mathematics

Mary Rees

Mary Rees 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 Mary Rees rather than just read about it. In short: Susan Mary Rees (born 31 July 1953) is a British mathematician and an emeritus professor of mathematics at the University of Liverpool since 2018, specialising in research in complex dynamical systems. Career Rees was born in Cambridge.

Key takeaways

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

Reference excerpt

Susan Mary Rees (born 31 July 1953) is a British mathematician and an emeritus professor of mathematics at the University of Liverpool since 2018, specialising in research in complex dynamical systems.

Career Rees was born in Cambridge. After obtaining her BA in 1974 and MSc in 1975 at St Hugh's College, Oxford, she did research in mathematics under the direction of Bill Parry at the University of Warwick, obtaining a PhD in 1978. Her first postdoctoral position was at the Institute for Advanced Study from 1978 to 1979. Later she worked at Institut des hautes études scientifiques and the University of Minnesota. Following this she worked at the University of Liverpool until her retirement. She became professor of mathematics in 2002 and retired in 2018, becoming an emeritus professor.

She was awarded a Whitehead Prize of the London Mathematical Society in 1988. The citation notes that, in particular, Her most spectacular theorem has been to show that in the space of rational maps of the Riemann sphere of degree d ≥ 2 those maps that are ergodic with respect to Lebesgue measure and leave invariant an absolutely continuous probability measure form a set of positive measure. She also spoke at the ICM at Kyoto in 1990. In recent years, much of Rees' work has focused on the dynamics of quadratic rational maps; i.e. rational maps of the Riemann sphere of degree two, including an extensive monograph. In 2004, she also presented an alternative proof of the Ending Laminations Conjecture of Thurston, which had been proved by Brock, Canary and Minsky shortly before.

FRS She was elected to a Fellowship of the Royal Society in 2002.

Family Her father David Rees was also a distinguished mathematician, who worked on Enigma in Hut 6 at Bletchley Park. Her sister Sarah Rees is also a mathematician.

Works Mary Rees (2010) "Multiple equivalent matings with the aeroplane polynomial". Ergodic Theory and Dynamical Systems, pp. 20 Mary Rees (2008) "William Parry FRS 1934–2006". Biographical Memoirs of the Royal Society, 54, pp. 229–243 Mary Rees (2004) "Teichmuller distance is not $C^{2+\varepsilon }$". Proc London Math, 88, pp. 114–134 Mary Rees (2003) "Views of Parameter Space: Topographer and Resident". Asterisque, 288, pp. 1–418 Mary Rees (2002) "Teichmuller distance for analytically finite surfaces is $C^{2}$." Proc. London Math. Soc. 85 (2002) 686 – 716.,85, pp. 686–716

References

Worked examples

Example 1 — a first encounter with Mary Rees

Start with the simplest possible case. Write down what Mary Rees 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 Mary Rees 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 Mary Rees 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 Mary Rees

In research: Mary Rees 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 Mary Rees 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: Mary Rees is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1953 births, 20th-century British mathematicians, 20th-century British women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mary Rees 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 Mary Rees in 20 minutes

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

Frequently asked questions

What is Mary Rees in simple terms?

Why does Mary Rees 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 Mary Rees?

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 Mary Rees.