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    • Research  (640)
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Show Results For

  • All HBS Web  (855)
    • News  (79)
    • Research  (640)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (636)
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  • February 2005 (Revised March 2005)
  • Background Note

Simple Regression Mathematics

By: Frances X. Frei and Dennis Campbell
Describes the underlying mathematics of regression. View Details
Keywords: Mathematical Methods
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Frei, Frances X., and Dennis Campbell. "Simple Regression Mathematics." Harvard Business School Background Note 605-061, February 2005. (Revised March 2005.)
  • 1977
  • Book

Applied Mathematical Programming

By: Stephen P. Bradley, Arnoldo C. Hax and Thomas L. Magnanti
Keywords: Mathematical Methods
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Bradley, Stephen P., Arnoldo C. Hax, and Thomas L. Magnanti. Applied Mathematical Programming. Reading, MA: Addison-Wesley Publishing Company, 1977.
  • Article

Overhead Allocation via Mathematical Programming Models

By: Robert S. Kaplan and Gerald Thompson
Keywords: Mathematical Methods
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Kaplan, Robert S., and Gerald Thompson. "Overhead Allocation via Mathematical Programming Models." Accounting Review 46, no. 2 (April 1971): 352–364.
  • 1981
  • Chapter

Mathematical Analysis and Convexity with Applications to Economics

By: Jerry R. Green and Walter P. Heller
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Green, Jerry R., and Walter P. Heller. "Mathematical Analysis and Convexity with Applications to Economics." In Handbook of Mathematical Economics, Vol. 1, edited by Kenneth J. Arrow and Michael D. Intriligator. Amsterdam: North-Holland Publishing Company, 1981.
  • 1982
  • Chapter

On the Mathematics and Economic Assumptions of Continuous-Time Financial Models

By: Robert C. Merton
Keywords: Mathematical Methods; Economics; Finance
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Merton, Robert C. "On the Mathematics and Economic Assumptions of Continuous-Time Financial Models." In Financial Economics: Essays in Honor of Paul Cootner, edited by W. F. Sharpe and C. M. Cootner. Englewood Cliffs, NJ: Prentice Hall, 1982. (Chapter 3 in Continuous-Time Finance.)
  • Article

High School Curriculum and Financial Outcomes: The Impact of Mandated Personal Finance and Mathematics Courses

By: Shawn Cole, Anna Paulson and Gauri Kartini Shastry
Financial literacy and cognitive capabilities are convincingly linked to the quality of financial decision-making. Yet, there is little evidence that education intended to improve financial decision-making is successful. Using plausibly exogenous variation in exposure... View Details
Keywords: Financial Literacy; Cognitive Capability; Secondary Education; Personal Finance; Decision Making
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Cole, Shawn, Anna Paulson, and Gauri Kartini Shastry. "High School Curriculum and Financial Outcomes: The Impact of Mandated Personal Finance and Mathematics Courses." Journal of Human Resources 51, no. 3 (Summer 2016): 656–698.
  • June 1994
  • Article

Influence of Mathematical Models in Finance on Practice: Past, Present and Future

By: Robert C. Merton
Keywords: Mathematical Methods; Finance
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Merton, Robert C. "Influence of Mathematical Models in Finance on Practice: Past, Present and Future." Series A. Philosophical Transactions of the Royal Society of London, Series A, Physical Sciences and Engineering 347 (June 1994): 451–463. (Reprinted in Financial Practice and Education, spring 1995.)
  • 2008
  • Conference Presentation

Analyzing and Using Data From Global Positioning Systems and Digital Imagery in Mathematics Courses

By: F. Wattenberg, K. Erickson, J. Helms, K. DeGregory and Hise O. Gibson
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Wattenberg, F., K. Erickson, J. Helms, K. DeGregory, and Hise O. Gibson. "Analyzing and Using Data From Global Positioning Systems and Digital Imagery in Mathematics Courses." Paper presented at the 20th International Conference for Technology in Collegiate Mathematics (ICTCM), San Antonio, TX, 2008.
  • 2007
  • Article

'One will make of Political Economy...what the Scholastics did with Philosophy': Henry Lloyd and the Mathematization of Economics

By: Sophus A. Reinert
Keywords: Government and Politics; Economy; Economics
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Reinert, Sophus A. "'One will make of Political Economy...what the Scholastics did with Philosophy': Henry Lloyd and the Mathematization of Economics." History of Political Economy 34, no. 4 (2007): 643–677.
  • March 2022 (Revised January 2025)
  • Technical Note

Linear Regression

By: Iavor I. Bojinov, Michael Parzen and Paul Hamilton
This note provides an overview of linear regression for an introductory data science course. It begins with a discussion of correlation, and explains why correlation does not necessarily imply causation. The note then describes the method of least squares, and how to... View Details
Keywords: Data Science; Linear Regression; Mathematical Modeling; Mathematical Methods; Analytics and Data Science
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Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Linear Regression." Harvard Business School Technical Note 622-100, March 2022. (Revised January 2025.)
  • March 2022 (Revised January 2025)
  • Technical Note

Statistical Inference

By: Iavor I. Bojinov, Michael Parzen and Paul Hamilton
This note provides an overview of statistical inference for an introductory data science course. First, the note discusses samples and populations. Next the note describes how to calculate confidence intervals for means and proportions. Then it walks through the logic... View Details
Keywords: Data Science; Statistics; Mathematical Modeling; Mathematical Methods; Analytics and Data Science
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Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Statistical Inference." Harvard Business School Technical Note 622-099, March 2022. (Revised January 2025.)
  • 2010
  • Other Unpublished Work

Is High School the Right Time to Teach Self-control? The Effect of Financial Education and Mathematics Courses on Savings Behavior

