mathematics

Murray R. Spiegel

Murray R. Spiegel 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 Murray R. Spiegel rather than just read about it. In short: Murray Ralph Spiegel (October 20, 1923 – April 28, 1991) was an author of textbooks on mathematics, including titles in a collection of Schaum's Outlines. Spiegel was a native of Brooklyn and a graduate of New Utrecht High School.

Key takeaways

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

Reference excerpt

Murray Ralph Spiegel (October 20, 1923 – April 28, 1991) was an author of textbooks on mathematics, including titles in a collection of Schaum's Outlines. Spiegel was a native of Brooklyn and a graduate of New Utrecht High School. He received his bachelor's degree in mathematics and physics from Brooklyn College in 1943. He earned a master's degree in 1947 and doctorate in 1949, both in mathematics and both at Cornell University. He was a teaching fellow at Harvard University in 1943–1945, a consultant with Monsanto Chemical Company in the summer of 1946, and a teaching fellow at Cornell University from 1946 to 1949. He was a consultant in geophysics for Beers & Heroy in 1950, and a consultant in aerodynamics for Wright Air Development Center from 1950 to 1954. Spiegel joined the faculty of Rensselaer Polytechnic Institute in 1949 as an assistant professor. He became an associate professor in 1954 and a full professor in 1957. He was assigned to the faculty Rensselaer Polytechnic Institute of Hartford, CT, when that branch was organized in 1955, where he served as chair of the mathematics department. His PhD dissertation, supervised by Marc Kac, was titled On the Random Vibrations of Harmonically Bound Particles in a Viscous Medium.

Works Schaum's Outline of College Algebra (First Edition: 1956) [Most Recent Edition: 2018] Schaum's Outline of College Physics Schaum's Outline of Statistics (FE: 1961) [MRE: 2018] Schaum's Outline of Advanced Calculus (1963) [2010] Schaum's Outline of Complex Variables (1964) [2009] Schaum's Outline of Laplace Transforms (1965) Schaum's Mathematical Handbook of Formulas and Tables (1968) [2008] Schaum's Outline of Vector Analysis [And An Introduction to Tensor Analysis] (1968) [2009] Schaum's Outline of Real Variables (1969) Schaum's Outline of Advanced Mathematics for Engineers and Scientists (1971) [2009] Schaum's Outline of Finite Differences and Difference Equations (1971) Schaum's Outline of Fourier Analysis with Applications to Boundary-Value Problems (1974) Schaum's Outline of Probability and Statistics (1975) [2013] Schaum's Outline of Theoretical Mechanics (1967) Applied Differential Equations (1963) [1980]

References

External links Murray R. Spiegel at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Murray R. Spiegel

Start with the simplest possible case. Write down what Murray R. Spiegel 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 Murray R. Spiegel 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 Murray R. Spiegel 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 Murray R. Spiegel

In research: Murray R. Spiegel 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 Murray R. Spiegel 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: Murray R. Spiegel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1923 births, 1991 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Murray R. Spiegel 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 Murray R. Spiegel in 20 minutes

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

Frequently asked questions

What is Murray R. Spiegel in simple terms?

Why does Murray R. Spiegel 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 Murray R. Spiegel?

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 Murray R. Spiegel.