Harold S. Shapiro
Encyclopedia
Harold Seymour Shapiro (born 1928 in Brooklyn
, New York) is a professor emeritus of mathematics
at the Royal Institute of Technology
in Stockholm
, Sweden
, best
known for inventing the so-called Shapiro polynomials
(also known as Golay–Shapiro polynomials or Rudin–Shapiro polynomials)
and for pioneering work on quadrature domains
.
His main research areas have been approximation theory
, complex analysis
, functional analysis
, and partial differential equation
s.
He is also interested in the pedagogy
of problem-solving.
Shapiro received his Ph.D.
in 1952 from the Massachusetts Institute of Technology
. He is the father of cosmologist Max Tegmark
, a graduate of the Royal Institute of Technology
and now a professor at MIT.
He earned a B.Sc. from the City College of New York
in 1949 and earned his M.S.
degree from MIT in 1951.
Brooklyn
Brooklyn is the most populous of New York City's five boroughs, with nearly 2.6 million residents, and the second-largest in area. Since 1896, Brooklyn has had the same boundaries as Kings County, which is now the most populous county in New York State and the second-most densely populated...
, New York) is a professor emeritus of mathematics
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...
at the Royal Institute of Technology
Royal Institute of Technology
The Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for one-third of Sweden’s technical research and engineering education...
in Stockholm
Stockholm
Stockholm is the capital and the largest city of Sweden and constitutes the most populated urban area in Scandinavia. Stockholm is the most populous city in Sweden, with a population of 851,155 in the municipality , 1.37 million in the urban area , and around 2.1 million in the metropolitan area...
, Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
, best
known for inventing the so-called Shapiro polynomials
Shapiro polynomials
In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude of specific trigonometric sums. In signal processing, the Shapiro polynomials have good autocorrelation properties and their values on the unit...
(also known as Golay–Shapiro polynomials or Rudin–Shapiro polynomials)
and for pioneering work on quadrature domains
Quadrature domains
In the branch of mathematics called potential theory, a quadrature domain in two dimensional real Euclidean space is a domain D together with...
.
His main research areas have been approximation theory
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
, complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, and partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s.
He is also interested in the pedagogy
Pedagogy
Pedagogy is the study of being a teacher or the process of teaching. The term generally refers to strategies of instruction, or a style of instruction....
of problem-solving.
Shapiro received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1952 from 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...
. He is the father of cosmologist Max Tegmark
Max Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...
, a graduate of the Royal Institute of Technology
Royal Institute of Technology
The Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for one-third of Sweden’s technical research and engineering education...
and now a professor at MIT.
He earned a B.Sc. from the City College of New York
City College of New York
The City College of the City University of New York is a senior college of the City University of New York , in New York City. It is also the oldest of the City University's twenty-three institutions of higher learning...
in 1949 and earned his M.S.
Master of Science
A Master of Science is a postgraduate academic master's degree awarded by universities in many countries. The degree is typically studied for in the sciences including the social sciences.-Brazil, Argentina and Uruguay:...
degree from MIT in 1951.
External links
- Shapiro's homepage
- Rudin–Shapiro Curve by Eric Rowland, The Wolfram Demonstrations Project.