Computational Finance, B.S.
Bachelor of Science in Computational Finance (BSCF)
Overview
The Mellon College of Science, the Heinz College of Public Policy and Management and the Tepper School of Business jointly offer a degree uniquely designed to meet the quantitative needs of the finance industry. Modeled after the highly successful Carnegie Mellon Master of Science in Computational Finance, this degree allows students to develop a deep knowledge of mathematics, probability, statistics, and the applications of these disciplines to finance. Students who complete this degree may directly enter the finance industry, enter other industries where applied mathematics training is appropriate, or pursue advanced degrees in economics, finance or the mathematical sciences. Students entering the work force upon completion of this degree may wish to later complement their undergraduate degree with a Master's degree in Business Administration or another professional degree. Students who might eventually pursue doctoral degrees in economics, finance, statistics or mathematics should seek advising on how to use their electives in order to prepare for graduate work in their chosen disciplines.
The Bachelor of Science in Computational Finance is an Intercollege Program. Students may pursue Computational Finance as their primary major with either the Mellon College of Science (MCS) or the Tepper School of Business (Tepper) as their home college. The coursework required for the major is essentially the same in each case, with a few minor exceptions outlined below. The general education requirements for the degree depend on the student's home college.
Additional Major
Students who pursue Computational Finance as an additional major will remain in the college of their primary major. Additional majors must complete the Major Requirements outlined below, but not the General Education Requirements outlined for MCS and Tepper students. Additional majors will complete the general education requirements for their home college.
Admission
Admission to the major in Computational Finance is by application. Applications are accepted each fall and spring semester. The application deadline has traditionally been just after the mid-semester break. Applicants must have taken (or be currently taking) at the time of application: 21-127 Concepts of Mathematics (or 21-128), 21-241 Matrices and Linear Transformations (or 21-242), 21-270 Introduction to Mathematical Finance. Students from any college or program at Carnegie Mellon are welcome to apply to enroll in the major. Additional information about computational finance and the Undergraduate Computational Finance Program at Carnegie Mellon can be found on the BSCF Program website.
Several majors are prohibited in combination with the Computational Finance major (either as Primary/Additional majors or as Dual Degrees) due to excessive overlap with the Computational Finance curriculum. These include the Business Administration major, the major in Mathematical Sciences (including any of the various concentrations), and the major in Economics and Mathematical Sciences.
BSCF Program Requirements
The major in Computational Finance is built around a core sequence of courses in mathematical finance. This core is supported by courses providing foundational mathematical skills and augmented with coursework in the related areas of Statistics, Computer Science, and Economics. Additionally the major provides training in the "soft skills" required for work in a corporate environment. The major also requires the completion of several depth electives, allowing students to tailor their education to their particular interests and needs.
The major requirements are the same for additional majors as they are for majors whose home college is MCS. There are a few slight differences for students whose home college is Tepper. These differences are described in the sections for Depth Electives and Professional Development below.
Foundations
| Units | ||
| 21-120 | Differential and Integral Calculus | 10 |
| 21-122 | Integration and Approximation | 10 |
| 21-127 | Concepts of Mathematics | 12 |
| 21-241 | Matrices and Linear Transformations | 11 |
| 21-259 | Calculus in Three Dimensions | 10 |
| 21-260 | Differential Equations | 9 |
| 21-369 | Numerical Methods | 12 |
| 70-122 | Introduction to Accounting | 9 |
Mathematical Finance
| 21-270 | Introduction to Mathematical Finance | 9 |
| 21-370 | Discrete Time Finance | 9 |
| 21-420 | Continuous-Time Finance | 9 |
| 46-977 | MSCF Studies in Financial Engineering | 6 |
The Mathematical Finance courses in the BSCF curriculum may not be double counted toward other graduation requirements.
Statistics
| 21-325 | Probability | 9 |
| 36-226 | Introduction to Statistical Inference | 9 |
| 36-401 | Modern Regression | 9 |
Programming
| 15-110 | Principles of Computing | 10 |
| 15-112 | Fundamentals of Programming and Computer Science | 12 |
| 15-122 | Principles of Imperative Computation | 12 |
Economics
| 73-102 | Principles of Microeconomics | 9 |
| or 73-104 | Principles of Microeconomics Accelerated | |
| 73-103 | Principles of Macroeconomics | 9 |
| 73-240 | Intermediate Macroeconomics | 9 |
Professional Development
| 94-700 | Organizational Design & Implementation | 6 |
| 70-340 | Business Communications | 9 |
| 70-345 | Business Presentations | 9 |
- Note:
Majors in the Tepper School of Business take 70-311 Organizational Behavior as part of the Functional Business Core curriculum. This course will satisfy the 94-700 Organizational Design & Implementation requirement for these students.
