To a great extent, the mathematics used by computer scientists and operations researchers overlap. The boundaries between operations research and computer science have become blurred. Important new theories and whole fields, like polyhedral combinatorics, have been and are being developed jointly by computer scientists, operations researchers, and applied mathematicians (who consider themselves a little bit of both). Presentations of new results on graphs and matroid theory can be heard at operations research conferences, while papers on linear programming, network flows, and matching in graphs are frequently presented at computer science conferences. The mathematical content of the papers has become greater and more diverse. Yet, in spite of this, few Ph.D. students graduate with an equally solid knowledge of all three areas.

The Ph.D. program in algorithms, combinatorics, and optimization is intended to fill this gap. It brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as:

• Network Optimization
• Combinatorial Optimization
• Integer Programming
• Polyhedral Theory
• Computational Algebra
• Convex and Discrete Geometry
• Number Theory

Course Study

The coordinating committee has established a challenging core curriculum in analysis, algebra, probability, combinatorics, linear and integer programming, graph theory, convex optimization, algorithms, and complexity theory. For more information, see the separate brochure for the Algorithms, Combinatorics, and Optimization program, or go to the ACO homepage.

Please visit our Ph.D. Student Profiles page to view the profiles of our current doctoral candidates.

Requirements

The Coordinating Committee has established a challenging core curriculum in Analysis, Algebra, Probability, Combinatorics, Linear and Integer Programming, Graph Theory, Convex Optimization, Algorithms, and Complexity Theory.

Besides the core courses, a host of other courses are available for the students to take. Some examples are combinatorial optimization, graph coloring, matroid theory, convex polytopes, location theory, sequencing and scheduling, large scale OR, parallel algorithms, probabilistic analysis of algorithms, approximation algorithms, machine learning theory, cryptography, nonlinear programming, and constraint programming. In the event that a student has already mastered a core course at the graduate level when entering the program, another course from the same department may be substituted. Approval must be obtained from the ACO Coordinating Committee and is given on a case-by-case basis. In addition, the students are expected to participate in the weekly research seminar on Algorithms, Combinatorics, and Optimization.

As in all other areas of study, the first-year and second-year research papers are required of all doctoral students.

At the end of their third semester in residence, the students take a comprehensive qualifying examination based on the material in five core courses. At this stage (or earlier), they choose a faculty member to supervise their research and dissertation. Approximately a year before the expected graduation date, the student must make a thesis proposal before a thesis committee, composed of the advisor and two or more faculty members of the student's choosing. The final transition point is the thesis defense, which is presented before the same committee. To graduate, the students will also need some teaching experience and must demonstrate adequate programming skills.

Carnegie Mellon is one of the few institutions at which the economics department for the university as a whole is housed in the business school. This creates an environment which is especially conducive to close integration between the various management studies and economics. The Tepper School of Business at Carnegie Mellon has long played a pioneering role in the application of new ideas and techniques in economics to financial problems.

Research Topics

Asset Pricing Theory

• Market Incompleteness
• The Effect of Incomplete Markets on Security Valuation
• Risk Preferences
• Asset Pricing and Investor Risk Preferences
• Mortgage Valuation
• The Valuation of Mortgage Loans

Tax Effects in Security Markets

• Treasury Bonds
• Tax Effects in the Relative Pricing of Treasury Bonds
• Municipal Bonds
• Term and Tax Effects in the Pricing of Municipal Bonds
• Capital Gains Taxation
• The Effect of Capital Gains Taxation on the Optimal Trading and Equilibrium Pricing of Financial Assets 

Corporate Finance

• Corporate Control
• Capital Structure And Corporate Control
• Optimal Bankruptcy Law

Market Microstructure

• Design of Financial Markets
• Limit and Market Orders
• Trading Strategies

International Finance

• Risk Premia in Currency Markets
• Lottery Bonds
   

Please visit our Ph.D. Student Profiles page to view the profiles of our current doctoral candidates.

Requirements for the Ph.D. in Financial Economics

Ph.D. students in Financial Economics must fulfill all of the general Tepper School Ph.D. requirements, in addition to any area specific requirements. 

The curriculum in financial economics reflects the close relationship between finance and economics. Students take most of the core economic courses, such as microeconomics, macroeconomics, econometrics, dynamic competitive analysis, and economics of contracts.

In addition, they typically elect courses from the mathematics and statistics departments and take the doctoral seminars in finance. Students are also encouraged to take Empirical Methods for Finance & Accounting.

