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Show Results For
- All HBS Web
(836)
- News (79)
- Research (641)
- Events (14)
- Multimedia (4)
- Faculty Publications (634)
- May 2009
- Article
Configurations of Extremal Even Unimodular Lattices
We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors. View Details
Keywords: Mathematical Methods
Kominers, Scott Duke. "Configurations of Extremal Even Unimodular Lattices." International Journal of Number Theory 5, no. 3 (May 2009): 457–464.
- 2010
- Article
On the Classification of Type II Codes of Length 24
By: Noam D. Elkies and Scott Duke Kominers
We give a new, purely coding-theoretic proof of Koch's criterion on the tetrad systems of Type II codes of length 24 using the theory of harmonic weight enumerators. This approach is inspired by Venkov's approach to the classification of the root systems of Type II... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "On the Classification of Type II Codes of Length 24." SIAM Journal on Discrete Mathematics 23, no. 4 (2010).
- March 2010
- Article
Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
By: Shaofang Hong and Scott Duke Kominers
For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any integer. In this paper, we show that, for integers alpha,r >= a and n >=... View Details
Keywords: Mathematical Methods
Hong, Shaofang, and Scott Duke Kominers. "Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Proceedings of the American Mathematical Society 138, no. 3 (March 2010): 809–813.
- August 2005 (Revised April 2008)
- Teaching Note
GuestFirst Hotel (B): Statistics Review with Data Desk (TN)
By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
- March 2004
- Teaching Note
Variance Analysis Tutorial (Instructor Guide)
By: David F. Hawkins
Instructor Guide to (9-104-709). View Details
Keywords: Mathematical Methods
- October 1979 (Revised March 1995)
- Background Note
Note on the Management of Queues
Contains four sections: 1) measuring the performance of queuing systems; 2) types of queuing systems; 3) the behavior of simple systems (elementary queuing theory); and 4) the management of queues (including a discussion of their psychology). View Details
Keywords: Mathematical Methods
Maister, David H. "Note on the Management of Queues." Harvard Business School Background Note 680-053, October 1979. (Revised March 1995.)
- 1997
- Chapter
On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios
By: Robert C. Merton
Keywords: Mathematical Methods
Merton, Robert C. "On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios." In The Legacy of Norbert Wiener: A Centennial Symposium. Vol. 60, edited by D. Jerison, I. M. Singer, and D. W. Stroock. Proceedings of Symposia in Pure Mathematics . Providence, RI: American Mathematical Society, 1997.
- 01 Mar 2009
- News
The Case for Studying Financial History
guide than certain other disciplines that are sometimes regarded as more rigorous, like economics, for example. Economists with their more mathematical approach to social science conspicuously failed to anticipate this crisis, whereas a... View Details
- Web
Introduction - Option Pricing in Theory & Practice: The Nobel Prize Research of Robert C. Merton - Exhibits - Historical Collections
more than twenty-five years ago to the impact and growth of his groundbreaking work in the current academic and financial communities. The Black-Scholes option pricing model established the everyday use of mathematical models as essential... View Details
- Web
Bibliography - Option Pricing in Theory & Practice: The Nobel Prize Research of Robert C. Merton - Exhibits - Historical Collections
the American Mathematical Society , no. 4. New York, N.Y.: American Mathematical Society, 1951. * Samuelson, Paul A. Foundations of Economic Analysis . Cambridge, Mass.: Harvard University Press, 1947. *... View Details
- 16 Oct 2019
- News
The Road to Impact
increasing the organization’s visibility. “We may have discovered a better way to teach young kids mathematics or to teach non-English speakers how to read English in third grade, or how to better inhibit suicidal patients from taking... View Details
- 01 Oct 1998
- News
Merton Named University Professor
mathematics from Columbia University in 1966, Merton studied applied mathematics at the California Institute of Technology and earned an MS in 1967. In 1970 he completed a Ph.D. in economics at MIT and... View Details
- 01 Dec 1997
- News
Merton's Economics Research Wins Nobel Prize
evaluation began when he was a graduate student in applied mathematics at the California Institute of Technology and intensified in the late 1960s, when he went to MIT to study economics under Nobel Laureate Paul Samuelson. At MIT, he... View Details
- 1970
- Dissertation
Analytical Optimal Control Theory as Applied to Stochastic and Non-Stochastic Economics
By: Robert C. Merton
Merton, Robert C. "Analytical Optimal Control Theory as Applied to Stochastic and Non-Stochastic Economics." Diss., Massachusetts Institute of Technology (MIT), 1970.
- January 2018
- Background Note
Math Tools for Strategists
By: Tarun Khanna and Jan W. Rivkin
Great strategists rely heavily on numbers as they go about their work. This note offers an overview of the highbrow and lowbrow quantitative tools that individuals commonly encounter during strategy courses and in actual strategy work. The note focuses especially on... View Details
Khanna, Tarun, and Jan W. Rivkin. "Math Tools for Strategists." Harvard Business School Background Note 718-477, January 2018.
- December 1998
- Background Note
Note on Low-Tech Marketing Math
By: Robert J. Dolan
Describes basic calculations useful in marketing analysis, break-even analysis, and price-volume relationships. View Details
Dolan, Robert J. "Note on Low-Tech Marketing Math." Harvard Business School Background Note 599-011, December 1998.
Parker Treacy
Competition in 2016, becoming the first Latin American startup to receive the award. In 2019, Cobli was elected by LinkedIn as one of the top ten startups in Brazil. Previously, Parker founded First Help Financial, the tenth largest independent vehicle finance company... View Details