mathematics

Stephen Schanuel

Stephen Schanuel 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 Stephen Schanuel rather than just read about it. In short: Stephen H. Schanuel (14 July 1933 – 21 July 2014) was an American mathematician working in the fields of abstract algebra and category theory, number theory, and measure theory.

Key takeaways

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

Reference excerpt

Stephen H. Schanuel (14 July 1933 – 21 July 2014) was an American mathematician working in the fields of abstract algebra and category theory, number theory, and measure theory.

Life While he was a graduate student at University of Chicago, he discovered Schanuel's lemma, an essential lemma in homological algebra. Schanuel received his Ph.D. in mathematics from Columbia University in 1963, under the supervision of Serge Lang.

Work Shortly thereafter he stated a conjecture in the field of transcendental number theory, which remains an important open problem to this day. Schanuel was a professor emeritus of mathematics at University at Buffalo.

Books Lawvere, F. William; Schanuel, Stephen Hoel (2009) [1997]. Conceptual Mathematics: A First Introduction to Categories (2nd ed.). Cambridge University Press. ISBN 978-0-521-89485-2.

References

External links Stephen Schanuel at the Mathematics Genealogy Project Weisstein, Eric W. "Schanuel's Conjecture". MathWorld.

Worked examples

Example 1 — a first encounter with Stephen Schanuel

Start with the simplest possible case. Write down what Stephen Schanuel 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 Stephen Schanuel 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 Stephen Schanuel 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 Stephen Schanuel

In research: Stephen Schanuel 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 Stephen Schanuel 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: Stephen Schanuel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1933 births, 2014 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Stephen Schanuel 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 Stephen Schanuel in 20 minutes

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

Frequently asked questions

What is Stephen Schanuel in simple terms?

Stephen H. Schanuel (14 July 1933 – 21 July 2014) was an American mathematician working in the fields of abstract algebra and category theory, number theory, and measure theory.

Why does Stephen Schanuel 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 Stephen Schanuel?

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 Stephen Schanuel.