mathematics

William A. Stein

William A. Stein 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 William A. Stein rather than just read about it. In short: William Arthur Stein (born February 21, 1974, in Santa Barbara, California) is a software developer and previously a professor of mathematics at the University of Washington. Stein received his PhD in 2000, from the University of California, Berkeley, for his dissertation ‘Explicit Approaches to Modular Abelian Varieties’, supervised by Hendrik W.

Key takeaways

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

Reference excerpt

William Arthur Stein (born February 21, 1974, in Santa Barbara, California) is a software developer and previously a professor of mathematics at the University of Washington. Stein received his PhD in 2000, from the University of California, Berkeley, for his dissertation ‘Explicit Approaches to Modular Abelian Varieties’, supervised by Hendrik W. Lenstra. He is the lead developer of SageMath and founder of CoCalc. Stein does computational and theoretical research into the problem of computing with modular forms and the Birch and Swinnerton-Dyer conjecture. He is considered "a leading expert in the field of computational arithmetic". Stein was the 2013 recipient of the Richard Dimick Jenks Memorial Prize Award, presented by SIGSAM, a special interest group of the Association for Computing Machinery.

Publications Stein, William (2009). Elementary Number Theory: Primes, Congruences, and Secrets. New York, NY: Springer Verlag. ISBN 978-0-387-85524-0. OCLC 268798336. Mazur, Barry; Stein, William (2016). Prime Numbers and the Riemann Hypothesis. New York, NY: Cambridge University Press. ISBN 978-1-107-49943-0.

References

External links Official website William A. Stein at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with William A. Stein

Start with the simplest possible case. Write down what William A. Stein 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 William A. Stein 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 William A. Stein 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 William A. Stein

In research: William A. Stein 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 William A. Stein 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: William A. Stein is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1974 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for William A. Stein 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 William A. Stein in 20 minutes

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

Frequently asked questions

What is William A. Stein in simple terms?

Why does William A. Stein 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 William A. Stein?

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 William A. Stein.