Depth Electives
Depth electives give students an opportunity to tailor their coursework to their particular interests. Students completing the major will take three depth electives (the minimum requirement is 24 units - the equivalent of two 9 unit courses and one 6 unit course).
- NOTE:
Tepper students are required to select 70-391 Finance as one of their depth electives.
Depth electives are intended to develop a student's background in an area that is applicable to the finance industry. Courses in finance or programming generally qualify as depth electives. Mathematics, Statistics, or Economics courses in areas applicable to finance also qualify. Computational Finance majors may have the opportunity to take MSCF courses (as described below) and these may also be counted as depth electives.
There is no definitive list of approved depth electives. The courses listed below have been taken as depth electives in recent years, but other courses could be approved upon request
| 07-280 | Artificial Intelligence and Machine Learning I | 12 |
| 10-301 | Introduction to Machine Learning | 12 |
| 10-423 | Generative AI | 12 |
| 10-424 | Bayesian Methods in Machine Learning | 12 |
| 10-425 | Introduction to Convex Optimization | 12 |
| 10-601 | Introduction to Machine Learning | 12 |
| 10-605 | Machine Learning with Large Datasets | 12 |
| 10-617 | Intermediate Deep Learning | 12 |
| 10-618 | Machine Learning for Structured Data | 12 |
| 10-623 | Generative AI | 12 |
| 10-625 | Introduction to Convex Optimization | 12 |
| 15-150 | Principles of Functional Programming | 12 |
| 15-210 | Parallel and Sequential Data Structures and Algorithms | 12 |
| 15-213 | Introduction to Computer Systems | 12 |
| 15-351 | Algorithms and Advanced Data Structures | 12 |
| 15-451 | Algorithm Design and Analysis | 12 |
| 21-326 | Markov Chains: Theory, Simulation and Applications | 9 |
| 21-355 | Principles of Real Analysis I | 9 |
| 21-378 | Mathematics of Fixed Income Markets | 9 |
| 21-393 | Operations Research II | 9 |
| 36-402 | Advanced Methods for Data Analysis | 9 |
| 36-410 | Introduction to Probability Modeling | 9 |
| 36-462 | Special Topics: Statistical Machine Learning | 9 |
| 36-463 | Special Topics: Multilevel and Hierarchical Models | 9 |
| 70-337 | Business of Blockchain | 9 |
| 70-391 | Finance | 9 |
| 70-492 | Investment Analysis | 9 |
| 70-495 | Corporate Finance | 9 |
| 70-497 | Derivative Securities | 9 |
| 73-337 | Business of Blockchain | 9 |
| 73-347 | Game Theory Applications for Economics and Business | 9 |
Courses counted toward the BSCF Depth Elective requirements may not be double counted toward other graduation requirements.
MSCF Courses
Computational Finance majors are required to take 46-977 MSCF Studies in Financial Engineering. They may also have the opportunity to take up to four more MSCF courses. Permission to enroll in these courses requires (1) approval from the BSCF program, (2) approval of the course instructor, and (3) space available in the course. The MSCF curriculum with course descriptions is described on the MSCF website.
Some MSCF courses cover material in the undergraduate curriculum and thus are not generally suitable. Other courses require background that is difficult to obtain as an undergraduate. Students interested in taking MSCF courses are encouraged to discuss their interest with their BSCF advisor as early as possible.
General Education Requirements
Students completing Computational Finance as an additional major will complete the general education requirements from their home department and college. Students completing Computational Finance as their primary major in either MCS or Tepper will complete a modified version of the general education requirements from their home college. These requirements can be found here:
Mellon College of Science (MCS) General Education Requirements
Tepper School of Business (TSB) General Education Requirements
Sample Curricula
MCS Sample Curriculum
What follows is the detailed curriculum for the degree Bachelor of Science in Computational Finance in the Mellon College of Science. This is an example of how an MCS student might meet the requirements of the Computational Finance major. It is not expected that every student will follow this sequence. In particular, well prepared students should consider taking 21-270 Introduction to Mathematical Finance during their First-Year Spring semester. Students intending to do so are encouraged to take 21-127 Concepts of Mathematics or 21-241 Matrices and Linear Transformations during their First-Year Fall semester.
