mathematics

John Toland (mathematician)

John Toland (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 Toland (mathematician) rather than just read about it. In short: John Francis Toland (born 28 April 1949 in Derry) is an Irish mathematician based in the UK. From 2011 to 2016 he served as director of the Isaac Newton Institute for Mathematical Sciences and N M Rothschild & Sons Professor of Mathematical Sciences at the University of Cambridge.

Key takeaways

John Toland (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 Toland (mathematician) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John Toland (mathematician) from memory before moving on to harder problems.

Reference excerpt

John Francis Toland (born 28 April 1949 in Derry) is an Irish mathematician based in the UK. From 2011 to 2016 he served as director of the Isaac Newton Institute for Mathematical Sciences and N M Rothschild & Sons Professor of Mathematical Sciences at the University of Cambridge.

Education Toland was educated at St Columb's College in Derry and Queen's University Belfast, where he was awarded a Bachelor of Science degree in 1970. He completed postgraduate study at the University of Sussex, where he was awarded a PhD in 1973 for research on topological methods for nonlinear eigenvalue problems supervised by Charles A. Stuart.

Career and research From 1982 to 2011 he was professor of mathematics at the University of Bath, where he held an Engineering and Physical Sciences Research Council (EPSRC) Senior Fellowship 1997–2002. In addition from 2002 to 2010 he was scientific director of the International Centre for Mathematical Sciences (ICMS) in Edinburgh. In 2011 he succeeded Sir David Wallace as director of the Isaac Newton Institute for Mathematical Sciences and N M Rothschild & Sons Professor of Mathematical Sciences at the University of Cambridge. In 2016 he was succeeded as director by Professor David Abrahams. His research interests include mathematical analysis and nonlinear partial differential equations with particular interest in the rigorous theory of steady water waves. In 1978, he proved George Gabriel Stokes' conjecture on the existence of gravity waves of maximum height on deep water, a previously open problem in mathematical hydrodynamics which dated back to the 19th century.

Awards and honours He was elected Fellow of the Royal Society (FRS) in 1999, and a Fellow of the Royal Society of Edinburgh (FRSE) in 2003. He was awarded the London Mathematical Society's Senior Berwick Prize in 2000; and the Royal Society's Sylvester Medal in 2012. He is an Honorary Fellow of University College London and was a Fellow of St John's College, Cambridge October 2011 – September 2016. The University of Bath awarded Toland an Honorary Doctorate of Science in December 2017.

References

Worked examples

Example 1 — a first encounter with John Toland (mathematician)

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

In research: John Toland (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 Toland (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 Toland (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1949 births, 20th-century mathematicians from Northern Ireland, 21st-century mathematicians from Northern Ireland, so understanding it makes those chapters shorter.
In everyday life: Look for John Toland (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 Toland (mathematician) in 20 minutes

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

Frequently asked questions

What is John Toland (mathematician) in simple terms?

Why does John Toland (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 Toland (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 Toland (mathematician).