mathematics

Ronald M. Foster

Ronald M. Foster 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 Ronald M. Foster rather than just read about it. In short: Ronald Martin Foster (3 October 1896 – 2 February 1998), was an American mathematician at Bell Labs whose work was of significance regarding electronic filters for use on telephone lines. He published an important paper, A Reactance Theorem, (see Foster's reactance theorem) which quickly inspired Wilhelm Cauer to begin his program of network synthesis filters which put the design of filters on a firm mathematical fo…

Key takeaways

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

Reference excerpt

Ronald Martin Foster (3 October 1896 – 2 February 1998), was an American mathematician at Bell Labs whose work was of significance regarding electronic filters for use on telephone lines. He published an important paper, A Reactance Theorem, (see Foster's reactance theorem) which quickly inspired Wilhelm Cauer to begin his program of network synthesis filters which put the design of filters on a firm mathematical footing. He is also known for the Foster census of cubic, symmetric graphs and the 90-vertex cubic symmetric Foster graph.

Education Foster was a Harvard College graduate S.B. (Mathematics), summa cum laude, Class of 1917. He also received two honorary Sc.D.s.

Professional career 1917 – 1943 Research & Development Department (later Bell Labs), American Telephone & Telegraph, as a Research Engineer (Applied Mathematician), New York City, New York. 1943 – 1963 Professor and Head of Department of Mathematics, Polytechnic Institute of Brooklyn, Brooklyn, New York City, New York.

Publications Campbell, GA, Foster, RM, Fourier Integrals for Practical Applications, "Bell System Technical Journal", pp. 639–707, 1928. Pierce, BO, Foster. RM. "A Short Table of Integrals", Fourth Edition, Ginn and Company, pp. 1–189, 1956.

References

Worked examples

Example 1 — a first encounter with Ronald M. Foster

Start with the simplest possible case. Write down what Ronald M. Foster 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 Ronald M. Foster 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 Ronald M. Foster 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 Ronald M. Foster

In research: Ronald M. Foster 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 Ronald M. Foster 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: Ronald M. Foster is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1896 births, 1998 deaths, 20th-century American engineers, so understanding it makes those chapters shorter.
In everyday life: Look for Ronald M. Foster 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 Ronald M. Foster in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ronald M. Foster 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 Ronald M. Foster in simple terms?

Why does Ronald M. Foster 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 Ronald M. Foster?

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 Ronald M. Foster.