astronomy

Leonard Carlitz

Leonard Carlitz is a astronomy 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 Leonard Carlitz rather than just read about it. In short: Leonard Carlitz (December 26, 1907 – September 17, 1999) was an American mathematician. Carlitz supervised 44 doctorates at Duke University and published more than 770 papers.

Key takeaways

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

Reference excerpt

Leonard Carlitz (December 26, 1907 – September 17, 1999) was an American mathematician. Carlitz supervised 44 doctorates at Duke University and published more than 770 papers.

Chronology 1907 Born Philadelphia, PA, USA 1927 BA, University of Pennsylvania 1930 PhD, University of Pennsylvania, 1930 under Howard Mitchell, who had studied under Oswald Veblen at Princeton 1930–31 at Caltech with E. T. Bell 1931 married Clara Skaler 1931–32 at Cambridge with G. H. Hardy 1932 Joined the faculty of Duke University where he served for 45 years 1938 to 1973 Editorial Board Duke Mathematical Journal (Managing Editor from 1945.) 1939 Birth of son Michael 1940 Supervision of his first doctoral student E. F. Canaday, awarded 1940 1945 Birth of son Robert 1964 First James B. Duke Professor in Mathematics 1971 Birth of granddaughter Natasha 1977 Supervised his 44th and last doctoral student, Jo Ann Lutz, awarded 1977 1977 Retired 1982 Birth of granddaughter Ruth 1990 Death of wife Clara, after 59 years of marriage 1999 September 17 Died in Pittsburgh, PA

Mathematical work The Carlitz module is generalized by the Drinfeld module An identity regarding Bernoulli numbers Carlitz wrote about Bessel polynomials He introduced Al-Salam–Carlitz polynomials. Carlitz' identity for bicentric quadrilaterals He conjectured the Carlitz-Wan conjecture, later proved by Daqing Wan.

Publications Leonard Carlitz published about 771 technical papers comprising approximately 7,000 pages. The effort to edit his collected works, undertaken originally by Professor John Brillhart, is ongoing. Carlitz' exceptional productivity is described by David Hayes as follows:

During the early 1960s, when I was one of his graduate students, Carlitz had a National Science Foundation grant that paid for a half-time secretary. On more than one day I observed him reading a journal paper raising a question that he found of interest, that evening writing up a paper of his own answering the question, and having it typed and sent off to a journal the following day. About 160 articles by Carlitz are about finite fields. The textbook by Rudolf Lidl and Harald Niederreiter on the topic has 141 articles authored or coauthored by Carlitz in its reference list.

See also Bateman polynomials Carlitz exponential Carlitz polynomial (disambiguation) Maillet's determinant Reciprocal Fibonacci constant

References

Further reading Brawley, Joel V. (2000), "In memoriam: Leonard Carlitz (1907–1999)", Finite Fields and Their Applications, 6 (3): 203–206, doi:10.1006/ffta.2000.0276, ISSN 1071-5797, MR 1772617 Brawley, Joel V. (1995), "Dedicated to Leonard Carlitz: the man and his work", Finite Fields and Their Applications, 1 (2): 135–151, doi:10.1006/ffta.1995.1011, ISSN 1071-5797, MR 1337739 Howard, F. T. (2000), "In memoriam—Leonard Carlitz", Fibonacci Quarterly, 38 (4): 316, doi:10.1080/00150517.2000.12428782, ISSN 0015-0517, MR 1775253

External links Obituary at Duke's Math Newsletter Leonard Carlitz at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Leonard Carlitz", MacTutor History of Mathematics Archive, University of St Andrews zbMATH.org author profile

Worked examples

Example 1 — a first encounter with Leonard Carlitz

Start with the simplest possible case. Write down what Leonard Carlitz claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Leonard Carlitz 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 Leonard Carlitz 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 Leonard Carlitz

In research: Leonard Carlitz appears in astronomy 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 Leonard Carlitz 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: Leonard Carlitz is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1907 births, 1999 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Leonard Carlitz 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 Leonard Carlitz in 20 minutes

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

Frequently asked questions

What is Leonard Carlitz in simple terms?

Leonard Carlitz (December 26, 1907 – September 17, 1999) was an American mathematician. Carlitz supervised 44 doctorates at Duke University and published more than 770 papers.

Why does Leonard Carlitz matter?

Because it connects several astronomy 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 Leonard Carlitz?

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 Leonard Carlitz.