mathematics

Lowell E. Jones

Lowell E. Jones 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 Lowell E. Jones rather than just read about it. In short: Lowell Edwin Jones (born 1945) is an American professor of mathematics at Stony Brook University. Jones' primary fields of interest are topology and geometry.

Key takeaways

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

Reference excerpt

Lowell Edwin Jones (born 1945) is an American professor of mathematics at Stony Brook University. Jones' primary fields of interest are topology and geometry. Jones is most well known for his collaboration with F. Thomas Farrell on the Farrell-Jones conjecture.

Education and career Jones received his Ph.D. from Yale University in 1970 under the guidance of Wu-Chung Hsiang. Jones' dissertation topic, assigned by Hsiang, concerned the fixed-point theorem of Paul Althaus Smith. Jones joined Stony Brook University in 1975.

Mathematical contributions When Farrell and Jones first started collaborating they gave the very first example of an Anosov diffeomorphism on a manifold which was not infranil. Later, Jones and Farrell, also a student of Hsiang, caused a paradigm shift in higher dimensional topology when they applied ideas from differential geometry, and dynamics to questions such as the Borel conjecture. The Farrell-Jones conjecture implies the Borel Conjecture for manifolds of dimension greater than four. Jones, and Farrell published about fifty papers during their 25-year collaboration. Jones was invited to speak at the 1990 International Congress of Mathematicians in Kyoto.

References

Worked examples

Example 1 — a first encounter with Lowell E. Jones

Start with the simplest possible case. Write down what Lowell E. Jones 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 Lowell E. Jones 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 Lowell E. Jones 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 Lowell E. Jones

In research: Lowell E. Jones 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 Lowell E. Jones 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: Lowell E. Jones is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American mathematicians, American geometers, so understanding it makes those chapters shorter.
In everyday life: Look for Lowell E. Jones 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 Lowell E. Jones in 20 minutes

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

Frequently asked questions

What is Lowell E. Jones in simple terms?

Lowell Edwin Jones (born 1945) is an American professor of mathematics at Stony Brook University. Jones' primary fields of interest are topology and geometry.

Why does Lowell E. Jones 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 Lowell E. Jones?

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 Lowell E. Jones.