Floyd Williams
Encyclopedia
Floyd Leroy Williams is a North American mathematician well-known for his work in Lie theory
and, most recently, mathematical physics
. In addition to Lie theory, his research interests are in homological algebra
and the mathematics of quantum mechanics
. He received his B.S.(1962) in Mathematics from Lincoln University of Missouri, and later his M.S.(1965) and Ph.D.(1972) from Washington University in St. Louis
. Williams was appointed professor
of mathematics at the University of Massachusetts Amherst
in 1984, and has been professor emeritus
since 2005.
. He was raised in extreme poverty
. His mother told him not to complain about their situation, but rather to have faith in God
and work hard. Her advice was taken, and it worked. He eventually was ordained in addition to being a mathematician
.
However, it was music
, not mathematics
, that appealed to him through high school
. "In fact," he admits, "mathematics was the only course in which I did not do well." Williams had not thought of going to college
until his last week in high school when he was offered a music scholarship
at Lincoln University of Missouri in Jefferson City, Missouri
.
It was in his sophomore year that he became intrigued by the theory of relativity
, which turned out to be his main motivation for studying mathematics
. In 1972 he completed his Ph.D.
from Washington University where his thesis
was in the field of Lie theory
. He was an instructor
and lecturer
at MIT from 1972-1975, before moving to the University of Massachusetts
as an assistant professor in 1975. In 1983 he received an MRI grant to continuing researching in this field, ushering him into the mainstream of mathematics.
As an African-American in a field that has had little minority
representation, Williams has felt the sting of discrimination
during his career. However, he has been a motivation and role model for many young minorities, encouraging them to enter science
and engineering
. Williams has helped to set up programs that allow pre-college students and undergraduates to meet and talk with mathematicians, scientists and engineers, most notably at a summer camp run at MIT. "All that many of these youngsters see is different courses," he says, "but they want to know what mathematicians do from 8 am to 5 pm. Once minorities commit to graduate
work in science
or engineering
," he continues, "they need extra help and support for what, for many, is the foreign environment of graduate school
. Such programs exist at few universities, but we need more of them."
has been in the area of Nikiforov-Uvarov theory of generalized hypergeometric differential equation
, used to solve the Schrödinger equation
and to obtain the quantization of energies from a single unified point of view. This theory
is developed and is also used to give a uniform approach to the theory of special functions
. This study furthers to connect the modern studies of pure mathematics
with physics
.
Lie theory
Lie theory is an area of mathematics, developed initially by Sophus Lie.Early expressions of Lie theory are found in books composed by Lie with Friedrich Engel and Georg Scheffers from 1888 to 1896....
and, most recently, mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
. In addition to Lie theory, his research interests are in homological algebra
Homological algebra
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...
and the mathematics of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. He received his B.S.(1962) in Mathematics from Lincoln University of Missouri, and later his M.S.(1965) and Ph.D.(1972) from Washington University in St. Louis
Washington University in St. Louis
Washington University in St. Louis is a private research university located in suburban St. Louis, Missouri. Founded in 1853, and named for George Washington, the university has students and faculty from all fifty U.S. states and more than 110 nations...
. Williams was appointed professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of mathematics at the University of Massachusetts Amherst
University of Massachusetts Amherst
The University of Massachusetts Amherst is a public research and land-grant university in Amherst, Massachusetts, United States and the flagship of the University of Massachusetts system...
in 1984, and has been professor emeritus
Emeritus
Emeritus is a post-positive adjective that is used to designate a retired professor, bishop, or other professional or as a title. The female equivalent emerita is also sometimes used.-History:...
since 2005.
Biographical Sketch
Floyd Williams was born on September 20 1939, and lived in Kansas City, MissouriKansas City, Missouri
Kansas City, Missouri is the largest city in the U.S. state of Missouri and is the anchor city of the Kansas City Metropolitan Area, the second largest metropolitan area in Missouri. It encompasses in parts of Jackson, Clay, Cass, and Platte counties...
. He was raised in extreme poverty
Poverty
Poverty is the lack of a certain amount of material possessions or money. Absolute poverty or destitution is inability to afford basic human needs, which commonly includes clean and fresh water, nutrition, health care, education, clothing and shelter. About 1.7 billion people are estimated to live...
