mathematics

Neil J. Calkin

Neil J. Calkin 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 Neil J. Calkin rather than just read about it. In short: Neil J. Calkin (born 29 March 1961) is a professor at Clemson University in the Algebra and Discrete Mathematics group of the School of Mathematical and Statistical Sciences.

Key takeaways

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

Reference excerpt

Neil J. Calkin (born 29 March 1961) is a professor at Clemson University in the Algebra and Discrete Mathematics group of the School of Mathematical and Statistical Sciences. His interests are in combinatorial and probabilistic methods, mainly as applied to number theory. Together with Herbert Wilf he founded The Electronic Journal of Combinatorics in 1994. He and Wilf developed the Calkin–Wilf tree and the associated Calkin–Wilf sequence.

Biography Neil Calkin was born 29 March 1961, in Hartford, Connecticut and moved to the UK around the age of 3. He grew up there and studied mathematics at Trinity College Cambridge before moving to Canada in 1984 to study in the Department of Combinatorics and Optimization at the University of Waterloo where he was awarded a PhD (1988) for his thesis "Sum-Free Sets and Measure Spaces" written under the supervision of Ian Peter Goulden. He was the Zeev Nehari Visiting Assistant Professor of Mathematics at Carnegie Mellon University (1988—1991), an assistant professor at Georgia Tech (1991—1997), and joined the Algebra and Discrete Mathematics group of the School of Mathematical and Statistical Sciences at Clemson University in 1997. Calkin has an Erdős number of 1. He was one of the last people to collaborate with Erdős and once said of him, "One of my greatest regrets is that I didn't know him when he was a million times faster than most people. When I knew him he was only hundreds of times faster."

Selected papers Calkin, Neil J.; Wilf, Herbert S. (1998). "The Number of Independent Sets in a Grid Graph". SIAM Journal on Discrete Mathematics. 11 (1). Society for Industrial & Applied Mathematics (SIAM): 54–60. doi:10.1137/s089548019528993x. hdl:1853/31277. ISSN 0895-4801. Calkin, Neil; Wilf, Herbert S. (2000). "Recounting the Rationals". The American Mathematical Monthly. 107 (4). Informa UK Limited: 360–363. doi:10.1080/00029890.2000.12005205. ISSN 0002-9890. S2CID 38140675. Calkin, Neil J.; Davis, Killian; Haithcock, Evan; Kenyon, Catherine M.; Wu, Sylvia (21 October 2021). "What Newton Might Have Known: Experimental Mathematics in the Classroom". The American Mathematical Monthly. 128 (9). Informa UK Limited: 845–855. doi:10.1080/00029890.2021.1964274. ISSN 0002-9890. S2CID 243765436. Neil j. Calkin; Beth Novick; Hayato Ushijima-Mwesigwa (2016). "What Moser Could Have Asked: Counting Hamilton Cycles in Tournaments". The American Mathematical Monthly. 123 (4). Informa UK Limited: 382. doi:10.4169/amer.math.monthly.123.4.382. ISSN 0002-9890. S2CID 119324841.

Books Bailey, David H. (2007). Experimental mathematics in action. Wellesley, Mass.: A.K. Peters. ISBN 978-1-56881-271-7. OCLC 70823291.

References

External links Neil Calkin at the Mathematics Genealogy Project Neil J. Calkin's Publications

Worked examples

Example 1 — a first encounter with Neil J. Calkin

Start with the simplest possible case. Write down what Neil J. Calkin 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 Neil J. Calkin 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 Neil J. Calkin 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 Neil J. Calkin

In research: Neil J. Calkin 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 Neil J. Calkin 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: Neil J. Calkin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1961 births, 20th-century English mathematicians, 21st-century English mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Neil J. Calkin 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 Neil J. Calkin in 20 minutes

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

Frequently asked questions

What is Neil J. Calkin in simple terms?

Neil J. Calkin (born 29 March 1961) is a professor at Clemson University in the Algebra and Discrete Mathematics group of the School of Mathematical and Statistical Sciences.

Why does Neil J. Calkin 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 Neil J. Calkin?

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 Neil J. Calkin.