mathematics

Willard L. Miranker

Willard L. Miranker 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 Willard L. Miranker rather than just read about it. In short: Willard L. Miranker (March 8, 1932 – April 28, 2011) was an American mathematician and computer scientist known for his contributions to applied mathematics and numerical mathematics.

Key takeaways

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

Reference excerpt

Willard L. Miranker (March 8, 1932 – April 28, 2011) was an American mathematician and computer scientist known for his contributions to applied mathematics and numerical mathematics.

Early life and education Miranker was raised in Brooklyn, New York. He received a bachelor of arts in 1952, master of science in 1953 and Ph.D. in 1957 all in mathematics from the Courant Institute at New York University. His doctoral thesis The Asymptotic Theory of Solutions of U + (K2)U = 0 was advised by Joseph Keller.

Career

Mathematics Upon graduating from New York University, he worked for the mathematics department at Bell Labs (1956–1958) before joining IBM Research (1961). Upon retirement from IBM, he joined the computer science faculty at Yale University (1989) as research faculty. He also held professor affiliations at California Institute of Technology (1963), City University of New York (1966–1967), Hebrew University of Jerusalem (1968), New York University (1970–1973), Yale University (1973) and University of Paris-Sud (1974). Miranker's work includes articles and books on stiff differential equations, interval arithmetic, analog computing, and neural networks and the modeling of consciousness.

Painting Miranker was also an accomplished and prolific painter. Over the course of his life, Willard Miranker painted ~4000 watercolors/aquarelles and ~200 oil paintings. He exhibited internationally in New York City, Paris and Bonn.

Awards Fellow of the American Association for the Advancement of Science

References

External links Works by Willard L. Miranker at Open Library Paintings by Will Miranker Willard L. Miranker at the Mathematics Genealogy Project short page at Yale University FindaGrave entry [1]

Worked examples

Example 1 — a first encounter with Willard L. Miranker

Start with the simplest possible case. Write down what Willard L. Miranker 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 Willard L. Miranker 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 Willard L. Miranker 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 Willard L. Miranker

In research: Willard L. Miranker 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 Willard L. Miranker 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: Willard L. Miranker is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1932 births, 2011 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Willard L. Miranker 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 Willard L. Miranker in 20 minutes

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

Frequently asked questions

What is Willard L. Miranker in simple terms?

Willard L. Miranker (March 8, 1932 – April 28, 2011) was an American mathematician and computer scientist known for his contributions to applied mathematics and numerical mathematics.

Why does Willard L. Miranker 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 Willard L. Miranker?

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 Willard L. Miranker.