| First-Year | |
|---|---|
| Fall | Spring |
| 15-110 Principles of Computing | 15-112 Fundamentals of Programming and Computer Science |
| 21-120 Differential and Integral Calculus | 21-122 Integration and Approximation |
| 76-101 Interpretation and Argument | 70-122 Introduction to Accounting |
| 99-101 Core@CMU | xx-xxx Science Requirement |
| xx-xxx Science Requirement | xx-xxx Elective |
| Second-Year | |
|---|---|
| Fall | Spring |
| 21-241 Matrices and Linear Transformations | 21-270 Introduction to Mathematical Finance |
| 21-259 Calculus in Three Dimensions | 21-127 Concepts of Mathematics |
| 21-260 Differential Equations | 21-369 Numerical Methods |
| 73-102 Principles of Microeconomics | 73-103 Principles of Macroeconomics |
| xx-xxx Humanities, Social Science or Fine Arts Elective | xx-xxx Elective |
| Third-Year | |
|---|---|
| Fall | Spring |
| 21-325 Probability | 21-420 Continuous-Time Finance |
| 21-370 Discrete Time Finance | 36-226 Introduction to Statistical Inference |
| 73-240 Intermediate Macroeconomics | xx-xxx Humanities, Social Sciences, or Fine Arts Elective |
| 15-122 Principles of Imperative Computation | xx-xxx Humanities, Social Sciences, or Fine Arts Elective |
| xx-xxx Elective | xx-xxx Depth Elective |
| Fourth-Year | |
|---|---|
| Fall | Spring |
| 46-977 MSCF Studies in Financial Engineering | 70-345 Business Presentations |
| 94-700 Organizational Design & Implementation | xx-xxx Depth Elective |
| 36-401 Modern Regression | xx-xxx Humanities, Social Sciences or Fine Arts Elective |
| 70-340 Business Communications | xx-xxx Elective |
| xx-xxx Depth Elective | xx-xxx Elective |
| xx-xxx Elective | xx-xxx Elective |
Tepper Sample Curriculum
What follows is the detailed curriculum for the degree Bachelor of Science in Computational Finance in the Tepper School of Business. This is an example of how a Tepper student might meet the requirements of the Computational Finance major. It is not expected that every student will follow this sequence. In particular, well prepared students should consider taking 21-270 Introduction to Mathematical Finance during their First-Year Spring semester. Students intending to do so are encouraged to take 21-127 Concepts of Mathematics or 21-241 Matrices and Linear Transformations during their First-Year Fall semester.
| First-Year | |
|---|---|
| Fall | Spring |
| 15-110 Principles of Computing | 15-112 Fundamentals of Programming and Computer Science |
| 21-120 Differential and Integral Calculus | 21-122 Integration and Approximation |
| 73-102 Principles of Microeconomics | 21-241 Matrices and Linear Transformations |
| 70-106 Business Science | 73-103 Principles of Macroeconomics |
| 76-101 Interpretation and Argument | xx-xxx University Core Course |
| 99-101 Core@CMU | xx-xxx University Core Course |
| Second-Year | |
|---|---|
| Fall | Spring |
| 21-127 Concepts of Mathematics | 21-270 Introduction to Mathematical Finance |
| 21-259 Calculus in Three Dimensions | 21-325 Probability |
| 21-260 Differential Equations | 70-311 Organizational Behavior |
| 70-122 Introduction to Accounting | 70-381 Marketing I |
| xx-xxx Elective | 73-240 Intermediate Macroeconomics |
| Third-Year | |
|---|---|
| Fall | Spring |
| 21-369 Numerical Methods | 21-420 Continuous-Time Finance |
| 21-370 Discrete Time Finance | 36-226 Introduction to Statistical Inference |
| 70-391 Finance | 70-371 Operations Management |
| 15-122 Principles of Imperative Computation | xx-xxx Breadth Course |
| xx-xxx Breadth Course | xx-xxx Breadth Course |
| Fourth-Year | |
|---|---|
| Fall | Spring |
| 36-401 Modern Regression | 70-345 Business Presentations |
| 46-977 MSCF Studies in Financial Engineering | xx-xxx Depth Elective |
| 70-332 Business, Society and Ethics | xx-xxx Breadth Course |
| 70-401 Management Game | xx-xxx Breadth Course |
| 70-340 Business Communications | xx-xxx Elective |
| xx-xxx Depth Elective | |