Elwyn Berlekamp
Encyclopedia
Elwyn Ralph Berlekamp is an American mathematician. He is a professor emeritus of mathematics
and EECS at the University of California, Berkeley
. Berlekamp is known for his work in information theory
and combinatorial game theory
.
. While an undergraduate at the Massachusetts Institute of Technology
(MIT), he was a Putnam Fellow in 1961. He completed his Bachelor's and Master's degrees in electrical engineering
in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were Claude Shannon, Robert G. Gallager
, Peter Elias
and John Wozencraft
. Berlekamp taught at the University of California, Berkeley
from 1964 until 1966, when he became a researcher at Bell Labs
. In 1971, Berlekamp returned to Berkeley where, as of 2010, he is a Professor of the Graduate School..
He is a member of the National Academy of Engineering
(1977) and the National Academy of Sciences
(1999). He was elected a Fellow of the American Academy of Arts and Sciences
in 1996. He received in 1991 the IEEE Richard W. Hamming Medal, and in 1998 the Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society
.
Berlekamp is one of the inventors of the Welch-Berlekamp and Berlekamp-Massey algorithm
s, which are used to implement Reed-Solomon error correction. In the mid-1980s, he was president of Cyclotomics, Inc., a corporation which developed error-correcting code technology. With John Horton Conway
and Richard K. Guy
, he co-authored Winning Ways for your Mathematical Plays
, leading to his recognition as one of the founders of combinatorial game theory
. He has studied various games, including Fox and Geese and other fox games
, dots and boxes
, and, especially, Go. With David Wolfe, Berlekamp co-authored the book Mathematical Go, which describes methods for analyzing certain classes of Go endgames.
Outside of mathematics and computer science, Berlekamp is active in money management
. In 1986, on behalf of Axcom Trading Advisors
, a futures trading company, Berlekamp began information-theoretic studies of commodity and financial futures. In 1989, Berlekamp owned the largest interest in Axcom. After the firm's futures trading algorithms were rewritten, Axcom's flagship fund had a return (in 1990) of 55%, net of all management fees and transaction costs. Today, this fund is known as the Medallion Fund and is managed by James Harris Simons
and his Renaissance Technologies
Corporation.
Berlekamp and his wife Jennifer have two daughters and a son and live in Piedmont, California
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and EECS at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
. Berlekamp is known for his work in information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
and combinatorial game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
.
Biography
Berlekamp was born in Dover, OhioDover, Ohio
Dover is a city in Tuscarawas County, Ohio, United States. The population was 12,210 at the 2000 census.-History and features:Dover was originally part of a grant to Col. James Morrison of Kentucky, who had received it from the federal government for Revolutionary War services...
. While an undergraduate at the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
(MIT), he was a Putnam Fellow in 1961. He completed his Bachelor's and Master's degrees in electrical engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were Claude Shannon, Robert G. Gallager
Robert G. Gallager
Robert Gray Gallager is an American electrical engineer known for his work on information theory and communications networks. He was elected an IEEE Fellow in 1968 and a member of the National Academy of Engineering in 1979. He received the Claude E. Shannon Award from the IEEE Information Theory...
, Peter Elias
Peter Elias
Peter Elias was a pioneer in the field of information theory. Born in New Brunswick, New Jersey, he was a member of the Massachusetts Institute of Technology faculty from 1953 to 1991....
and John Wozencraft
John Wozencraft
John McReynolds "Jack" Wozencraft was an electrical engineer and information theorist, professor emeritus at the Massachusetts Institute of Technology...
. Berlekamp taught at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
from 1964 until 1966, when he became a researcher at Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...
. In 1971, Berlekamp returned to Berkeley where, as of 2010, he is a Professor of the Graduate School..
He is a member of the National Academy of Engineering
National Academy of Engineering
The National Academy of Engineering is a government-created non-profit institution in the United States, that was founded in 1964 under the same congressional act that led to the founding of the National Academy of Sciences...
(1977) and the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
(1999). He was elected a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1996. He received in 1991 the IEEE Richard W. Hamming Medal, and in 1998 the Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society
IEEE Information Theory Society
The IEEE Information Theory Society , formerly the IEEE Information Theory Group, is a professional society of the Institute of Electrical and Electronics Engineers focused on several aspects of information: its processing, transmission, storage, and usage; and the "foundations of the...
.
Berlekamp is one of the inventors of the Welch-Berlekamp and Berlekamp-Massey algorithm
Berlekamp-Massey algorithm
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear feedback shift register for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field....
s, which are used to implement Reed-Solomon error correction. In the mid-1980s, he was president of Cyclotomics, Inc., a corporation which developed error-correcting code technology. With John Horton Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
and Richard K. Guy
Richard K. Guy
Richard Kenneth Guy is a British mathematician, Professor Emeritus in the Department of Mathematics at the University of Calgary....
, he co-authored Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games...
