mathematics

Kevin McCrimmon

Kevin McCrimmon 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 Kevin McCrimmon rather than just read about it. In short: Kevin Mor McCrimmon (born September 1941) is an American mathematician, specializing in Jordan algebras. He is known for his introduction of quadratic Jordan algebras in 1966.

Key takeaways

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

Reference excerpt

Kevin Mor McCrimmon (born September 1941) is an American mathematician, specializing in Jordan algebras. He is known for his introduction of quadratic Jordan algebras in 1966. McCrimmon attended secondary school in Champaign-Urbana, Illinois and then received his bachelor's degree in mathematics in 1960 from Reed College in Portland, Oregon. He received his Ph.D. from Yale University in 1965 with thesis Norms and Noncommutative Jordan Algebras supervised by Nathan Jacobson. McCrimmon spent his final year as a graduate student at the University of Chicago, when Nathan Jacobson spent a year of unpaid leave visiting Chicago and Japan for the academic year 1964–1965. As a postdoc, McCrimmon was at Massachusetts Institute of Technology from 1965 to 1967, for one year as an Air Force Research Laboratory Postdoctoral Fellow and for the next year as a C. L. E. Moore instructor. He became in 1967 a member of the Center for Advanced Studies at the University of Virginia (UVA), in 1968 an associate professor at UVA, and in 1972, a full professor at UVA, retiring there as professor emeritus. He was chair of the mathematics department from 1972 to 1975. McCrimmon was a Sloan Fellow in 1968 and an Invited Speaker of the International Congress of Mathematicians in 1974 in Vancouver. He spent several years on sabbatical in Europe. He was elected a Fellow of the American Mathematical Society in 2017.

Selected publications McCrimmon, K.; Schafer, R. D. (1966). "On a class of noncommutative Jordan algebras". Proceedings of the National Academy of Sciences of the United States of America. 56 (1): 1–4. Bibcode:1966PNAS...56....1M. doi:10.1073/pnas.56.1.1. PMC 285663. PMID 5338591. McCrimmon, Kevin (1966). "A general theory of Jordan rings". Proceedings of the National Academy of Sciences of the United States of America. 56 (4): 1072–1079. Bibcode:1966PNAS...56.1072M. doi:10.1073/pnas.56.4.1072. PMC 220000. PMID 16591377. McCrimmon, Kevin (1969). "The radical of a Jordan algebra". Proceedings of the National Academy of Sciences of the United States of America. 62 (3): 671–678. Bibcode:1969PNAS...62..671M. doi:10.1073/pnas.62.3.671. PMC 223650. PMID 16591736. McCrimmon, Kevin (1969). "The Freudenthal-Springer-Tits constructions of exceptional Jordan algebras". Transactions of the American Mathematical Society. 139: 495–510. doi:10.2307/1995337. JSTOR 1995337. McCrimmon, Kevin (1969). "On Herstein's theorems relating Jordan and associative algebras". Journal of Algebra. 13 (3): 382–392. doi:10.1016/0021-8693(69)90081-7. McCrimmon, Kevin (1971). "Noncommutative Jordan rings". Transactions of the American Mathematical Society. 158: 1–33. doi:10.1090/S0002-9947-1971-0310024-7. McCrimmon, Kevin (1971). "Inner ideals in quadratic Jordan algebras". Transactions of the American Mathematical Society. 159: 445–468. doi:10.1090/S0002-9947-1971-0279145-1. McCrimmon, Kevin (1978). "Jordan algebras and their applications". Bulletin of the American Mathematical Society. 84 (4): 612–627. doi:10.1090/S0002-9904-1978-14503-0. Hogben, Leslie; McCrimmon, Kevin (1981). "Maximal modular inner ideals and the Jacobson radical of a Jordan algebra". Journal of Algebra. 68 (1): 155–169. doi:10.1016/0021-8693(81)90291-X. McCrimmon, Kevin; Zelmanov, Efim (1988). "The structure of strongly prime quadratic Jordan algebras". Advances in Mathematics. 69 (2): 133–222. doi:10.1016/0001-8708(88)90001-1. A taste of Jordan algebras. Universitext. Springer Science & Business Media. 2006. doi:10.1007/b97489. ISBN 0-387-95447-3.

References

Worked examples

Example 1 — a first encounter with Kevin McCrimmon

Start with the simplest possible case. Write down what Kevin McCrimmon 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 Kevin McCrimmon 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 Kevin McCrimmon 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 Kevin McCrimmon

In research: Kevin McCrimmon 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 Kevin McCrimmon 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: Kevin McCrimmon is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1941 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kevin McCrimmon 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 Kevin McCrimmon in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kevin McCrimmon means in your own words.
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Frequently asked questions

What is Kevin McCrimmon in simple terms?

Kevin Mor McCrimmon (born September 1941) is an American mathematician, specializing in Jordan algebras. He is known for his introduction of quadratic Jordan algebras in 1966.

Why does Kevin McCrimmon 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 Kevin McCrimmon?

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 Kevin McCrimmon.