Milton Abramowitz

Key takeaways

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

Reference excerpt

Milton Abramowitz (19 February 1915 – 5 July 1958) was an American mathematician at the National Bureau of Standards (NBS) who, with Irene Stegun, edited a classic book of mathematical tables called Handbook of Mathematical Functions, widely known as "Abramowitz and Stegun".

Education and career Abramowitz was born in Brooklyn, NY. He received a B. A. in mathematics in 1937 from Brooklyn College. He joined the NBS Math Tables Project in 1938, first as a member of the technical planning staff, while continuing his graduate studies at Brooklyn College in the evening. He obtained his M. A. in mathematics in 1940 and went on to attend the Ph.D. program in Mathematics at New York University, where he was supervised by Kurt Otto Friedrichs and graduated in 1948.

In 1954, Abramowitz became the Chief of the Computation Laboratory of the NBS Applied Mathematics Division. In 1958, he died while mowing the lawn of his home in suburban Washington, when the heat caused a heart attack.

Research In 1953, Abramowitz studied the behavior of the integral f ( x ) := ∫ 0 ∞ e − u 2 − x / u d u {\displaystyle f(x):=\int _{0}^{\infty }e^{-u^{2}-x/u}du} as a function of x, which was previously studied in physical problems where particle velocities were distributed according to a Maxwellian distribution. He found a power series expression for this function useful for small x, as well as the asymptotic f ( x ) ≈ π 3 e − 3 ( x / 2 ) 2 / 3 {\displaystyle f(x)\approx {\sqrt {\frac {\pi }{3}}}e^{-3(x/2)^{2/3}}} for large x. More generally, he showed that the integral f m ( x ) := ∫ 0 ∞ u m e − u 2 − x / u d u {\displaystyle f_{m}(x):=\int _{0}^{\infty }u^{m}e^{-u^{2}-x/u}du} asymptotes to π 3 ⋅ 3 − m / 2 ⋅ z m / 2 e − z {\displaystyle {\sqrt {\frac {\pi }{3}}}\cdot 3^{-m/2}\cdot z^{m/2}e^{-z}} where z := 3 ( x / 2 ) 2 / 3 {\displaystyle z:=3(x/2)^{2/3}} for large x. In 1957, Abramowitz and Stegun proposed an algorithm for numerically computing the values of Bessel functions J n ( x ) {\displaystyle J_{n}(x)} and Y n ( x ) {\displaystyle Y_{n}(x)} in the regime where both the index n and the argument x were large, using a recurrence relation.

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Illustrations

Worked examples

Example 1 — a first encounter with Milton Abramowitz

Start with the simplest possible case. Write down what Milton Abramowitz 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 Milton Abramowitz 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 Milton Abramowitz 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 Milton Abramowitz

In research: Milton Abramowitz 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 Milton Abramowitz 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: Milton Abramowitz is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1915 births, 1958 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Milton Abramowitz 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.

How to study Milton Abramowitz in 20 minutes

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

Frequently asked questions

What is Milton Abramowitz in simple terms?

Milton Abramowitz (19 February 1915 – 5 July 1958) was an American mathematician at the National Bureau of Standards (NBS) who, with Irene Stegun, edited a classic book of mathematical tables called Handbook of Mathematical Functions, widely known as "Abramowitz and Stegun". Education and career Ab…

Why does Milton Abramowitz 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 Milton Abramowitz?

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 Milton Abramowitz.