Students take qualifying exams at the end of the third semester. The required exams are:  microeconomics (choice of 2 out of 3 questions), macroeconomics (choice of 2 out of 3 questions), econometrics (choice of 2 out of 3 questions) and finance (all questions. Typically, there are 4 questions).

Students with appropriate preparation prior to their entry to the program may choose to take the qualifying exams prior to the third semester, however, they must take the entire set of qualifiers as outlined above. For further information, visit the qualifying examinations page.

The purpose of the first and second year papers is to give students the opportunity to conduct original research. In many cases, these papers, and in particular the second year summer paper, lead to a thesis topic. Finally, you must attend the weekly Finance seminar. This is the only place where you can “see” research being done in public through the presentation and discussions. Also, attend seminars in economics, accounting, and others. 

The goal of the doctoral program in economics is to help students learn to do original, creative research. Unlike most graduate programs in economics, we have chosen not to impose rigid course requirements on students. Instead, we emphasize involving students in research early in their graduate careers. Students in the doctoral program in economics at the Tepper School of Business at Carnegie Mellon take courses in order to learn the fundamental principles of economic theory underlying all areas of application, and to master the analytic and modeling techniques of the practicing research economist. In-depth knowledge of specialized areas is required as a by-product of research activity.

At the completion of the Ph.D. program in economics at the Tepper School, a student should have mastered the fundamental principles of economic theory and the quantitative tools required for basic and applied research. Additionally, the student should have attained a level of skill in research techniques which will serve as the basis for continued self-development.

• Students are expected to obtain knowledge of substantive research areas by taking elective courses, attending and participating in seminars, working with the faculty, and reading research papers.
• Students are urged to actively involve themselves in the intellectual life of the school.
• Seminars are a fundamental mechanism for exchange of information throughout the profession, and they are an essential professional activity of a successful research economist.
• Students should plan to attend weekly seminars throughout their stay at the business school.

Research Topics

• Real Business Cycles
• Expectations and Indeterminacy of Monetary Equilibrian Experimental Economies
• Consistent Incentive Mechanism (Contract) Design
• Corporate Financial Policy Under Asymmetric Information
• Bargaining Foundations of Product Innovation
• Variation in Wages and Hours of Work Over the Business Cycle
• Individual Adjustment to Changing Labor Markets
• The Distribution of Income Within and Across Households
• The Results of Deregulation
• Macroeconomic Policy
• International Trade Policy
• Female Labor Supply and Fertility
• The Economics Behind Marketing "New and Improving" Products
• Risk Analysis and Management
• Estimation and Inference for Dynamic Economic Models
• The Duration of Interorganizational Relationships
• The Endogeneity of Appropriability and R&D Investment
• Takeovers

Please visit our Ph.D. Student Profiles page to view the profiles of our current doctoral candidates.

Requirements for a Ph.D. in Economics

PhD students in Economics must fulfill all of the general Tepper School Ph.D. requirements, in addition to any area specific requirements. 

Preliminaries

• Math for Economists
• No Qualifying exam, but the course is highly recommended

Microeconomics Sequence

• Microeconomics I
• Microeconomics II
• Microeconomics III
• Qualifying exam, with a question based on each of these three courses

Macroeconomics Sequence

• Macroeconomics I
• Macroeconomics II
• Macroeconomics III
• Qualifying exam, with a question based on each of these three courses

Econometrics Sequence

• Econometrics I
• Econometrics II
• Econometrics III
• Qualifying exam, with a question based on each of these three courses

Advanced Economic Analysis (AEA) / Elective Sequence 

A subset of 6 classes from the following list will be offered every year:

• Structural Models in Microeconomics
• Industrial Organization
• Advanced Econometrics
• Market Design
• Mechanism Design
• Information Economics
• Economics of Networks
• Dynamic Competitive Analysis
• Computational Methods
• Macro Finance
• Public Economics
• Qualifying exam based on four questions out of the six.

The second-year paper concludes the requirements for year two. At this time, students begin formulating a thesis topic and preparing for a formal thesis proposal. 

The curriculum builds foundations for students that allow them to investigate highly relevant technology questions with strong economic theoretical underpinnings. The BT group at the Tepper School is tightly integrated with other areas at Tepper School such as Marketing and Economics, as well as other schools such as the School of Computer Science. Students have the opportunity to collaborate with world-class economists and computer scientists and are encouraged to take advantage of the many interdisciplinary resources available at Carnegie Mellon.

