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William M. Boothby

William M. Boothby is a astronomy 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 William M. Boothby rather than just read about it. In short: William Munger Boothby (April 1, 1918 – February 14, 2021) was an American mathematician and professor emeritus of mathematics at Arts and Sciences at Washington University in St. Louis, known for his work in differential geometry including the book An introduction to differentiable manifolds and Riemannian geometry (1975; 2nd ed. 1986).

Key takeaways

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

Reference excerpt

William Munger Boothby (April 1, 1918 – February 14, 2021) was an American mathematician and professor emeritus of mathematics at Arts and Sciences at Washington University in St. Louis, known for his work in differential geometry including the book An introduction to differentiable manifolds and Riemannian geometry (1975; 2nd ed. 1986).

Education and career Boothby was originally from Detroit. He received a six-year scholarship to attend the Cranbrook Academy in Bloomfield Hills, and received a degree from the University of Michigan in 1940. He started graduate studies in mathematics, which were interrupted by World War II; he became a pilot for the United States Army Air Forces between 1942 and 1945. After the war, he returned at the University of Michigan and completed his Ph.D. in 1949. His dissertation, A Topological Study of the Level Curves of Harmonic Functions, was supervised by Wilfred Kaplan. He then moved to Northwestern University as junior faculty; during 1950-51 he had a one-year fellowship at ETH Zurich. In 1959 he became professor of mathematics at the Washington University in St. Louis, where he worked until his retirement in 1988. In 1960-61 he visited the Institute for Advanced Study.

Research His early research concerned differential geometry, including harmonic functions, Hermitian manifolds and contact structures. In particular, he worked on contact manifolds together with Hsien Chung Wang, describing what is now known as the Boothby-Wang construction. In 1975 he published a very popular textbook, An Introduction to Differentiable Manifolds and Riemannian Geometry, which "defined the curriculum and standard of the introductory graduate differential geometry course worldwide". After publishing this book, his research interests shifted to control theory.

References

Worked examples

Example 1 — a first encounter with William M. Boothby

Start with the simplest possible case. Write down what William M. Boothby claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 William M. Boothby 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 William M. Boothby 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 William M. Boothby

In research
William M. Boothby appears in astronomy 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 William M. Boothby 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
William M. Boothby is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1918 births, 2021 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for William M. Boothby 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 William M. Boothby in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what William M. Boothby means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain William M. Boothby out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is William M. Boothby in simple terms?

William Munger Boothby (April 1, 1918 – February 14, 2021) was an American mathematician and professor emeritus of mathematics at Arts and Sciences at Washington University in St. Louis, known for his work in differential geometry including the book An introduction to differentiable manifolds and R…

Why does William M. Boothby matter?

Because it connects several astronomy 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 William M. Boothby?

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 William M. Boothby.

Tags

  • 1918 births
  • 2021 deaths
  • 20th-century American mathematicians
  • American control theorists
  • American men centenarians
  • Differential geometers
  • Northwestern University faculty
  • United States Army Air Forces pilots of World War II
  • University of Michigan alumni
  • Washington University in St. Louis mathematicians

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