By: Shawn A. Cole and Gauri Kartini Shastry
Household financial behavior affects household welfare and the economy at large. Yet our understanding of how to improve financial decisions is limited. Recent literature and policy attention have focused on financial education, for example, in high school. We use... View Details
Keywords: Saving; Financial Management; Secondary Education; Behavior; Decision Choices and Conditions; Personal Finance; Household
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Cole, Shawn A., and Gauri Kartini Shastry. "Is High School the Right Time to Teach Self-control? The Effect of Financial Education and Mathematics Courses on Savings Behavior." June 2010.
  • 2012
  • Article

Demand and Capacity Management in Air Transportation

This paper summarizes research trends and opportunities in the area of managing air transportation demand and capacity. Capacity constraints and resulting congestion and low schedule reliability currently impose large costs on airlines and their passengers. Significant... View Details
Keywords: Demand Management; Capacity Management; Mathematical Modeling; Congestion And Delays; Trends And Opportunities; Demand and Consumers; Air Transportation; Mathematical Methods; Performance Capacity; Air Transportation Industry
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Barnhart, Cynthia, Douglas S. Fearing, Amedeo Odoni, and Vikrant Vaze. "Demand and Capacity Management in Air Transportation." EURO Journal on Transportation and Logistics 1, nos. 1-2 (2012): 135–155.
  • November 2018
  • Case

Sportradar (A): From Data to Storytelling

By: Ramon Casadesus-Masanell, Karen Elterman and Oliver Gassmann
In 2013, the Swiss sports data company Sportradar debated whether to expand from its core business of data provision to bookmakers into sports media products. Sports data was becoming a commodity, and in the future, sports leagues might reduce their dependence on... View Details
Keywords: Sports Data; Data; Sport; Sportradar; Football; Soccer; Gambling; Betting; Betting Markets; Statistics; Odds; Live Data; Bookmakers; Betradar; Visualization; Integrity; Monitoring; Gaming; Streaming; 2013; St.Gallen; Algorithm; Mathematical Modeling; Carsten Koerl; Betandwin; Bwin; Wagering; Probability; Sports; Analytics and Data Science; Mathematical Methods; Games, Gaming, and Gambling; Transition; Strategy; Media; Sports Industry; Technology Industry; Information Technology Industry; Media and Broadcasting Industry; Europe; Switzerland; Asia; Austria; Germany; England
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Casadesus-Masanell, Ramon, Karen Elterman, and Oliver Gassmann. "Sportradar (A): From Data to Storytelling." Harvard Business School Case 719-429, November 2018.
  • February 2021
  • Tutorial

What is AI?

By: Tsedal Neeley
This video explores the elements that constitute artificial intelligence (AI). From its mathematical basis to current advances in AI, this video introduces students to data, tools, and statistical models that make a computer 'intelligent.' Through an explanation of... View Details
Keywords: Artificial Intelligence; Digital; Technological Innovation; Leadership; AI and Machine Learning; Mathematical Methods
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Neeley, Tsedal. What is AI? Harvard Business School Tutorial 421-713, February 2021. (https://hbsp.harvard.edu/product/421713-HTM-ENG?Ntt=tsedal%20neeley%20what%20is%20ai.)
  • Article

Bilateral Contracts

By: Jerry R. Green and Seppo Honkapohja
A mathematical characterization of self-enforcing bilateral contracts is given. Contracts where both parties exercise some control over the quantity traded can sometimes be superior to contracts that rest control entirely with one side. Some qualitative characteristics... View Details
Keywords: Contracts; Mathematical Methods
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Green, Jerry R., and Seppo Honkapohja. "Bilateral Contracts." Journal of Mathematical Economics 11, no. 2 (1983): 171–187.
  • August 2005 (Revised September 2006)
  • Case

Polyphonic HMI: Mixing Music and Math

By: Anita Elberse, Jehoshua Eliashberg and Julian Villanueva
In 2003, Mike McCready, CEO of Barcelona-based Polyphonic HMI, was preparing to launch an artificial intelligence tool that could create significant value for music businesses. The technology, referred to as Hit Song Science (HSS), analyzed the mathematical... View Details
Keywords: Forecasting and Prediction; Music Entertainment; Business History; Leadership; Marketing Strategy; Strategic Planning; Problems and Challenges; Mathematical Methods; Entertainment and Recreation Industry
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Elberse, Anita, Jehoshua Eliashberg, and Julian Villanueva. "Polyphonic HMI: Mixing Music and Math." Harvard Business School Case 506-009, August 2005. (Revised September 2006.) (Spanish version also available.)
  • May 2005 (Revised January 2006)
  • Background Note

Note on Forward Contracts and Swaps

Introduces forward contracts and derives graphically through basic arbitrage principles the spot-forward parity. Introduces swap contracts as simply a portfolio of forward contracts. Also covers briefly the mathematics behind swaps as an extension of spot-forward... View Details
Keywords: Financial Instruments
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Chacko, George C., Peter A. Hecht, Vincent Dessain, and Anders Sjoman. "Note on Forward Contracts and Swaps." Harvard Business School Background Note 205-118, May 2005. (Revised January 2006.)
  • 2005
  • Working Paper

Macro for Managers

By: David A. Moss
This note attempts to provide a conceptual overview of macroeconomics. Designed for managers and students of management, it emphasizes fundamental ideas and relationships, rather than mathematical models and formulas. The note identifies—and is structured around—three... View Details
Keywords: Macroeconomics; Money; Relationships; Performance Expectations
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Moss, David A. "Macro for Managers." Harvard Business School Working Paper, No. 05-042, January 2005.
  • Research Summary

Overview

My background is rooted in mathematics and science, so I am interested in strategy theory. I have a broad interest in a variety of fields, and am open to research topics. My senior thesis was on copula modelling of heating oil and natural gas futures. View Details
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