mathematics

Philip J. Davis

Philip J. Davis 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 Philip J. Davis rather than just read about it. In short: Philip J. Davis (January 2, 1923 – March 14, 2018) was an American academic applied mathematician.

Key takeaways

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

Reference excerpt

Philip J. Davis (January 2, 1923 – March 14, 2018) was an American academic applied mathematician.

Biography Davis was born in Lawrence, Massachusetts. He was known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics. He earned his degrees in mathematics from Harvard University (SB, 1943; PhD, 1950, advisor Ralph P. Boas, Jr.), and his final position was Professor Emeritus at the Division of Applied Mathematics at Brown University. He served briefly in an aerodynamics research position in the Air Force in World War II before joining the National Bureau of Standards (now the National Institute of Standards and Technology). He became Chief of Numerical Analysis there and worked on the well-known Abramowitz and Stegun Handbook of Mathematical Functions before joining Brown in 1963. He was awarded the Chauvenet Prize for mathematical writing in 1963 for an article on the gamma function, and won numerous other prizes, including being chosen to deliver the 1991 Hendrick Lectures of the MAA (which became the basis for his book Spirals: From Theodorus to Chaos). He was a frequent invited lecturer and authored several books. Among the best known are The Mathematical Experience (with Reuben Hersh), a popular survey of modern mathematics and its history and philosophy; Methods of Numerical Integration (with Philip Rabinowitz), long the standard work on the subject of quadrature; and Interpolation and Approximation, still an important reference in this area. For The Mathematical Experience (1981), Davis and Hersh won a National Book Award in Science. Davis also wrote an autobiography, The Education of a Mathematician; some of his other books include autobiographical sections as well. In addition, he published works of fiction. His best-known book outside the field of mathematics is The Thread: A Mathematical Yarn (1983, 2nd ed. 1989), which "has raised Digression into a literary form" (Gerard Piel); it takes off from the name of the Russian mathematician Tschebyscheff, and in the course of explaining why he insists on that "barbaric, Teutonic, non-standard orthography" (in the words of a reader of Interpolation and Approximation who wrote him to complain), he digresses in many amusing directions. Davis died on March 14, 2018, at the age of 95.

Publications Ancient Loons: Stories David Pingree Told Me (2016) Circulant matrices Descartes' Dream: The World According to Mathematics by Philip J. Davis and Reuben Hersh Interpolation and approximation Mathematical Encounters of the Second Kind Mathematics & Common Sense: A Case of Creative Tension (2006) Mathematics, Substance and Surmise: Views on the Meaning and Ontology of Mathematics by Ernest Davis and Philip J. Davis Methods of numerical integration Numerical Integration by Philip Davis, Philip J & Rabinowitz Spirals: From Theodorus to Chaos The Companion Guide to the Mathematical Experience: by Philip J. Davis and Reuben Hersh The Education of a Mathematician (2000) The Lore of Large Numbers (1961) The Mathematical Experience (Modern Birkhäuser Classics) (2011) The mathematics of matrices: A first book of matrix theory and linear algebra The Schwarz Function and Its Applications (Carus Mathematical Monographs #17) (1974) The Thread: A Mathematical Yarn Thomas Gray, Philosopher Cat (1988) Thomas Gray in Copenhagen: In Which the Philosopher Cat Meets the Ghost of Hans Christian Andersen (1995) Unity and Disunity and Other Mathematical Essays, American Math Society, (2015)

Notes

References

External links Personal web site at Brown University. Official web site at Brown University. Interview at SIAM Philip J. Davis at the Mathematics Genealogy Project Bibliography Posthumous Publications

Worked examples

Example 1 — a first encounter with Philip J. Davis

Start with the simplest possible case. Write down what Philip J. Davis 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 Philip J. Davis 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 Philip J. Davis 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 Philip J. Davis

In research: Philip J. Davis 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 Philip J. Davis 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: Philip J. Davis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1923 births, 2018 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Philip J. Davis 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 Philip J. Davis in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Philip J. Davis 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.
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Frequently asked questions

What is Philip J. Davis in simple terms?

Philip J. Davis (January 2, 1923 – March 14, 2018) was an American academic applied mathematician.

Why does Philip J. Davis 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 Philip J. Davis?

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 Philip J. Davis.