mathematics

James Glimm

James Glimm 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 James Glimm rather than just read about it. In short: James Gilbert Glimm (born March 24, 1934) is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University. He has made many contributions in the areas of pure and applied mathematics.

Key takeaways

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

Reference excerpt

James Gilbert Glimm (born March 24, 1934) is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University. He has made many contributions in the areas of pure and applied mathematics.

Life and career

James Glimm was born in Peoria, Illinois, United States on March 24, 1934. He received his BA in engineering from Columbia University in 1956. He continued on to graduate school at Columbia where he received his Ph.D. in mathematics in 1959; his advisor was Richard V. Kadison. Glimm was at New York University, and at Rockefeller University, before arriving at Stony Brook University in 1989. He has been noted for contributions to C*-algebras, quantum field theory, partial differential equations, fluid dynamics, scientific computing, and the modeling of petroleum reservoirs. Together with Arthur Jaffe, he has founded a subject called constructive quantum field theory. His early work in the theory of operator algebras was seminal, and today the "Glimm algebras" that bear his name continue to play an important role in this area of research. More recently, the United States Department of Energy adopted Glimm's front-track methodology for shock-wave calculations, e.g., simulating weapons performance. Glimm was elected to the National Academy of Sciences in 1984. He was an Invited Speaker of the ICM in 1970 at Nice and a Plenary Speaker of the ICM in 1974 at Vancouver. In 1993, Glimm was awarded the Leroy P. Steele Prize for his contribution to solving hyperbolic systems of partial differential equations. He won the National Medal of Science in 2002 "For his original approaches and creative contribution to an array of disciplines in mathematical analysis and mathematical physics". Starting January 1, 2007, he served a 2-year term as president of the American Mathematical Society. In 2012 he became a fellow of the American Mathematical Society.

Appointments

See also Axioms by Glimm and Jaffe

Selected publications Glimm, James (1965), "Solutions in the large for nonlinear hyperbolic systems of equations", Communications on Pure and Applied Mathematics, 18 (4): 697–715, doi:10.1002/cpa.3160180408 Glimm, James (May 1960), "On a certain class of operator algebras.", Transactions of the American Mathematical Society, 95 (2): 318–340, doi:10.2307/1993294, JSTOR 1993294 Glimm, James (September 1960), "A Stone-Weierstrass theorem for C*-algebras.", Annals of Mathematics, Second Series, 72 (2): 216–244, doi:10.2307/1970133, JSTOR 1970133 Glimm, James (May 1961), "Type I C*-algebras.", Annals of Mathematics, Second Series, 73 (3): 572–612, doi:10.2307/1970319, JSTOR 1970319 Glimm, James; et al. (1998), "Three-Dimensional Front Tracking", SIAM J. Sci. Comput., 19 (3): 703–727, Bibcode:1998SJSC...19..703G, CiteSeerX 10.1.1.57.569, doi:10.1137/S1064827595293600 {{citation}}: Cite uses deprecated parameter |citeseerx= (help) Glimm, James; et al. (March 1981), "Front tracking for hyperbolic systems", Advances in Applied Mathematics, 2 (1): 91–119, doi:10.1016/0196-8858(81)90040-3 Glimm, James; Jaffe, Arthur (March 1970), "The λ (φ4) 2 quantum field theory without cutoffs: II. the field operators and the approximate vacuum", Annals of Mathematics, Second Series, 91 (2): 362–401, doi:10.2307/1970582, JSTOR 1970582 Glimm, James; Jaffe, Arthur (1973), "Positivity of the φ 34 Hamiltonian.", Fortschritte der Physik, 21 (7): 327–376, Bibcode:1973ForPh..21..327G, doi:10.1002/prop.19730210702 (Book) Glimm, James; Jaffe, Arthur (1981), Quantum physics : a functional integral point of view, New york, NY: Springer, ISBN 9781468401219 (Book) Glimm, James; Lax, Peter (1970), Decay of solutions of systems of nonlinear hyperbolic conservation laws, Memoirs of the American Mathematical Society, vol. 101, ISBN 0-8218-1801-5

References

External links James Glimm at the Mathematics Genealogy Project Home Page Archived February 19, 2020, at the Wayback Machine, at Stony Brook

Illustrations

Worked examples

Example 1 — a first encounter with James Glimm

Start with the simplest possible case. Write down what James Glimm 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 James Glimm 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 James Glimm 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 James Glimm

In research: James Glimm 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 James Glimm 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: James Glimm is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1934 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James Glimm 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 James Glimm in 20 minutes

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

Frequently asked questions

What is James Glimm in simple terms?

Why does James Glimm 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 James Glimm?

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 James Glimm.