mathematics

Henry Crapo (mathematician)

Henry Crapo (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 Henry Crapo (mathematician) rather than just read about it. In short: Henry Howland Crapo (KRAY-poh; August 12, 1932 – September 3, 2019) was an American-Canadian mathematician who worked in algebraic combinatorics. Over the course of his career, he held positions at several universities and research institutes in Canada and France.

Key takeaways

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

Reference excerpt

Henry Howland Crapo (KRAY-poh; August 12, 1932 – September 3, 2019) was an American-Canadian mathematician who worked in algebraic combinatorics. Over the course of his career, he held positions at several universities and research institutes in Canada and France. He is noted for his work in matroid theory and lattice theory.

Education and career Crapo was born in Detroit, Michigan, in 1932. He received his Ph.D. in 1964 under the supervision of Gian-Carlo Rota and Kenneth Hoffman, with thesis On the theory of combinatorial independence. While working on his thesis, he was an assistant professor at Northeastern University in Boston. He subsequently held academic positions at the University of Waterloo, Université de Montréal, INRIA Rocquencourt, and École des Hautes Études en Sciences Sociales. During his time in Waterloo, Crapo became a Canadian citizen. Crapo is known for his early work in matroid theory, and for related work in lattice theory. He introduced the beta invariant of a matroid, and published the first paper on the Tutte polynomial (though Tutte had already defined an equivalent polynomial in his thesis). Together with Gian-Carlo Rota, Crapo wrote the first book on matroid theory. He is also known for Crapo's Complementation Theorem in poset Möbius Inversion. Crapo wrote 65 mathematical publications during his career. Upon his retirement, Crapo moved to the south of France. He continued some mathematical activity, and hosted several small conferences at his house there. He died on September 3, 2019.

Awards and honors A special 1999 issue of the journal Advances in Applied Mathematics was dedicated to Crapo on the occasion of his 67th birthday.

Personal life

Crapo was a patron of the arts. At the University of Waterloo he donated a collection of rare books on the history of dance and ballet, as well as a copy of the Porcellino sculpture of Florence; the latter shoulder-high bronze sculpture of a wild boar later became a mascot for the University of Waterloo Faculty of Arts. He also donated The Temptation of St. Anthony by James Ensor to the Royal Museum of Fine Arts in Antwerp and Corpse of Man by Hyman Bloom to the Rose Art Museum at Brandeis University.

References

Illustrations

Worked examples

Example 1 — a first encounter with Henry Crapo (mathematician)

Start with the simplest possible case. Write down what Henry Crapo (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 Henry Crapo (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 Henry Crapo (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 Henry Crapo (mathematician)

In research: Henry Crapo (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 Henry Crapo (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: Henry Crapo (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1932 births, 2019 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henry Crapo (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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Henry Crapo (mathematician)” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Henry Crapo (mathematician) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henry Crapo (mathematician) 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 Henry Crapo (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Henry Crapo (mathematician) in simple terms?

Why does Henry Crapo (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 Henry Crapo (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 Henry Crapo (mathematician).