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mathematics

Martin Scharlemann

Martin Scharlemann 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 Martin Scharlemann rather than just read about it. In short: Martin George Scharlemann (born 6 December 1948) is an American topologist who is a professor at the University of California, Santa Barbara. He obtained his Ph.D. from the University of California, Berkeley under the guidance of Robion Kirby in 1974.

Key takeaways

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

Reference excerpt

Martin George Scharlemann (born 6 December 1948) is an American topologist who is a professor at the University of California, Santa Barbara. He obtained his Ph.D. from the University of California, Berkeley under the guidance of Robion Kirby in 1974. A conference in his honor was held in 2009 at the University of California, Davis. He is a Fellow of the American Mathematical Society, for his "contributions to low-dimensional topology and knot theory." Abigail Thompson was a student of his. Together they solved the graph planarity problem: There is an algorithm to decide whether a finite graph in 3-space can be moved in 3-space into a plane. He gave the first proof of the classical theorem that knots with unknotting number one are prime. He used hard combinatorial arguments for this. Simpler proofs are now known.

Selected publications

References

Worked examples

Example 1 — a first encounter with Martin Scharlemann

Start with the simplest possible case. Write down what Martin Scharlemann 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 Martin Scharlemann 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 Martin Scharlemann 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 Martin Scharlemann

In research
Martin Scharlemann 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 Martin Scharlemann 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
Martin Scharlemann is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1948 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Martin Scharlemann 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 Martin Scharlemann in 20 minutes

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

Frequently asked questions

What is Martin Scharlemann in simple terms?

Martin George Scharlemann (born 6 December 1948) is an American topologist who is a professor at the University of California, Santa Barbara. He obtained his Ph.D. from the University of California, Berkeley under the guidance of Robion Kirby in 1974.

Why does Martin Scharlemann 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 Martin Scharlemann?

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 Martin Scharlemann.

Tags

  • 1948 births
  • 20th-century American mathematicians
  • 21st-century American mathematicians
  • American topologists
  • Fellows of the American Mathematical Society
  • Living people
  • University of California, Berkeley alumni
  • University of California, Santa Barbara faculty

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