mathematics

Trevor Wooley

Trevor Wooley 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 Trevor Wooley rather than just read about it. In short: Trevor Dion Wooley is a British mathematician, the Andris A. Zoltners Distinguished Professor of Mathematics at Purdue University.

Key takeaways

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

Reference excerpt

Trevor Dion Wooley is a British mathematician, the Andris A. Zoltners Distinguished Professor of Mathematics at Purdue University. His fields of interest include analytic number theory, Diophantine equations and Diophantine problems, harmonic analysis, the Hardy-Littlewood circle method, and the theory and applications of exponential sums. He has made significant breakthroughs on Waring's problem, for which he was awarded the Salem Prize in 1998.

Education and career Wooley read mathematics in Gonville and Caius College, Cambridge, receiving a bachelor's degree from the University of Cambridge in 1987 with first class honours, and a master's degree in 1991. Meanwhile, he completed his PhD, supervised by Bob Vaughan, in 1990 from Imperial College London. After postdoctoral research in the Institute for Advanced Study in Princeton, New Jersey, he became an assistant professor of mathematics at the University of Michigan in 1991. He was promoted to associate professor in 1995, and full professor in 1998; he chaired the mathematics department from 2002 to 2005. In 2007 he returned to the UK as a professor of pure mathematics at the University of Bristol, where he became head of pure mathematics from 2015 to 2016. At Bristol, his doctoral students included Thomas Bloom. He took his current position as Andris A. Zoltners Distinguished Professor of Mathematics at Purdue University in 2019.

Awards and honours Wooley was the recipient of the 1993 Berwick Prize of the London Mathematical Society. He was awarded the 1998 Salem Prize "for his work in additive number theory, in particular on problems of Waring's type". He was an invited speaker at the International Congress of Mathematicians (ICM), held in Beijing in 2002, and after receiving the 2012 Fröhlich Prize he spoke again at the 2014 ICM in Seoul. He was elected as a Fellow of the Royal Society (FRS) in 2007, and as a Fellow of the American Mathematical Society in 2012.

Selected publications Wooley, Trevor D. (1992). "Large improvements in Waring's problem". The Annals of Mathematics. 135 (1): 131–164. doi:10.2307/2946566. JSTOR 2946566. MR 1147960. Zbl 0754.11026. Wooley, Trevor D. (1994). "Quasi-diagonal behaviour in certain mean value theorems of additive number theory". Journal of the American Mathematical Society. 7 (1): 221–245. doi:10.1090/s0894-0347-1994-1224595-9. MR 1224595. Zbl 0786.11053. Wooley, Trevor D. (1995). "Breaking classical convexity in Waring's problem: Sums of cubes and quasi-diagonal behaviour". Inventiones Mathematicae. 122 (1): 421–451. Bibcode:1995InMat.122..421W. doi:10.1007/bf01231451. hdl:2027.42/46588. MR 1359599. Zbl 0851.11055. Wooley, Trevor (1 May 2012). "Vinogradov's mean value theorem via efficient congruencing". Annals of Mathematics. 175 (3): 1575–1627. arXiv:1101.0574. doi:10.4007/annals.2012.175.3.12. MR 2912712. S2CID 13286053. Zbl 1267.11105.

References

External links Official website

Illustrations

Worked examples

Example 1 — a first encounter with Trevor Wooley

Start with the simplest possible case. Write down what Trevor Wooley 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 Trevor Wooley 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 Trevor Wooley 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 Trevor Wooley

In research: Trevor Wooley 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 Trevor Wooley 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: Trevor Wooley is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century British mathematicians, 21st-century British mathematicians, Alumni of Gonville and Caius College, Cambridge, so understanding it makes those chapters shorter.
In everyday life: Look for Trevor Wooley 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 Trevor Wooley in 20 minutes

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

Frequently asked questions

What is Trevor Wooley in simple terms?

Trevor Dion Wooley is a British mathematician, the Andris A. Zoltners Distinguished Professor of Mathematics at Purdue University.

Why does Trevor Wooley 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 Trevor Wooley?

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 Trevor Wooley.