mathematics

Judy A. Holdener

Judy A. Holdener 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 Judy A. Holdener rather than just read about it. In short: Judy Holdener (née Newhauser) is an American mathematician and educator. She is a professor of mathematics at Kenyon College.

Key takeaways

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

Reference excerpt

Judy Holdener (née Newhauser) is an American mathematician and educator. She is a professor of mathematics at Kenyon College. She was born in 1965. Holdener's primary interest is in number theory. She discovered a simpler proof of the theorem of Touchard, which states that every perfect number is of the form 2k, 12k+1, or 36k+9. Holdener earned her B.S. in mathematics at Kent State University and her M.S. and Ph.D. in mathematics at the University of Illinois at Urbana-Champaign. Holdener joined the faculty of Kenyon College in 1997, where she is currently the John B. McCoy Distinguished Teaching Chair. The poem Euler's Daughter by award-winning South African poet Athol Williams is dedicated to Holdener in celebration of her love of mathematics and life.

References

Holdener, J. A. (2002), "A Theorem of Touchard and the Form of Odd Perfect Numbers", American Mathematical Monthly, 109 (7), Mathematical Association of America: 661–663, doi:10.2307/3072433, JSTOR 3072433. Touchard, Jacques (1953), "On prime numbers and perfect numbers", Scripta Mathematica, 19: 35–39. This article incorporates material from Judy Holdener on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

External links Biography Page at Kenyon College Archived 2020-08-15 at the Wayback Machine

Worked examples

Example 1 — a first encounter with Judy A. Holdener

Start with the simplest possible case. Write down what Judy A. Holdener 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 Judy A. Holdener 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 Judy A. Holdener 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 Judy A. Holdener

In research: Judy A. Holdener 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 Judy A. Holdener 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: Judy A. Holdener is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1965 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Judy A. Holdener 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 Judy A. Holdener in 20 minutes

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

Frequently asked questions

What is Judy A. Holdener in simple terms?

Judy Holdener (née Newhauser) is an American mathematician and educator. She is a professor of mathematics at Kenyon College.

Why does Judy A. Holdener 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 Judy A. Holdener?

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 Judy A. Holdener.