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Holbrook Mann MacNeille

Holbrook Mann MacNeille 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 Holbrook Mann MacNeille rather than just read about it. In short: Holbrook Mann MacNeille (May 11, 1907 – September 30, 1973) was an American mathematician who worked for the United States Atomic Energy Commission before becoming the first Executive Director of the American Mathematical Society. Personal life MacNeille was born May 11, 1907, in New York City and was raised in Summit, New Jersey, the first of two brothers.

Key takeaways

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

Reference excerpt

Holbrook Mann MacNeille (May 11, 1907 – September 30, 1973) was an American mathematician who worked for the United States Atomic Energy Commission before becoming the first Executive Director of the American Mathematical Society.

Personal life MacNeille was born May 11, 1907, in New York City and was raised in Summit, New Jersey, the first of two brothers. His father was Perry Robinson MacNeille, an architect and urban planner and his mother Clausine Mann MacNeille who was active on the Summit Board of Education. His aunts were the Jungian analysts Kristine Mann and Anna Mann Richardson. MacNeille went to the Summit Public Schools and summered in Bailey Island, Maine. At Bailey Island he became acquainted with Frank Aydelotte who encouraged him to go to Swarthmore College from which he graduated with highest honors in 1928. Following in Aydelotte's footsteps he was a Rhodes Scholar at Balliol College, Oxford, England 1928–1930 receiving a B.A. in 1930 and an M.A. in 1947. He received a Ph.D. in Mathematics from Harvard University in 1935 where he was the first student of Marshall Harvey Stone, was a Sterling Fellow at Yale University from 1935–1936 and a Benjamin Peirce Instructor at Harvard between 1936–1938. During the summers he was also a partner in the Dave Richardson Laboratories in Bailey Island, Maine, which produced dogfish prepared for dissection at school laboratories. MacNeille's Ph.D work resulted in the MacNeille completion theorem, a generalization of the construction of real numbers from the ordered set of rationals by Dedekind cuts. Upon completing his studies, he taught mathematics at Kenyon College as an associate professor (1938–1941), full professor (1941–1947) and chairman of the department (1945–1947).

World War II During several of the years at Kenyon College he was on leave as Scientific Liaison Officer (1944–1945) and Head of Mission (1945–1946) London Mission of the Office of Scientific Research and Development, American Embassy in London, England. During (1946–1948) he was Scientific Director of the London Branch Office of the U.S. Office of Naval Research and then during (1948–1949) spent more than a year as chief of the fundamental research branch of the Atomic Energy Commission in Washington, D.C. In 1948 he received the President's Certificate of Merit from President Harry S. Truman.

After World War II In November 1949 he became executive director of the American Mathematical Society where he served until 1954. From 1954–1961 he was professor and chairman of the Department of Mathematics in the College of Arts and Sciences at Washington University in St. Louis, and then from 1961 professor and chairman of the Department of Mathematics at Case Western Reserve University in Cleveland, Ohio, until his death. During this latter period he became interested in teaching, and directed several educational movies as part of the Calculus Film Project of the Educational Media Committee of the Mathematical Association of America. He was killed accidentally when hit by a car while riding his bicycle.

Filmography "Area under a curve" "The definite integral" "Volume of a solid of revolution" "Infinite acres" "Volume of a solid of a revolution" "Volume by shells" "Theorem of the Mean Policeman"

Awards and other positions Rhodes Scholarship (1928) (Swarthmore College, Balliol) John William Sterling Research Fellowship, Yale University (1936–1936) Benjamin Peirce Instructor in Mathematics, Harvard University (1936–1938) President's Certificate of Merit, President Harry S. Truman (1948) Society for Industrial and Applied Mathematics council (1961–1964) Fellow of the American Association for the Advancement of Science council (1964) Chairman of the Mathematics Association of America committee on Educational Media (1962–1963) Phi Beta Kappa Associate editor Sigma Xi Mathematics Magazine (1962–1963)

Publications 1936: "Extensions of Partially Ordered Sets", Proceedings of the National Academy of Sciences, Vol. 22(1): 45–50 1937: Partially Ordered Sets, Transactions of the American Mathematical Society, Vol. 42(3): 416–460 1938: "Extensions of Measure", Proceedings of the National Academy of Sciences, Vol. 24, No. 4 (Apr. 15, 1938), pp. 188–193 1939: "Lattices and Boolean Rings", Bulletin of the American Mathematical Society 1939: Extension of a distributive lattice to a Boolean ring, Bulletin of the American Mathematical Society 1941: A Unified Theory of Integration, Proceedings of the National Academy of Sciences, Vol. 27

References

P.T. Johnstone, (August 14, 1986) Stone Spaces, Cambridge University Press, ISBN 0-521-33779-8 Everett Pitcher (1997) A History of the Second Fifty Years, American Mathematical Society, 1939-1988, page 251, American Mathematical Society ISBN 0-8218-0125-2 Who was who in America (1976) Marquis Who's Who, Volume VI, 1974–1976, Chicago, ISBN 0-8379-0207-X

Worked examples

Example 1 — a first encounter with Holbrook Mann MacNeille

Start with the simplest possible case. Write down what Holbrook Mann MacNeille 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 Holbrook Mann MacNeille 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 Holbrook Mann MacNeille 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 Holbrook Mann MacNeille

In research
Holbrook Mann MacNeille 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 Holbrook Mann MacNeille 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
Holbrook Mann MacNeille is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1907 births, 1973 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Holbrook Mann MacNeille 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 Holbrook Mann MacNeille in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Holbrook Mann MacNeille 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 Holbrook Mann MacNeille out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Holbrook Mann MacNeille in simple terms?

Holbrook Mann MacNeille (May 11, 1907 – September 30, 1973) was an American mathematician who worked for the United States Atomic Energy Commission before becoming the first Executive Director of the American Mathematical Society. Personal life MacNeille was born May 11, 1907, in New York City and…

Why does Holbrook Mann MacNeille 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 Holbrook Mann MacNeille?

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 Holbrook Mann MacNeille.

Tags

  • 1907 births
  • 1973 deaths
  • 20th-century American mathematicians
  • Alumni of Balliol College, Oxford
  • American Rhodes Scholars
  • Bailey Island (Maine)
  • Fellows of the American Association for the Advancement of Science
  • Harvard University Department of Mathematics faculty
  • Harvard University alumni
  • Kenyon College faculty
  • Mathematicians from New York (state)
  • Mathematicians from New York City

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