The program has a track record of producing exceptional Ph.D. graduates who have received placements as assistant professors in top schools in not only Business Technology/Information Systems but also Marketing departments.

Our graduates have placed as assistant professors at:

• Harvard Business School
• Stern School of Business at New York University
• Ross School of Business at University of Michigan
• Heinz College at Carnegie Mellon University
• Sloan School of Management at Massachusetts Institute of Technology
• Olin School of Business at Washington University
• McCombs School of Business at University of Texas at Austin
• Foster School of Business at University of Washington
• Marshall School of Business at University of Southern California

Below are some of our recent placement records (first placement):

• Nikhil Malik (2021) - Marshall School of Business, University of Southern California
• Shunyuan Zhang (2019) - Harvard Business School
• Elina Hwang (2015) - Foster School of Business University of Washington
• Yan Huang (2013) - Ross School of Business University of Michigan
• Baojun Jiang (2011) - Olin School of Business Washington University
• Liye Ma (2011) - Smith School of Business University of Maryland
• Vineet Kumar (2010) - Harvard Business School
• Ashish Agarwal (2009) - McCombs School of Business University of Texas Austin
• Anindya Ghose (2004) - Stern School of Business New York University
• Rahul Telang (2002) - Heinz College Carnegie Mellon University
• M.S. Krishnan (1996) - Ross School of Management University of Michigan

Visit our Ph.D. Student Profiles page to view the profiles of our current doctoral candidates.

Requirements for a Ph.D. in Business Technologies

The requirements for the Ph.D. in Business Technologies include all of those for Tepper Ph.D. students, including the First Year Paper and the Second Year Paper, plus the following:

Core Courses*

• Microeconomics I
• Microeconomics II
• Econometrics I
• Econometrics II
• Machine Learning
• BT Seminar – Econo-mining
• BT Seminar – Estimating Dynamic and Structural Models
• BT Seminar III and IV – Topics will change every year

*The content covered in these courses will be part of the qualifiers, as a result, they should be completed by the end of the 3rd semester.

Recommended Courses

• Microeconomics III
• Topics in Applied Economics: Structural Models
• Topics in Applied Economics: Advanced Econometrics
• Topics in Applied Economics: IO
• Topics in Applied Economics: Causality
• Bayesian Statistics in Marketing
• Analytical Models in Marketing
• Deep Reinforcement Learning and Control
• Convex Optimization
• Probabilistic graphic models
• Dynamic Programming

All students in BT take Economics as the reference discipline. 

Qualifiers

By the end of the third semester, students must pass the qualifying exams in Business Technologies (see below), and a subset of the Economics qualifying exams focusing on micro-economics and econometrics.   Students with appropriate preparation prior to their entry to the program may choose to take the qualifying exams prior to the third semester, however, they must take the entire set of qualifiers as outlined below. 

There will be two BT exams: Breadth and Depth

• BT Breadth Exam: The breadth exam tests the student on the content covered in the seminars.
• BT Depth Exam: The depth exam tests the student’s knowledge on a chosen topic.  

Economics: Students are required to take the following qualifiers:

• Microeconomics I and II
• Econometrics I and II

• Accounting concepts, standards, measurements, and the conceptual framework that integrates them
• The effect of accounting information and auditing on the design of organizations, and on the ensuing behavior of individuals and groups
• Analysis of the relationship between accounting information and stock prices
• The institutional environment of accounting and accounting public policies that are generated therein
• Technological development relating to information processing and its impact on accounting and auditing concepts and standards in tax accounting and their role in formulating and implementing tax policies
• Multisector systems of national accounts and their relationship with private accounting

Please visit our Ph.D. Student Profiles page to view the profiles of our current doctoral candidates.

Requirements for a Ph.D. in Accounting

Students successfully completing the accounting doctoral degree program are awarded a Ph.D. in Accounting. 

Ph.D. students in Accounting must fulfill all of the general Tepper School Ph.D. requirements, in addition to any area specific requirements. 

• Students are expected to attend and participate in our workshops and annual conference.
• By the end of the third semester, Accounting students must pass a qualifying exam on Accounting and the Economics qualifying exams on Microeconomics I and II and Economics I and II.
• Students with specific interests can substitute qualifying exams in Operations Research or Organizational Behavior for Economics, with faculty approval.
• Students with appropriate preparation prior to their entry to the program may choose to take the qualifying exams prior to the third semester, however, they must take the entire set of qualifiers as outlined above. 

With the assistance of an adviser, students enjoy considerable flexibility in working out their actual programs of study.