. His mother told him not to complain about their situation, but rather to have faith in God
God
God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....
and work hard. Her advice was taken, and it worked. He eventually was ordained in addition to being a mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
However, it was music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, not 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...
, that appealed to him through high school
High school
High school is a term used in parts of the English speaking world to describe institutions which provide all or part of secondary education. The term is often incorporated into the name of such institutions....
. "In fact," he admits, "mathematics was the only course in which I did not do well." Williams had not thought of going to college
College
A college is an educational institution or a constituent part of an educational institution. Usage varies in English-speaking nations...
until his last week in high school when he was offered a music scholarship
Scholarship
A scholarship is an award of financial aid for a student to further education. Scholarships are awarded on various criteria usually reflecting the values and purposes of the donor or founder of the award.-Types:...
at Lincoln University of Missouri in Jefferson City, Missouri
Jefferson City, Missouri
Jefferson City is the capital of the U.S. state of Missouri and the county seat of Cole County. Located in Callaway and Cole counties, it is the principal city of the Jefferson City metropolitan area, which encompasses the entirety of both counties. As of the 2010 census, the population was 43,079...
.
It was in his sophomore year that he became intrigued by the theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
, which turned out to be his main motivation for studying 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...
. In 1972 he completed 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...
from Washington University where his thesis
Thesis
A dissertation or thesis is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings...
was in the field of Lie theory
Lie theory
Lie theory is an area of mathematics, developed initially by Sophus Lie.Early expressions of Lie theory are found in books composed by Lie with Friedrich Engel and Georg Scheffers from 1888 to 1896....
. He was an instructor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
and lecturer
Lecturer
Lecturer is an academic rank. In the United Kingdom, lecturer is a position at a university or similar institution, often held by academics in their early career stages, who lead research groups and supervise research students, as well as teach...
at MIT from 1972-1975, before moving to the University of Massachusetts
University of Massachusetts
This article relates to the statewide university system. For the flagship campus often referred to as "UMass", see University of Massachusetts Amherst...
as an assistant professor in 1975. In 1983 he received an MRI grant to continuing researching in this field, ushering him into the mainstream of mathematics.
As an African-American in a field that has had little minority
Minority group
A minority is a sociological group within a demographic. The demographic could be based on many factors from ethnicity, gender, wealth, power, etc. The term extends to numerous situations, and civilizations within history, despite the misnomer of minorities associated with a numerical statistic...
representation, Williams has felt the sting of discrimination
Discrimination
Discrimination is the prejudicial treatment of an individual based on their membership in a certain group or category. It involves the actual behaviors towards groups such as excluding or restricting members of one group from opportunities that are available to another group. The term began to be...
during his career. However, he has been a motivation and role model for many young minorities, encouraging them to enter science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
and engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
. Williams has helped to set up programs that allow pre-college students and undergraduates to meet and talk with mathematicians, scientists and engineers, most notably at a summer camp run at MIT. "All that many of these youngsters see is different courses," he says, "but they want to know what mathematicians do from 8 am to 5 pm. Once minorities commit to graduate
Postgraduate education
Postgraduate education involves learning and studying for degrees or other qualifications for which a first or Bachelor's degree generally is required, and is normally considered to be part of higher education...
work in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
or engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
," he continues, "they need extra help and support for what, for many, is the foreign environment of graduate school
Graduate school
A graduate school is a school that awards advanced academic degrees with the general requirement that students must have earned a previous undergraduate degree...
. Such programs exist at few universities, but we need more of them."
Mathematics
Williams' recent contribution to quantum mechanicsQuantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
has been in the area of Nikiforov-Uvarov theory of generalized hypergeometric differential equation
Hypergeometric differential equation
In mathematics, the Gaussian or ordinary hypergeometric function 2F1 is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation...
, used to solve the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
and to obtain the quantization of energies from a single unified point of view. This theory
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
is developed and is also used to give a uniform approach to the theory of special functions
Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
. This study furthers to connect the modern studies of pure mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
with physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
.