mathematics

Michael P. Drazin

Michael P. Drazin 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 Michael P. Drazin rather than just read about it. In short: Michael Peter Drazin (born 5 June 1929) is a British and American mathematician, working in noncommutative algebra. Background The Drazins (Дразин) were a Russian Jewish family who moved to the United Kingdom in the years before World War I.

Key takeaways

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

Reference excerpt

Michael Peter Drazin (born 5 June 1929) is a British and American mathematician, working in noncommutative algebra.

Background The Drazins (Дразин) were a Russian Jewish family who moved to the United Kingdom in the years before World War I. Isaac Drazin founded in 1927 a well-known electrical goods shop in Heath Street, Hampstead, which existed for over 50 years. Isaac Drazin married Leah Wexler, and had three sons, of whom Michael was the eldest, and Philip Drazin, also a mathematician, was the youngest, the middle son being David; and died 1 January 1993.

Life Michael Drazin was born in London on 5 June 1929. His younger brother Philip was educated as a boarder at St Christopher School, Letchworth during World War II. The self-published memoirs of Roger Atkinson, a school friend of Michael (Mike), indicate that Drazin attended King Alfred School, London, located in Hampstead, retaining contacts at the school when it was evacuated in wartime to Royston, Hertfordshire; Atkinson was a boarder at St Christopher School, Letchworth from September 1942. In 1946 Atkinson and Drazin visited Paris together. Drazin was a student at the University of Cambridge, graduating B.A. in 1950 and M.A. in 1953. He was awarded a Ph.D. in 1953 for a dissertation Contributions to Abstract Algebra written with advisers Robert Rankin and David Rees. He was a Fellow of Trinity College, Cambridge from 1952 to 1956, during that period relocating to the United States. In the academic year 1957–8 Drazin was Visiting Lecturer at Northwestern University. In 1958 he began a period at RIAS Inc. (the Research Institute for Advanced Studies) in Baltimore as senior scientist, after which he took a position as associate professor at Purdue University in 1962.

Works Drazin gave his name to a type of generalized inverse in ring theory and semigroup theory he introduced in 1958, now known as the Drazin inverse. It was later extended to contexts in operator theory. While at RIAS, Drazin worked with Emilie Virginia Haynsworth, then at the National Bureau of Standards, within its numerical analysis program. He also worked with the metallurgist Henry Martin Otte of RIAS, and they published a book of crystallographic tables.

Worked examples

Example 1 — a first encounter with Michael P. Drazin

Start with the simplest possible case. Write down what Michael P. Drazin 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 Michael P. Drazin 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 Michael P. Drazin 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 Michael P. Drazin

In research: Michael P. Drazin 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 Michael P. Drazin 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: Michael P. Drazin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1929 births, 20th-century American mathematicians, 20th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Michael P. Drazin 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 Michael P. Drazin in 20 minutes

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

Frequently asked questions

What is Michael P. Drazin in simple terms?

Michael Peter Drazin (born 5 June 1929) is a British and American mathematician, working in noncommutative algebra. Background The Drazins (Дразин) were a Russian Jewish family who moved to the United Kingdom in the years before World War I.

Why does Michael P. Drazin 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 Michael P. Drazin?

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 Michael P. Drazin.