mathematics

Michael Barr (mathematician)

Michael Barr (mathematician) 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 Barr (mathematician) rather than just read about it. In short: Michael Barr (born January 22, 1937) is an American mathematician who is the Peter Redpath Emeritus Professor of Pure Mathematics at McGill University. Early life and education He was born in Philadelphia, Pennsylvania, and graduated from the 202nd class of Central High School in June 1954.

Key takeaways

Michael Barr (mathematician) 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 Barr (mathematician) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Michael Barr (mathematician) from memory before moving on to harder problems.

Reference excerpt

Michael Barr (born January 22, 1937) is an American mathematician who is the Peter Redpath Emeritus Professor of Pure Mathematics at McGill University.

Early life and education He was born in Philadelphia, Pennsylvania, and graduated from the 202nd class of Central High School in June 1954. He graduated from the University of Pennsylvania in February 1959 and received a PhD from the same school in June 1962.

Career Barr studied mathematics at the University of Pennsylvania, graduating with a bachelor's degree in 1959 and a doctorate in 1962 under David Kent Harrison (Cohomology of Commutative Algebras). He was then an instructor at Columbia University and from 1964 Assistant Professor and later Associate Professor at the University of Illinois Urbana-Champaign. In 1968 he became Associate Professor and in 1972 Professor at McGill University. In 1967 and 1975/76 he was a visiting scientist at ETH Zurich and in 1970/71 at the University of Fribourg and in 1989/90 a visiting professor at the University of Pennsylvania. In 1970 he was an invited speaker at the International Congress of Mathematicians in Nice (Non-abelian full embedding: outline). His earlier work was in homological algebra, but his principal research area for a number of years has been category theory. He is well known to theoretical computer scientists for his book Category Theory for Computing Science (1990) with Charles Wells, as well as for the development of *-autonomous categories and Chu spaces which have found various applications in computer science. His monograph *-autonomous categories (1979), and his books Toposes, Triples, and Theories (1985), also coauthored with Wells, and Acyclic Models (2002), are aimed at more specialized audiences. In 2011 Michael Barr and his wife Marcia published an English translation of Grothendieck's fundamental Tôhoku paper. Barr is on the editorial boards of Mathematical Structures in Computer Science and the electronic journal Homology, Homotopy and Applications, and is editor of the electronic journal Theory and Applications of Categories.

References

External links Toposes, Triples and Theories, updated edition of text first published in 1985. Category Theory for Computing Science, updated 3rd edition of the book. Some aspects of homological Algebra, translation of Grothendieck's Tôhoku paper http://www.tac.mta.ca/tac (Theory and Applications of Categories) https://web.archive.org/web/20080704125156/http://www.math.rutgers.edu/hha/geninfo.html (Homology, Homotopy and Applications) Michael Barr at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Michael Barr (mathematician)

Start with the simplest possible case. Write down what Michael Barr (mathematician) 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 Barr (mathematician) 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 Barr (mathematician) 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 Barr (mathematician)

In research: Michael Barr (mathematician) 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 Barr (mathematician) 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 Barr (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1937 births, Academic staff of McGill University, Anglophone Quebec people, so understanding it makes those chapters shorter.
In everyday life: Look for Michael Barr (mathematician) 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 Barr (mathematician) in 20 minutes

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Close the page and write down what Michael Barr (mathematician) means in your own words.
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Work through the three examples above with pen and paper.
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Frequently asked questions

What is Michael Barr (mathematician) in simple terms?

Michael Barr (born January 22, 1937) is an American mathematician who is the Peter Redpath Emeritus Professor of Pure Mathematics at McGill University. Early life and education He was born in Philadelphia, Pennsylvania, and graduated from the 202nd class of Central High School in June 1954.

Why does Michael Barr (mathematician) 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 Barr (mathematician)?

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 Barr (mathematician).