Jim Propp
Encyclopedia
James Gary "Jim" Propp is a professor
of mathematics
at the University of Massachusetts Lowell
.
In high school, Propp was one of the national winners of the United States of America Mathematical Olympiad
(USAMO), and an alumnus of the Hampshire College Summer Studies in Mathematics
. Propp obtained his A.B.
in mathematics in 1982 at Harvard
. After advanced study at Cambridge
, he obtained his Ph.D.
from the University of California at Berkeley. He has held professorships at seven universities, including Harvard, MIT, and the University of Wisconsin.
Propp is the co-editor of the book Microsurveys in Discrete Probability (1998) and has written more than thirty journal articles on game theory
, combinatorics
and probability
, and recreational mathematics
. He lectures extensively and has served on the Mathematical Olympiad Committee of the Mathematical Association of America
, which sponsors the USAMO. In the early 90s Propp lived in Boston
and later in Arlington, Massachusetts
.
In 1996, Propp and David Wilson invented coupling from the past
, a method for sampling
from the stationary distribution
of a Markov chain
among Markov chain Monte Carlo
(MCMC) algorithms. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from the stationary distribution. His papers have discussed the use of surcomplex number
s in game theory
; the solution to the counting of alternating sign matrices
; and occurrences of Grandi's series
as an Euler characteristic
of infinite-dimensional real projective space
.
Propp is a member of the National Puzzlers' League
under the nom
Aesop. He was recruited for the organization by colleague Henri Picciotto, cruciverbalist and co-author of the league's first cryptic crossword collection. Propp is the creator of the "Self-Referential Aptitude Test", a humorous multiple-choice test in which all questions except the last make self-reference
s to their own answers. It was created in the early 90s for a puzzlers' party.
Propp is the author of Tuscanini, a 1992 children's book about a musical elephant, illustrated by Ellen Weiss.
He is married to research psychologist Alexandra (Sandi) Gubin. They have a son Adam and a daughter Eliana.
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
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 University of Massachusetts Lowell
University of Massachusetts Lowell
The University of Massachusetts Lowell is a public university in Lowell, Massachusetts, and part of the University of Massachusetts system...
.
In high school, Propp was one of the national winners of the United States of America Mathematical Olympiad
United States of America Mathematical Olympiad
The United States of America Mathematical Olympiad is a high school mathematics competition held annually in the United States. Since its debut in 1972, it has served as the final round of the AMC series of contests...
(USAMO), and an alumnus of the Hampshire College Summer Studies in Mathematics
Hampshire College Summer Studies in Mathematics
The Hampshire College Summer Studies in Mathematics is a residential program for mathematically talented high school students. The program has been conducted each summer since 1971, with the exceptions of 1981 and 1996, and has more than 1500 alumni....
. Propp obtained his A.B.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in mathematics in 1982 at Harvard
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
. After advanced study at Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
, he obtained 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 the University of California at Berkeley. He has held professorships at seven universities, including Harvard, MIT, and the University of Wisconsin.
Propp is the co-editor of the book Microsurveys in Discrete Probability (1998) and has written more than thirty journal articles on game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
and probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, and recreational mathematics
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
. He lectures extensively and has served on the Mathematical Olympiad Committee of the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
, which sponsors the USAMO. In the early 90s Propp lived in Boston
Boston
Boston is the capital of and largest city in Massachusetts, and is one of the oldest cities in the United States. The largest city in New England, Boston is regarded as the unofficial "Capital of New England" for its economic and cultural impact on the entire New England region. The city proper had...
and later in Arlington, Massachusetts
Arlington, Massachusetts
Arlington is a town in Middlesex County, Massachusetts, United States, six miles northwest of Boston. The population was 42,844 at the 2010 census.-History:...
.
In 1996, Propp and David Wilson invented coupling from the past
Coupling from the past
Among Markov chain Monte Carlo algorithms, coupling from the past is a method for sampling from the stationary distribution of a Markov chain. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from the stationary distribution...
, a method for sampling
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
from the stationary distribution
Stationary distribution
Stationary distribution may refer to:* The limiting distribution in a Markov chain* The marginal distribution of a stationary process or stationary time series* The set of joint probability distributions of a stationary process or stationary time series...
of a Markov chain
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...
among Markov chain Monte Carlo
Markov chain Monte Carlo
Markov chain Monte Carlo methods are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its equilibrium distribution. The state of the chain after a large number of steps is then used as a sample of the...
(MCMC) algorithms. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from the stationary distribution. His papers have discussed the use of surcomplex number
Surcomplex number
A surcomplex number is a number of the form a+ib , where a and b are surreal numbers. The surcomplex numbers form an algebraically closed field, isomorphic to the algebraic closure of the field generated by extending the rational numbers by a proper class of algebraically independent...
s in game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
; the solution to the counting of alternating sign matrices
Alternating sign matrix
In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. These matrices arise naturally when using Dodgson condensation to compute a determinant...
; and occurrences of Grandi's series
Occurrences of Grandi's series
-Parables:Guido Grandi illustrated the series with a parable involving two brothers who share a gem.Thomson's lamp is a supertask in which a hypothetical lamp is turned on and off infinitely many times in a finite time span. One can think of turning the lamp on as adding 1 to its state, and turning...
as an Euler characteristic
Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent...
of infinite-dimensional real projective space
Real projective space
In mathematics, real projective space, or RPn, is the topological space of lines through 0 in Rn+1. It is a compact, smooth manifold of dimension n, and a special case of a Grassmannian.-Construction:...
.
Propp is a member of the National Puzzlers' League
National Puzzlers' League
The National Puzzlers' League is a nonprofit organization focused on puzzling, primarily in the realm of word play and word games. Founded in 1883, it is the oldest puzzlers' organization in the world...
under the nom
Pseudonym
A pseudonym is a name that a person assumes for a particular purpose and that differs from his or her original orthonym...
Aesop. He was recruited for the organization by colleague Henri Picciotto, cruciverbalist and co-author of the league's first cryptic crossword collection. Propp is the creator of the "Self-Referential Aptitude Test", a humorous multiple-choice test in which all questions except the last make self-reference
Self-reference
Self-reference occurs in natural or formal languages when a sentence or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding...
s to their own answers. It was created in the early 90s for a puzzlers' party.
Propp is the author of Tuscanini, a 1992 children's book about a musical elephant, illustrated by Ellen Weiss.
He is married to research psychologist Alexandra (Sandi) Gubin. They have a son Adam and a daughter Eliana.