mathematics

John Edwin Luecke

John Edwin Luecke 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 Edwin Luecke rather than just read about it. In short: John Edwin Luecke is an American mathematician who works in topology and knot theory. He got his Ph.D. in 1985 from the University of Texas at Austin and is now a professor in the department of mathematics at that institution.

Key takeaways

John Edwin Luecke 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 Edwin Luecke to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John Edwin Luecke from memory before moving on to harder problems.

Reference excerpt

John Edwin Luecke is an American mathematician who works in topology and knot theory. He got his Ph.D. in 1985 from the University of Texas at Austin and is now a professor in the department of mathematics at that institution.

Work Luecke specializes in knot theory and 3-manifolds. In a 1987 paper Luecke, Marc Culler, Cameron Gordon, and Peter Shalen proved the cyclic surgery theorem. In a 1989 paper Luecke and Cameron Gordon proved that knots are determined by their complements, a result now known as the Gordon–Luecke theorem. Dr Luecke received a NSF Presidential Young Investigator Award in 1992 and Sloan Foundation fellow in 1994. In 2012 he became a fellow of the American Mathematical Society.

References

External links John Edwin Luecke at the Mathematics Genealogy Project Luecke's home page at the University of Texas at Austin

Worked examples

Example 1 — a first encounter with John Edwin Luecke

Start with the simplest possible case. Write down what John Edwin Luecke 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 Edwin Luecke 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 Edwin Luecke 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 Edwin Luecke

In research: John Edwin Luecke 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 Edwin Luecke 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 Edwin Luecke is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, 21st-century American mathematicians, American mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for John Edwin Luecke 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 Edwin Luecke in 20 minutes

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

Frequently asked questions

What is John Edwin Luecke in simple terms?

Why does John Edwin Luecke 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 Edwin Luecke?

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 Edwin Luecke.