mathematics

Lynn Harold Loomis

Lynn Harold Loomis 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 Lynn Harold Loomis rather than just read about it. In short: Lynn Harold Loomis (April 25, 1915 – June 9, 1994) was an American mathematician working on analysis. Together with Hassler Whitney, he discovered the Loomis–Whitney inequality.

Key takeaways

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

Reference excerpt

Lynn Harold Loomis (April 25, 1915 – June 9, 1994) was an American mathematician working on analysis. Together with Hassler Whitney, he discovered the Loomis–Whitney inequality. Loomis received his PhD in 1942 from Harvard University under Salomon Bochner with thesis Some Studies on Simply-Connected Riemann Surfaces: I. The Problem of Imbedding II. Mapping on the Boundary for Two Classes of Surfaces. After completing his PhD, Loomis was a professor at Radcliffe College and from 1949 at Harvard. From 1956, he was a member of the American Academy of Arts and Sciences.

Selected works

Articles Loomis, Lynn H. (1942). "On an inequality of Seidel and Walsh". Bull. Amer. Math. Soc. 48 (12): 908–911. doi:10.1090/s0002-9904-1942-07820-7. MR 0008629. Loomis, Lynn H. (1943). "The converse of the Fatou theorem for positive harmonic functions". Trans. Amer. Math. Soc. 53 (2): 239–250. doi:10.1090/s0002-9947-1943-0007832-1. MR 0007832. Loomis, Lynn H. (1944). "A short proof of the completeness of the Laguerre functions". Bull. Amer. Math. Soc. 50 (6): 386–387. doi:10.1090/s0002-9904-1944-08151-2. MR 0010222. Loomis LH (1946). "On a theorem of von Neumann". Proc Natl Acad Sci U S A. 32 (8): 213–215. Bibcode:1946PNAS...32..213L. doi:10.1073/pnas.32.8.213. PMC 1078923. PMID 16578206. Loomis, Lynn H. (1946). "A note on the Hilbert transform". Bull. Amer. Math. Soc. 52 (12): 1082–1086. doi:10.1090/s0002-9904-1946-08713-3. MR 0019155. with Hassler Whitney: Loomis, L. H.; Whitney, H. (1949). "An inequality related to the isoperimetric inequality". Bull. Amer. Math. Soc. 55 (10): 961–962. doi:10.1090/S0002-9904-1949-09320-5. MR 0031538.

Books Introduction to Abstract Harmonic Analysis, Van Nostrand 1953 with Shlomo Sternberg Advanced Calculus, Addison-Wesley 1968 (revised 1990, Jones and Bartlett; reprinted 2014, World Scientific) [a challenging text for (first-year) undergraduate students treating calculus on Banach spaces and differentiable manifolds; see Math 55] Introduction to Calculus, Addison-Wesley 1975 Calculus, Addison-Wesley 1974, 1982

Notes

External links Lynn Harold Loomis at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Lynn Harold Loomis

Start with the simplest possible case. Write down what Lynn Harold Loomis 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 Lynn Harold Loomis 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 Lynn Harold Loomis 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 Lynn Harold Loomis

In research: Lynn Harold Loomis 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 Lynn Harold Loomis 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: Lynn Harold Loomis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1915 births, 1994 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lynn Harold Loomis 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 Lynn Harold Loomis in 20 minutes

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Frequently asked questions

What is Lynn Harold Loomis in simple terms?

Lynn Harold Loomis (April 25, 1915 – June 9, 1994) was an American mathematician working on analysis. Together with Hassler Whitney, he discovered the Loomis–Whitney inequality.

Why does Lynn Harold Loomis 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 Lynn Harold Loomis?

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 Lynn Harold Loomis.