Henry Wallman
Encyclopedia
Henry Wallman (1915 – 1992) was an American mathematician, known for his work in lattice theory, dimension theory
, topology
, and electronic circuit design
.
A native of Brooklyn and a 1933 graduate of Brooklyn College
, Wallman received his Ph.D. in mathematics
from Princeton University
in 1937, under the supervision of Solomon Lefschetz
and became a faculty member at the Massachusetts Institute of Technology
, where he was associated with the Radiation Laboratory
. During World War II
he did classified
work at MIT, possibly involving radar
. In 1948, he left MIT to become a professor of electrotechnics at the Chalmers University of Technology
in Gothenburg
, Sweden
, which awarded him the Chalmers medal in 1980 and where he eventually retired. In 1950 he was elected as a foreign member to the Swedish Royal Academy
. He was elected a member of the Royal Swedish Academy of Engineering Sciences
in 1960 and of the Royal Swedish Academy of Engineering Sciences
in 1970.
The disjunction property of Wallman
is named after Wallman, as is the Wallman compactification
, and he co-authored an important monograph on dimension theory with Witold Hurewicz
. Wallman was also a radio
enthusiast, and in the postwar period co-authored a book comprehensively documenting what was known at the time about vacuum tube
amplification
technology, including new developments such as showing how the central limit theorem
could be used to describe the rise time
of cascaded circuits. At Chalmers, Wallman helped build the Electronic Differential Analyser, an early example of an analog computer
, and performed pioneering research in biomedical engineering
combining video
displays with X-ray
imaging.
Dimension theory
In mathematics, dimension theory is a branch of general topology dealing with dimensional invariants of topological spaces.-See also:*Lebesgue covering dimension*Inductive dimensions *Dimension...
, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, and electronic circuit design
Electronic circuit design
Electronic design comprises the analysis and synthesis of electronic circuits-Methods:To design any electrical circuit, either analog or digital, electrical engineers need to be able to predict the voltages and currents at all places within the circuit...
.
A native of Brooklyn and a 1933 graduate of Brooklyn College
Brooklyn College
Brooklyn College is a senior college of the City University of New York, located in Brooklyn, New York, United States.Established in 1930 by the New York City Board of Higher Education, the College had its beginnings as the Downtown Brooklyn branches of Hunter College and the City College of New...
, Wallman received his Ph.D. in 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...
from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1937, under the supervision of Solomon Lefschetz
Solomon Lefschetz
Solomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.-Life:...
and became a faculty member 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...
, where he was associated with the Radiation Laboratory
Radiation Laboratory
The Radiation Laboratory, commonly called the Rad Lab, was located at the Massachusetts Institute of Technology in Cambridge, Massachusetts and functioned from October 1940 until December 31, 1945...
. During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
he did classified
Classified information
Classified information is sensitive information to which access is restricted by law or regulation to particular groups of persons. A formal security clearance is required to handle classified documents or access classified data. The clearance process requires a satisfactory background investigation...
work at MIT, possibly involving radar
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
. In 1948, he left MIT to become a professor of electrotechnics at the Chalmers University of Technology
Chalmers University of Technology
Chalmers University of Technology , is a Swedish university located in Gothenburg that focuses on research and education in technology, natural science and architecture.-History:...
in Gothenburg
Gothenburg
Gothenburg is the second-largest city in Sweden and the fifth-largest in the Nordic countries. Situated on the west coast of Sweden, the city proper has a population of 519,399, with 549,839 in the urban area and total of 937,015 inhabitants 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....
, which awarded him the Chalmers medal in 1980 and where he eventually retired. In 1950 he was elected as a foreign member to the Swedish Royal Academy
Swedish Royal Academies
The Royal Academies are independent organisations, founded on Royal command, that act to promote the arts, culture, and science in Sweden. The Swedish Academy and Academy of Sciences are also responsible for the selection of Nobel Prize laureates in Literature, Physics, Chemistry, and the Prize in...
. He was elected a member of the Royal Swedish Academy of Engineering Sciences
Royal Swedish Academy of Engineering Sciences
The Royal Swedish Academy of Engineering Sciences or Kungl. Ingenjörsvetenskapsakademien , founded in 1919 by King Gustaf V, is one of the Royal Academies in Sweden...
in 1960 and of the Royal Swedish Academy of Engineering Sciences
Royal Swedish Academy of Engineering Sciences
The Royal Swedish Academy of Engineering Sciences or Kungl. Ingenjörsvetenskapsakademien , founded in 1919 by King Gustaf V, is one of the Royal Academies in Sweden...
in 1970.
The disjunction property of Wallman
Disjunction property of Wallman
In mathematics, especially in order theory, a partially ordered set with a unique minimal element 0 has the disjunction property of Wallman when for every pair of elements of the poset, either b ≤ a or there exists an element c ≤ b such that c ≠ 0 and c has no nontrivial common predecessor with a...
is named after Wallman, as is the Wallman compactification
Wallman compactification
In mathematics, the Wallman compactification is a compactification of T1 topological spaces that was constructed by .The points of the Wallman compactification ωX of a space X are the maximal families Φ of closed nonempty subsets of X such that Φ is closed under finite intersections...
, and he co-authored an important monograph on dimension theory with Witold Hurewicz
Witold Hurewicz
Witold Hurewicz was a Polish mathematician.- Early life and education :Witold Hurewicz was born to a Jewish family in Łódź, Russian Empire ....
. Wallman was also a radio
Radio
Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
enthusiast, and in the postwar period co-authored a book comprehensively documenting what was known at the time about vacuum tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...
amplification
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...
technology, including new developments such as showing how the central limit theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
could be used to describe the rise time
Rise time
In electronics, when describing a voltage or current step function, rise time refers to the time required for a signal to change from a specified low value to a specified high value...
of cascaded circuits. At Chalmers, Wallman helped build the Electronic Differential Analyser, an early example of an analog computer
Analog computer
An analog computer is a form of computer that uses the continuously-changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved...
, and performed pioneering research in biomedical engineering
Biomedical engineering
Biomedical Engineering is the application of engineering principles and design concepts to medicine and biology. This field seeks to close the gap between engineering and medicine: It combines the design and problem solving skills of engineering with medical and biological sciences to improve...
combining video
Video
Video is the technology of electronically capturing, recording, processing, storing, transmitting, and reconstructing a sequence of still images representing scenes in motion.- History :...
displays with X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
imaging.