, leading to his recognition as one of the founders of combinatorial game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
. He has studied various games, including Fox and Geese and other fox games
Fox games
Fox games are a category of board games where one player is the fox and tries to eat the geese/sheep, and the other player directs the geese/sheep and attempts to trap the fox, or reach a destination on the board. In another variant, Fox and Hounds, the fox merely tries to evade the hounds...
, dots and boxes
Dots and Boxes
Dots and Boxes is a pencil and paper game for two players first published in 1889 by Édouard Lucas.Starting with an empty grid of dots, players take turns, adding a single...
, and, especially, Go. With David Wolfe, Berlekamp co-authored the book Mathematical Go, which describes methods for analyzing certain classes of Go endgames.
Outside of mathematics and computer science, Berlekamp is active in money management
Money management
Money management is the process of managing money which includes investment, budgeting, banking and taxes. It is also called investment management....
. In 1986, on behalf of Axcom Trading Advisors
Axcom Trading Advisors
Axcom Trading Advisors was an early alternative investment management company founded by Elwyn Berlekamp and based in Berkeley, CA. It was acquired by Renaissance Technologies Corp in 1992, whereafter its investment instruments were either subsumed into Renaissance's flagship Medallion Fund. The...
, a futures trading company, Berlekamp began information-theoretic studies of commodity and financial futures. In 1989, Berlekamp owned the largest interest in Axcom. After the firm's futures trading algorithms were rewritten, Axcom's flagship fund had a return (in 1990) of 55%, net of all management fees and transaction costs. Today, this fund is known as the Medallion Fund and is managed by James Harris Simons
James Harris Simons
James Harris "Jim" Simons is an American hedge fund manager, mathematician, and philanthropist.In 1982, Simons founded Renaissance Technologies, a private investment firm based in New York with over $15 billion under management; Simons is still at the helm, as CEO, of what is now one of the...
and his Renaissance Technologies
Renaissance Technologies
Renaissance Technologies is a hedge fund management company of about 275 employees and more than $ billion in assets under management in three funds...
Corporation.
Berlekamp and his wife Jennifer have two daughters and a son and live in Piedmont, California
Piedmont, California
Piedmont is a small, affluent city in Alameda County, California, United States. It is surrounded by the city of Oakland. The population was 10,667 at the 2010 census. Piedmont was incorporated in 1907 and was developed significantly in the 1920s and 1930s...
.
Selected publications
- Block coding with noiseless feedback. Thesis, Massachusetts Institute of TechnologyMassachusetts Institute of TechnologyThe Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
, Dept. of Electrical Engineering, 1964. - Algebraic Coding Theory, New YorkNew York CityNew York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
: McGraw-HillMcGraw-HillThe McGraw-Hill Companies, Inc., is a publicly traded corporation headquartered in Rockefeller Center in New York City. Its primary areas of business are financial, education, publishing, broadcasting, and business services...
, 1968. Revised ed., Aegean Park Press, 1984, ISBN 0894120638. - (with John Horton ConwayJohn Horton ConwayJohn Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
and Richard K. GuyRichard K. GuyRichard Kenneth Guy is a British mathematician, Professor Emeritus in the Department of Mathematics at the University of Calgary....
) Winning Ways for your Mathematical PlaysWinning Ways for your Mathematical PlaysWinning Ways for your Mathematical Plays by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games...
. - 1st edition, New York: Academic PressAcademic PressAcademic Press is an academic book publisher. Originally independent, it was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier....
, 2 vols., 1982; vol. 1, hardback: ISBN 0-12-091150-7, paperback: ISBN 0-12-091101-9; vol. 2, hardback: ISBN 0-12-091152-3, paperback: ISBN 0-12-091102-7. - 2nd edition, WellesleyWellesley, MassachusettsWellesley is a town in Norfolk County, Massachusetts, United States. It is part of Greater Boston. The population was 27,982 at the time of the 2010 census.It is best known as the home of Wellesley College and Babson College...
, MassachusettsMassachusettsThe Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010...
: A. K. Peters Ltd., 4 vols., 2001–2004; vol. 1: ISBN 1-56881-130-6; vol. 2: ISBN 1-56881-142-X; vol. 3: ISBN 1-56881-143-8; vol. 4: ISBN 1-56881-144-6. - (with David Wolfe) Mathematical Go. Wellesley, Massachusetts: A. K. Peters Ltd., 1994. ISBN 1-56881-032-6.
- The Dots-and-Boxes Game. NatickNatick, MassachusettsNatick is a town in Middlesex County, Massachusetts, United States. Natick is located near the center of the MetroWest region of Massachusetts, with a population of 33,006 at the 2010 census. Only west from Boston, Natick is considered part of the Greater Boston area...
, MassachusettsMassachusettsThe Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010...
: A. K. Peters Ltd., 2000. ISBN 1-56881-129-2.
External links
- Elwyn Berlekamp home page at the University of California, Berkeley..