor.columbia.edu/undergraduate/electives.
Third and Fourth Year Degree Track: Operations Research: Analytics
| Third Year | ||
|---|---|---|
| Semester V | ||
| Required courses:1 | ||
| STOCHASTIC SYSTEMS AND APPLICATIONS | ||
| FOUNDATIONS OF OPTIMIZATION | ||
| STATISTICS AND DATA ANALYSIS | ||
| Data Analytics ＆ Machine Learning for OR | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Semester VI | ||
| Required courses:1 | ||
| SIMULATION MODELING AND ANALYSIS | ||
| ADVANCED OPTIMIZATION | ||
| BUSINESS ANALYTICS | ||
| Policy for Privacy Technologies | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Fourth Year | ||
| Semester VII | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
| Semester VIII | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
- 1
Taking required courses later than the prescribed semester is not permitted.
- 2
15 points total. At least 6 points need to be at least 3000 level with the prefix IEOR, ORCS, or CSOR. The complete list is available at ieor.columbia.edu/undergraduate/electives.
- 3
3 points total. Cannot double-count non-technical electives. The complete list is available at ieor.columbia.edu/undergraduate/electives.
Third and Fourth Year Degree Track: Operations Research Program: Engineering Management Systems
| Third Year | ||
|---|---|---|
| Semester V | ||
| Required courses:1 | ||
| STOCHASTIC SYSTEMS AND APPLICATIONS | ||
| FOUNDATIONS OF OPTIMIZATION | ||
| STATISTICS AND DATA ANALYSIS | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Semester VI | ||
| Required courses:1 | ||
| PRODUCTN-INVENTORY PLAN-CONTRL | ||
| SIMULATION MODELING AND ANALYSIS | ||
| ADVANCED OPTIMIZATION | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Fourth Year | ||
| Semester VII | ||
| Required courses:1 | ||
| CORPORATE FINANCE FOR ENGINEERS | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
| Semester VIII | ||
| Required courses:1 | ||
| MANAG TECH INNOV ＆ ENTREPRENEURSHIP | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (15 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (3 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
- 1
Taking required courses later than the prescribed semester is not permitted.
- 2
15 points total. At least 6 points need to be at least 3000 level with the prefix IEOR, ORCS, or CSOR. The complete list is available at ieor.columbia.edu/undergraduate/electives.
- 3
3 points total. Cannot double-count non-technical electives. The complete list is available at ieor.columbia.edu/undergraduate/electives.
Third and Fourth Year Degree Track: Operations Research Program: Financial Engineering
| Third Year | ||
|---|---|---|
| Semester V | ||
| Required courses:4 | ||
| STOCHASTIC SYSTEMS AND APPLICATIONS | ||
| FOUNDATIONS OF OPTIMIZATION | ||
| CORPORATE FINANCE FOR ENGINEERS | ||
| STATISTICS AND DATA ANALYSIS | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (12 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (6 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Semester VI | ||
| Required courses:1 | ||
| SIMULATION MODELING AND ANALYSIS | ||
| ADVANCED OPTIMIZATION | ||
| INTRO TO FINANCIAL ENGINEERING | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (12 points) (taken Semester V, Vl, Vll, or Vlll)2 | ||
| Management Electives (6 points) (taken Semester V, Vl, Vll, or Vlll)3 | ||
| Fourth Year | ||
| Semester VII | ||
| Required courses:1 | ||
| APPLICATIONS PROGRAMMNG FOR FE | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (12 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (6 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
| Semester VIII | ||
| Nontech Electives: (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll) | ||
| Tech Electives (12 points) (taken Semester V, Vl, Vll, or Vlll)5 | ||
| Management Electives (6 points) (taken Semester V, Vl, Vll, or Vlll)6 | ||
- 1
Taking required courses later than the prescribed semester is not permitted.
- 2
12 points total. At least 6 points need to be at least 3000 level with the prefix IEOR, ORCS, or CSOR. The complete list is available at ieor.columbia.edu/undergraduate/electives.
- 3
6 points total. Cannot double-count non-technical electives. The complete list is available at ieor.columbia.edu/undergraduate/electives.