mathematics

Richard D. Schafer

Richard D. Schafer 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 Richard D. Schafer rather than just read about it. In short: Richard Donald Schafer (February 25, 1918 – December 28, 2014) was an American mathematician. Education Richard Schafer studied at the University at Buffalo, where he received his bachelor's degree in 1938 and his master's degree in 1940.

Key takeaways

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

Reference excerpt

Richard Donald Schafer (February 25, 1918 – December 28, 2014) was an American mathematician.

Education Richard Schafer studied at the University at Buffalo, where he received his bachelor's degree in 1938 and his master's degree in 1940. He received in 1942 from the University of Chicago his PhD under Abraham Adrian Albert with dissertation Alternative Algebras over an Arbitrary Field.

Career After service in the U.S. Naval Reserve from 1942 to 1945, he was an instructor at the University of Michigan for the academic year 1945–1946. From 1946 to 1948 he was at the Institute for Advanced Study. From 1948 to 1953 he was a professor at the University of Pennsylvania. From 1953 to 1958 he was at University of Connecticut as professor and head of the mathematics department. He spent the academic year 1958–1959 at the Institute for Advanced Study. From 1959 until his retirement in 1988, he was a professor at the Massachusetts Institute of Technology. In 2012 he was elected was a Fellow of the American Mathematical Society. In 1954 he studied algebras based on the Cayley–Dickson construction. Schafer did research on algebra, specifically on Jordan algebras and Lie algebras. He is best known for his textbook An Introduction to Nonassociative Algebras, first published in 1966, which has been freely available since 2008 from Project Gutenberg. He and Kevin McCrimmon investigated non-commutative Jordan algebras. Richard Schafer was married to the mathematician Alice Turner Schafer (1915–2009) from 1942 until her death. Upon his death he was survived by two sons, three grandchildren, and two great-grandchildren.

References

Worked examples

Example 1 — a first encounter with Richard D. Schafer

Start with the simplest possible case. Write down what Richard D. Schafer 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 Richard D. Schafer 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 Richard D. Schafer 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 Richard D. Schafer

In research: Richard D. Schafer 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 Richard D. Schafer 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: Richard D. Schafer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1918 births, 2014 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard D. Schafer 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 Richard D. Schafer in 20 minutes

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

Frequently asked questions

What is Richard D. Schafer in simple terms?

Richard Donald Schafer (February 25, 1918 – December 28, 2014) was an American mathematician. Education Richard Schafer studied at the University at Buffalo, where he received his bachelor's degree in 1938 and his master's degree in 1940.

Why does Richard D. Schafer 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 Richard D. Schafer?

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 Richard D. Schafer.