mathematics

Jim Propp

Jim Propp is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Jim Propp rather than just read about it. In short: James Gary Propp is a professor of mathematics at the University of Massachusetts Lowell. Education and career 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.

Key takeaways

Jim Propp belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Jim Propp to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Jim Propp from memory before moving on to harder problems.

Reference excerpt

James Gary Propp is a professor of mathematics at the University of Massachusetts Lowell.

Education and career 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 AB in mathematics in 1982 at Harvard. After advanced study at Cambridge, he obtained his PhD from the University of California at Berkeley. He has held professorships at seven universities, including Harvard, MIT, the University of Wisconsin, and the University of Massachusetts Lowell.

Mathematical research Propp is the co-editor of the book Microsurveys in Discrete Probability (1998) and has written more than fifty 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 numbers 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.

Other contributions Propp was a member of the National Puzzlers' League under the pseudonym Aesop. He was recruited for the organisation 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-references to their own answers. It was created in the early 1990s for a puzzlers' party. Propp is the author of Tuscanini, a 1992 children's book about a musical elephant, illustrated by Ellen Weiss.

Awards and honours In 2015 he was elected as a fellow of the American Mathematical Society "for contributions to combinatorics and probability, and for mentoring and exposition."

Personal He is married to research psychologist Alexandra (Sandi) Gubin. They have a son Adam and a daughter Eliana.

Notes

External links

Propp's website Jim Propp at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Jim Propp

Start with the simplest possible case. Write down what Jim Propp claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jim Propp before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jim Propp ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jim Propp

In research: Jim Propp appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Jim Propp in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Jim Propp is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, 21st-century American mathematicians, Alumni of the University of Cambridge, so understanding it makes those chapters shorter.
In everyday life: Look for Jim Propp outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Jim Propp in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jim Propp means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Jim Propp out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jim Propp in simple terms?

James Gary Propp is a professor of mathematics at the University of Massachusetts Lowell. Education and career 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.

Why does Jim Propp matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jim Propp?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jim Propp.