mathematics

Michelle L. Wachs

Michelle L. Wachs 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 Michelle L. Wachs rather than just read about it. In short: Michelle Lynn Wachs is an American mathematician who specializes in algebraic combinatorics and works as a professor of mathematics at the University of Miami. Contributions Wachs and her advisor Adriano Garsia are the namesakes of the Garsia–Wachs algorithm for optimal binary search trees, which they published in 1977.[A] She is also known for her research on shellings for simplicial complexes,[F] partially ordered…

Key takeaways

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

Reference excerpt

Michelle Lynn Wachs is an American mathematician who specializes in algebraic combinatorics and works as a professor of mathematics at the University of Miami.

Contributions Wachs and her advisor Adriano Garsia are the namesakes of the Garsia–Wachs algorithm for optimal binary search trees, which they published in 1977.[A] She is also known for her research on shellings for simplicial complexes,[F] partially ordered sets,[C] and Coxeter groups,[B] and on random permutation statistics[E] and set partition statistics.[D]

Education Wachs earned her doctorate in 1977 from the University of California, San Diego, under the supervision of Adriano Garsia. Her dissertation was Discrete Variational Techniques in Finite Mathematics.

Recognition In 2012 Wachs became one of the inaugural fellows of the American Mathematical Society. In 2013 she and her husband, mathematician Gregory Galloway (the chair of the mathematics department at Miami) were recognized as Simons Fellows. A conference in her honor was held in January 2015 at the University of Miami.

Selected publications

References

Illustrations

Worked examples

Example 1 — a first encounter with Michelle L. Wachs

Start with the simplest possible case. Write down what Michelle L. Wachs 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 Michelle L. Wachs 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 Michelle L. Wachs 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 Michelle L. Wachs

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

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

Frequently asked questions

What is Michelle L. Wachs in simple terms?

Michelle Lynn Wachs is an American mathematician who specializes in algebraic combinatorics and works as a professor of mathematics at the University of Miami. Contributions Wachs and her advisor Adriano Garsia are the namesakes of the Garsia–Wachs algorithm for optimal binary search trees, which t…

Why does Michelle L. Wachs 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 Michelle L. Wachs?

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 Michelle L. Wachs.