mathematics

J. Laurie Snell

J. Laurie Snell 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 J. Laurie Snell rather than just read about it. In short: James Laurie Snell (January 15, 1925 in Wheaton, Illinois – March 19, 2011 in Hanover, New Hampshire) was an American mathematician and educator. Biography J.

Key takeaways

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

Reference excerpt

James Laurie Snell (January 15, 1925 in Wheaton, Illinois – March 19, 2011 in Hanover, New Hampshire) was an American mathematician and educator.

Biography J. Laurie Snell was the son of Roy Snell, an adventure author, and Lucille, a concert pianist. Lucille taught the three sons (Jud, John and Laurie) to play piano, cello, and violin. The family had a life-lease on a cabin in Isle Royale National Park where they would go for summer holidays.

Graduate work Snell studied mathematics at the University of Illinois with Joseph L. Doob from 1948 through 1951; Doob introduced him to martingales, an aspect of probability theory. Doob assigned such topics by having students attempt to solve a series of problems that he kept on file cards. Snell earned his Ph.D. in 1951 ("Applications of Martingale System Theorems"), with Doob as his supervisor.

Dartmouth College At Dartmouth College Snell became involved in a mathematics department project to develop a course on modern mathematics used in biological and social sciences. He worked with John G. Kemeny and Gerald L. Thompson to write Introduction to Finite Mathematics (1957) which described probability theory, linear algebra, and applications in sociology, genetics, psychology, anthropology, and economics. They found "the basic ideas of finite mathematics were easier to state and theorems about them considerably easier to prove than their infinite counterparts." A French translation was made by M. C. Loyau and published in 1960 by Donod. Another colleague at Dartmouth, Hazleton Mirkil, joined the team to write Finite Mathematical Structures (1959) for sophomores at Dartmouth studying science. Infinite problems are considered after their finite counterparts are fully developed in the text. In 1962 the publisher Prentice-Hall issued a third book from a Dartmouth team: Kemeny, Snell, Thompson, and Arthur Schleifer Jr. wrote Finite Mathematics with Business Applications which included applications: computer circuits, critical path analysis, flow diagrams for computing and accounting procedures, Monte Carlo simulation of decision processes, reliability, decision theory, waiting line theory, a simple approach to mathematics of finance, matrix games, and the simplex method for solving linear programming problems. A second edition of the first text came out in 1966.

Writings In 1959 Snell published a survey article on Markov chains. He worked the material into a book Finite Markov Chains with Kemeny. As the "first self-contained account in English", it attracted wide interest. While one reviewer said "the exposition is of high quality", other reviewers found fault: Too little attention paid to assumptions inherent in a model. "Interest builds steadily as one peruses the book." But "little attention to historical development." "From the point of view of an undergraduate ... the opening chapter on mathematical prerequisites is rather frightening." "Does not supersede the corresponding chapters in Feller's classic Introduction to Probability; "No index and not even the sketchiest bibliography." Snell started Chance News in 1992 to "review news and journal articles pertaining to probability and statistics in the real world." One feature is Forsooth for statistical gaffes in media reports, a column originally found in the newsletter of the Royal Statistical Society. In 2005 Chance News was moved to Chance Wiki where there is an archive of Forsooths and previous News. Out of collaborations in Chance News with Charles M. Grinstead and William P. Peterson, a book Probability Tales (2011) was published by American Mathematical Society in the Student Mathematical Library. The book covers four topics: streaks in sports as streaks of successful Bernoulli trials (like hitting streaks), constructing stock market models, estimating expected value of a lottery ticket, and reliability of fingerprint identification.

Legacy Snell retired in 1995 and was elected as a fellow of the American Statistical Association in 1996. The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. The Snell envelope refers to results in a 1952 paper Applications of martingale system theorems.

Books 1957: (with John G. Kemeny and Gerald L. Thompson) Introduction to Finite Mathematics Prentice Hall Online 1959: (with Kemeny, Thompson & Hazleton Mirkil) Finite Mathematical Structures 1960: (with John G. Kemeny) Finite Markov Chains, D. van Nostrand Company ISBN 0-442-04328-7 1962: (with Kemeny, Thompson & Arthur Schleifer Jr.) Finite Mathematics with Business Applications 1962: (with John G. Kemeny) Mathematical Models in the Social Sciences, Ginn and Company 1966: (with J.G. Kemeny & A.W. Knapp) Denumerable Markov Chains, second edition 1976, Springer-Verlag 1980: (with Ross Kindermann) Markov Random Fields and Their Applications, American Mathematical Society ISBN 0-8218-5001-6, ISBN 978-0-8218-5001-5 1980: (with Ross P. Kindermann) "On the relation between Markov random fields and social networks", Journal of Mathematical Sociology 7(1): 1–13. 1984: (with Peter G. Doyle) Random Walks and Electrical Networks, Mathematical Association of America ISBN 0-88385-024-9 1988: Introduction To Probability, Random House ISBN 0-394-34485-5 1997: (with Charles Grinsted) Introduction to Probability second edition, American Mathematical Society, ISBN 0-8218-0749-8, ISBN 978-0-8218-0749-1 (online Archived 2011-07-27 at the Wayback Machine) 2011: (with C.M. Grinstead & W.P. Peterson) Probability Tales, American Mathematical Society ISBN 978-0-8218-5261-3

Notes

References

External links Literature by and about J. Laurie Snell in the German National Library catalogue Website at Dartmouth College Archived 2010-01-12 at the Wayback Machine J. Laurie Snell at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with J. Laurie Snell

Start with the simplest possible case. Write down what J. Laurie Snell 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 J. Laurie Snell 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 J. Laurie Snell 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 J. Laurie Snell

In research: J. Laurie Snell 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 J. Laurie Snell 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: J. Laurie Snell is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1925 births, 2011 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for J. Laurie Snell 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.

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How to study J. Laurie Snell in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what J. Laurie Snell 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 J. Laurie Snell out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is J. Laurie Snell in simple terms?

James Laurie Snell (January 15, 1925 in Wheaton, Illinois – March 19, 2011 in Hanover, New Hampshire) was an American mathematician and educator. Biography J.

Why does J. Laurie Snell 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 J. Laurie Snell?

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 J. Laurie Snell.