mathematics

Joe P. Buhler

Joe P. Buhler 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 Joe P. Buhler rather than just read about it. In short: Joe Peter Buhler (born 1950 in Vancouver, Washington) is an American mathematician known for his contributions to algebraic number theory, algebra and cryptography. Education and career Buhler received his undergraduate degree from Reed College in 1972, and his Ph.D. from Harvard University in 1977 with thesis Icosahedral Galois Representations and thesis advisor John Tate.

Key takeaways

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

Reference excerpt

Joe Peter Buhler (born 1950 in Vancouver, Washington) is an American mathematician known for his contributions to algebraic number theory, algebra and cryptography.

Education and career Buhler received his undergraduate degree from Reed College in 1972, and his Ph.D. from Harvard University in 1977 with thesis Icosahedral Galois Representations and thesis advisor John Tate. Buhler was a professor at Reed College in Portland, Oregon from 1980 until his retirement in 2005. From 2004 to 2017, he was director of the IDA Center for Communications Research in La Jolla, California. In 1997, he introduced, with Zinovy Reichstein, the concept of essential dimension. Buhler is involved in a project to numerically verify the Kummer–Vandiver conjecture of Harry Vandiver and Ernst Eduard Kummer concerning the class number of cyclotomic fields. Vandiver proved it with a desk calculator up to class number 600, Derrick Lehmer (in the late 1940s) to about 5000, and Buhler with colleagues (in 2001) to 12 million. He continues the project with David Harvey and others. He was elected a Fellow of the American Mathematical Society in 2012.

References

External links Homepage photo and biography on the occasion of a lecture author's profile in the database zbMATH

Worked examples

Example 1 — a first encounter with Joe P. Buhler

Start with the simplest possible case. Write down what Joe P. Buhler 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 Joe P. Buhler 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 Joe P. Buhler 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 Joe P. Buhler

In research: Joe P. Buhler 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 Joe P. Buhler 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: Joe P. Buhler is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1950 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Joe P. Buhler 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 Joe P. Buhler in 20 minutes

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

Frequently asked questions

What is Joe P. Buhler in simple terms?

Joe Peter Buhler (born 1950 in Vancouver, Washington) is an American mathematician known for his contributions to algebraic number theory, algebra and cryptography. Education and career Buhler received his undergraduate degree from Reed College in 1972, and his Ph.D. from Harvard University in 1977…

Why does Joe P. Buhler 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 Joe P. Buhler?

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 Joe P. Buhler.