mathematics

Kathryn E. Hare

Kathryn E. Hare 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 Kathryn E. Hare rather than just read about it. In short: Kathryn Elizabeth Hare (born 1959) is a Canadian mathematician specializing in harmonic analysis and fractal geometry. She was the Chair of the Pure Mathematics Department at the University of Waterloo from 2014 to 2018.

Key takeaways

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

Reference excerpt

Kathryn Elizabeth Hare (born 1959) is a Canadian mathematician specializing in harmonic analysis and fractal geometry. She was the Chair of the Pure Mathematics Department at the University of Waterloo from 2014 to 2018. She retired from the University of Waterloo in 2021.

Education and career Hare did her undergraduate studies at the University of Waterloo, graduating in 1981. She earned a Ph.D. from the University of British Columbia in 1986. Her dissertation, under the supervision of John J. F. Fournier, was Thin Sets and Strict-Two-Associatedness, and concerned group representation theory. She was an assistant professor at the University of Alberta from 1986 to 1988, before she moved back to Waterloo.

Awards and recognition In 2011, the Chalmers University of Technology awarded her an Honorary Doctorate for her "prominent research, both in extent and depth, within classical and abstract harmonic analysis". In 2020 she was named as a Fellow of the Canadian Mathematical Society.

Selected publications Hare, Kathryn E.; Klemes, Ivo (1995), "On permutations of lacunary intervals", Transactions of the American Mathematical Society, 347 (10): 4105–4127, doi:10.2307/2155216, JSTOR 2155216. Graham, Colin C.; Hare, Kathryn E. (2013), Interpolation and Sidon Sets for Compact Groups, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer, New York, doi:10.1007/978-1-4614-5392-5, ISBN 978-1-4614-5391-8. Hare, Kathryn E.; He, Jimmy. (2017), "The absolute continuity of convolution products of orbital measures in exceptional symmetric spaces", Monatshefte für Mathematik, 182 (3): 619–635, arXiv:1511.05799, doi:10.1007/s00605-016-0999-5.

References

Worked examples

Example 1 — a first encounter with Kathryn E. Hare

Start with the simplest possible case. Write down what Kathryn E. Hare 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 Kathryn E. Hare 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 Kathryn E. Hare 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 Kathryn E. Hare

In research: Kathryn E. Hare 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 Kathryn E. Hare 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: Kathryn E. Hare is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1959 births, 20th-century Canadian mathematicians, 20th-century Canadian women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kathryn E. Hare 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 Kathryn E. Hare in 20 minutes

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

Frequently asked questions

What is Kathryn E. Hare in simple terms?

Why does Kathryn E. Hare 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 Kathryn E. Hare?

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 Kathryn E. Hare.