mathematics

Mark Ainsworth

Mark Ainsworth 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 Mark Ainsworth rather than just read about it. In short: Mark Ainsworth is a British mathematician. He is the Francis Wayland Professor of Applied Mathematics at Brown University.

Key takeaways

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

Reference excerpt

Mark Ainsworth is a British mathematician. He is the Francis Wayland Professor of Applied Mathematics at Brown University.

Education Ainsworth studied mathematics at Durham University, where he graduated in 1986 with first-class honours and received the Collingwood Memorial Prize for the strongest performance in final exams. He completed his doctorate in 1989 from the same institution under the supervision of A. W. Craig.

Research and career Ainsworth held the 1825 Chair at the University of Strathclyde before joining Brown University. He received the Whitehead Prize from the London Mathematical Society in 2004 for his contributions to numerical analysis.

Selected publications

Books Ainsworth, Mark; Oden, J. Tinsley (2000). A Posteriori Error Estimation in Finite Element Analysis. Wiley-Interscience. doi:10.1002/9781118032824. ISBN 978-0471294115.

Articles Ainsworth, Mark; Craig, Alan (1991). "A posteriori error estimators in the finite element method". Numerische Mathematik. 60 (4): 429–464. doi:10.1007/BF01385730. Ainsworth, Mark; Fu, Guosheng (2017). "Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations". arXiv:1706.05778 [math.NA]. Ainsworth, Mark; Vejchodský, Tomáš (2019). "A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems". Computer Methods in Applied Mechanics and Engineering. 353: 373–390. arXiv:1812.07972. Bibcode:2019CMAME.353..373A. doi:10.1016/j.cma.2019.05.014.

References

External links Mark Ainsworth publications indexed by Google Scholar

Worked examples

Example 1 — a first encounter with Mark Ainsworth

Start with the simplest possible case. Write down what Mark Ainsworth 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 Mark Ainsworth 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 Mark Ainsworth 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 Mark Ainsworth

In research: Mark Ainsworth 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 Mark Ainsworth 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: Mark Ainsworth is common in secondary-school and first-year university syllabi. It links to neighbouring topics Alumni of Grey College, Durham, British mathematicians, Brown University faculty, so understanding it makes those chapters shorter.
In everyday life: Look for Mark Ainsworth 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 Mark Ainsworth in 20 minutes

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

Frequently asked questions

What is Mark Ainsworth in simple terms?

Mark Ainsworth is a British mathematician. He is the Francis Wayland Professor of Applied Mathematics at Brown University.

Why does Mark Ainsworth 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 Mark Ainsworth?

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 Mark Ainsworth.