mathematics

John Coleman Moore

John Coleman Moore 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 John Coleman Moore rather than just read about it. In short: John Coleman Moore (May 27, 1923 – January 1, 2016) was an American mathematician. The Borel−Moore homology and Eilenberg–Moore spectral sequence are named after him.

Key takeaways

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

Reference excerpt

John Coleman Moore (May 27, 1923 – January 1, 2016) was an American mathematician. The Borel−Moore homology and Eilenberg–Moore spectral sequence are named after him.

Early life and education Moore was born in 1923 in Staten Island, New York. He received his B.A. in 1948 from the Massachusetts Institute of Technology and his Ph.D. in 1952 from Brown University under the supervision of George W. Whitehead.

Career Moore began his career at Princeton University as an instructor, and was eventually promoted to full professor in 1961. He retired from Princeton in 1989, after which he took a half-time position at the University of Rochester. His most-cited paper is on Hopf algebras, co-authored with John Milnor. As a faculty member at Princeton University, he advised 24 students and is the academic ancestor of over 1000 mathematicians. He was an Invited Speaker at the International Congress of Mathematicians in 1958 in Edinburgh and in 1970 in Nice. In 1983, a conference on K-theory was held at Princeton in honor of Moore's 60th birthday. In 2012, he became a fellow of the American Mathematical Society. He died in 2016 at the age of 92.

Publications Moore, John C. (May 1954). "On Homotopy Groups of Spaces with a Single Non-Vanishing Homology Group". Annals of Mathematics. 2. 59 (3): 549–557. doi:10.2307/1969718. JSTOR 1969718. MR 0061382. Cohen, Frederick R.; Moore, John C.; Neisendorfer, Joseph A. (1979). "Torsion in homotopy groups". Annals of Mathematics. (2). 109 (1): 121–168. doi:10.2307/1971269. JSTOR 1971269. MR 0519355. Cohen, Frederick R.; Moore, John C.; Neisendorfer, Joseph A. (1979). "The double suspension and exponents of the homotopy groups of spheres". Annals of Mathematics. (2). 110 (3): 549–565. doi:10.2307/1971238. JSTOR 1971238. MR 0519355.

References

Worked examples

Example 1 — a first encounter with John Coleman Moore

Start with the simplest possible case. Write down what John Coleman Moore 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 John Coleman Moore 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 John Coleman Moore 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 John Coleman Moore

In research: John Coleman Moore 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 John Coleman Moore 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: John Coleman Moore is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1923 births, 2016 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John Coleman Moore 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 John Coleman Moore in 20 minutes

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

Frequently asked questions

What is John Coleman Moore in simple terms?

John Coleman Moore (May 27, 1923 – January 1, 2016) was an American mathematician. The Borel−Moore homology and Eilenberg–Moore spectral sequence are named after him.

Why does John Coleman Moore 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 John Coleman Moore?

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 John Coleman Moore.