mathematics

Linda Keen

Linda Keen 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 Linda Keen rather than just read about it. In short: Linda Jo Goldway Keen (born August 9, 1940, in New York City, New York) is an American mathematician and a fellow of the American Mathematical Society. Since 1965, she has been a professor in the Department of Mathematics and Computer Science at Lehman College of the City University of New York and a Professor of Mathematics at Graduate Center of the City University of New York.

Key takeaways

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

Reference excerpt

Linda Jo Goldway Keen (born August 9, 1940, in New York City, New York) is an American mathematician and a fellow of the American Mathematical Society. Since 1965, she has been a professor in the Department of Mathematics and Computer Science at Lehman College of the City University of New York and a Professor of Mathematics at Graduate Center of the City University of New York.

Professional career As a high school student she attended the Bronx High School of Science. She received her Bachelor of Science degree from the City College of New York, then studied at the Courant Institute of Mathematical Sciences, earning her Doctor of Philosophy in mathematics in 1964. She wrote her thesis on Riemann surfaces under the direction of Lipman Bers at New York University. Keen has worked at the Institute for Advanced Study, Hunter College, University of California at Berkeley, Columbia University, Boston University, Princeton University, and the Massachusetts Institute of Technology, as well as at various mathematical institutes in Europe and South America. After her initial appointment in 1965, in 1974 Keen was promoted to Full Professor at Lehman College and the CUNY Graduate Center. She served as Executive Officer of the Mathematics Program at the Graduate Center before retiring in 2017. Keen served as president of the Association for Women in Mathematics during 1985-1986 and as vice-president of the American Mathematical Society during 1992-1995. She served on the board of trustees of the American Mathematical Society from 1999-2009 and as Associate Treasurer from 2009-2011. Keen worked with the mathematicians Paul Blanchard, Robert L. Devaney, Jane Gilman, Lisa Goldberg, Yunping Jiang, Nikola Lakic and Caroline Series among many others. In 1975, Keen presented an AMS invited address and in 1989 she presented an MAA joint invited address. In 1993 she was selected as a Noether Lecturer by the Association for Women in Mathematics.

Contributions In addition to studying Riemann surfaces, Keen has worked in hyperbolic geometry, Kleinian groups and Fuchsian groups, complex analysis, and hyperbolic dynamics. In the field of hyperbolic geometry, she is known for the Collar lemma.

Personal She is married to Jonathan Brezin and resides in New York.

Awards and honors She has been honored with:

AAUW Postdoctoral Fellowship Award, 1964–65 National Science Foundation Postdoctoral Fellow, 1964–65 Edwin S. Webster-Abby Rockefeller Mauze Award, Massachusetts Institute of Technology 1990 Finnish Mathematical Society Invited Foreign Speaker, January 1991 Association for Women in Mathematics Emmy Noether Lecturer, 1993 Joint Irish and London Mathematical Societies Invited Speaker, 1998 Lehman College Foundation Faculty Award, 1998 MAA Invited hour Address, Boulder, Colorado, 1989 Swedish Royal Academy of Sciences Kovalevsky Days Programme Main Speaker, 2006 In 2012 she became a fellow of the American Mathematical Society. In 2017, she was selected as a fellow of the Association for Women in Mathematics in the inaugural class.

Books Hyperbolic Geometry from a Local Viewpoint (with Nikola Lakic, London Mathematical Society Student Texts 68, Cambridge University Press, 2007) The Legacy of Sonya Kovalevskaya (edited, Contemporary Mathematics 64, American Mathematical Society, 1987) Chaos and Fractals: The Mathematics Behind the Computer Graphics (edited with Robert L. Devaney, Proc. Symposia in Appl. Math, 39, American Mathematical Society, 1989) Lipa's Legacy: Proceedings of the 1st Bers Colloquium (edited with Józef Dodziuk, Contemporary Mathematics 211, American Mathematical Society, 1997) Complex dynamics. Twenty-five years after the appearance of the Mandelbrot set (edited with Robert L. Devaney, Contemporary Mathematics 396, American Mathematical Society, 2006) Lipman Bers, a Life in Mathematics (edited with Irwin Kra and Rubí E. Rodríguez, American Mathematical Society, 2015)

References

External links

Linda Keen Understanding Chaos Archived August 25, 2007, at the Wayback Machine Linda Keen

Illustrations

Worked examples

Example 1 — a first encounter with Linda Keen

Start with the simplest possible case. Write down what Linda Keen 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 Linda Keen 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 Linda Keen 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 Linda Keen

In research: Linda Keen 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 Linda Keen 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: Linda Keen is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1940 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Linda Keen 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 Linda Keen in 20 minutes

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

Frequently asked questions

What is Linda Keen in simple terms?

Why does Linda Keen 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 Linda Keen?

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 Linda Keen.