mathematics

Lawrence C. Washington

Lawrence C. Washington 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 Lawrence C. Washington rather than just read about it. In short: Lawrence Clinton Washington (born 1951 in Vermont) is an American mathematician at the University of Maryland who specializes in number theory. Biography Washington studied at Johns Hopkins University, where in 1971 he received his B.A. and master's degree.

Key takeaways

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

Reference excerpt

Lawrence Clinton Washington (born 1951 in Vermont) is an American mathematician at the University of Maryland who specializes in number theory.

Biography Washington studied at Johns Hopkins University, where in 1971 he received his B.A. and master's degree. In 1974 he earned his PhD at Princeton University under Kenkichi Iwasawa with thesis Class numbers and Z p {\displaystyle Z_{p}} extensions. He then became an assistant professor at Stanford University and from 1977 at the University of Maryland, where he became in 1981 an associate professor and in 1986 a professor. He held visiting positions at several institutions, including IHES (1980/81), Max-Planck-Institut für Mathematik (1984), the Institute for Advanced Study (1996), and MSRI (1986/87), as well as at the University of Perugia, Nankai University and the State University of Campinas. In 1979–1981 he was a Sloan Fellow.

Recognition In 2011 he was awarded a Distinguished Scholar-Teacher award from the University of Maryland.

He was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to number theory, especially cyclotomic fields, and for mentoring at all levels".

Research Washington wrote a standard work on cyclotomic fields. He also worked on p-adic L-functions. He wrote a treatise with Allan Adler on their discovery of a connection between higher-dimensional analogues of magic squares and p-adic L-functions. Washington has done important work on Iwasawa theory, Cohen-Lenstra heuristics, and elliptic curves and their applications to cryptography. In Iwasawa theory he proved with Bruce Ferrero in 1979 a conjecture of Kenkichi Iwasawa, that the μ {\displaystyle \mu } -invariant vanishes for cyclotomic Zp-extensions of abelian number fields (Theorem of Ferrero-Washington). More recently, Washington has published on arithmetic dynamics, sums of powers of primes, and Iwasawa invariants of non-cyclotomic Zp extensions

Selected works Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, Springer, 1982, 2nd edn. 1996 Galois Cohomology in Cornell, Silverman, Stevens (eds.): Modular forms and Fermat's Last Theorem, Springer, 1997 Elliptic Curves: Number theory and cryptography, CRC Press, 2003, 2nd edn. 2008 with James Kraft: An Introduction to Number Theory with Cryptography, CRC Press, 2003, 2nd edn. with Wade Trappe: Introduction to Cryptography and Coding Theory, Prentice-Hall, 2002, 2nd edn. 2005

Sources Joseph Oesterlé Travaux de Ferrero et Washington sur le nombre de classes d'idéaux des corps cyclotomiques, Séminaire Bourbaki, Nr. 535, 1978/79 Archived 2014-12-19 at the Wayback Machine Lawrence C. Washington, Curriculum Vita

References

External links Homepage Lawrence C. Washington at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Lawrence C. Washington

Start with the simplest possible case. Write down what Lawrence C. Washington 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 Lawrence C. Washington 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 Lawrence C. Washington 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 Lawrence C. Washington

In research: Lawrence C. Washington 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 Lawrence C. Washington 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: Lawrence C. Washington is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1951 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lawrence C. Washington 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 Lawrence C. Washington in 20 minutes

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

Frequently asked questions

What is Lawrence C. Washington in simple terms?

Lawrence Clinton Washington (born 1951 in Vermont) is an American mathematician at the University of Maryland who specializes in number theory. Biography Washington studied at Johns Hopkins University, where in 1971 he received his B.A. and master's degree.

Why does Lawrence C. Washington 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 Lawrence C. Washington?

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 Lawrence C. Washington.