mathematics

John B. Little (mathematician)

John B. Little (mathematician) 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 John B. Little (mathematician) rather than just read about it. In short: John Brittain Little (born 1956) is a retired American mathematician, the author of several books in algebraic geometry and the history of mathematics. He is distinguished professor emeritus in the departments of mathematics and computer science at the College of the Holy Cross.

Key takeaways

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

Reference excerpt

John Brittain Little (born 1956) is a retired American mathematician, the author of several books in algebraic geometry and the history of mathematics. He is distinguished professor emeritus in the departments of mathematics and computer science at the College of the Holy Cross.

Education and career Little was born January 15, 1956, in Elmira, New York. He majored in mathematics at Haverford College, graduating in 1976, and completed a Ph.D. at Yale University in 1980. His dissertation, Translation Manifolds and the Converse of Abel's Theorem, was supervised by Bernard Saint-Donat. He joined the College of the Holy Cross as an assistant professor in 1980, became an associate professor in 1986, and was promoted to full professor in 2003. He was Anthony and Renee Marlon Professor in the Sciences from 2012 to 2015.

Books Little's textbooks include:

Using Algebraic Geometry (with David Cox and Donal O'Shea, Springer, Graduate Texts in Mathematics, 1998; 2nd ed., 2005) Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (with David Cox and Donal O'Shea, Springer, 1992; 4th ed., 2015) A Course in Linear Algebra (with David B. Damiano, Dover, 2011) Toric Varieties (with David Cox and Henry K. Schenck, AMS, Graduate Studies in Mathematics, 2011) Modeling and Data Analysis: An Introduction with Environmental Applications (American Mathematical Society, Holy Cross Bookshelf 41, 2019) In his retirement he has shifted his interests to focus more on the history of mathematics and the translation of works in ancient Greek mathematics. His books in this area include:

Practical Geometry (Clavius) (Holy Cross Bookshelf 57, 2022) Pappus of Alexandria, Book VIII of the Mathematical Collection (Holy Cross Bookshelf 62, 2023) Pappus of Alexandria, Book III of the Mathematical Collection (Holy Cross Bookshelf 63, 2023)

Recognition Little's book Ideals, Varieties, and Algorithms was the 2016 winner of the Leroy P. Steele Prize for mathematical exposition. Little received the 2020 Paul R. Halmos – Lester R. Ford Award for his paper "The many lives of the twisted cubic", published in The American Mathematical Monthly.

References

External links Home page John B. Little publications indexed by Google Scholar

Worked examples

Example 1 — a first encounter with John B. Little (mathematician)

Start with the simplest possible case. Write down what John B. Little (mathematician) 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 John B. Little (mathematician) 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 John B. Little (mathematician) 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 John B. Little (mathematician)

In research: John B. Little (mathematician) 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 John B. Little (mathematician) 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: John B. Little (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1956 births, Algebraic geometers, American historians of mathematics, so understanding it makes those chapters shorter.
In everyday life: Look for John B. Little (mathematician) 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 John B. Little (mathematician) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John B. Little (mathematician) 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 John B. Little (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John B. Little (mathematician) in simple terms?

Why does John B. Little (mathematician) 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 John B. Little (mathematician)?

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 John B. Little (mathematician).