mathematics

Karen E. Smith

Karen E. Smith 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 Karen E. Smith rather than just read about it. In short: Karen Ellen Smith (born 1965 in Red Bank, New Jersey) is an American mathematician, specializing in commutative algebra and algebraic geometry. She completed her bachelor's degree in mathematics at Princeton University before earning her PhD in mathematics at the University of Michigan in 1993.

Key takeaways

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

Reference excerpt

Karen Ellen Smith (born 1965 in Red Bank, New Jersey) is an American mathematician, specializing in commutative algebra and algebraic geometry. She completed her bachelor's degree in mathematics at Princeton University before earning her PhD in mathematics at the University of Michigan in 1993. Currently she is the Keeler Professor of Mathematics at the University of Michigan. In addition to being a researcher in algebraic geometry and commutative algebra, Smith with others wrote the textbook An Invitation to Algebraic Geometry.

Biography Smith graduated in 1987 with a bachelor's degree in mathematics from Princeton University, where she was influenced in her freshman year by Charles Fefferman. She was a high school mathematics teacher in the academic year 1987/1988. In 1988 she became a graduate student at the University of Michigan, where in 1993 she earned her PhD with thesis Tight closure of parameter ideals and f-rationality under the supervision of Melvin Hochster. In the academic year 1993–1994 she was a postdoc at Purdue University working with Craig Huneke. In 1994 she became a C.L.E. Moore Instructor and then an associate professor at MIT. Since 1997 she has been a professor at the University of Michigan. In 1991 she married the Finnish mathematician Juha Heinonen. He died in 2007.

Honors In 2001 Smith won the Ruth Lyttle Satter Prize in Mathematics for her development of tight closure methods, introduced by Hochster and Huneke, in commutative algebra and her application of these methods in algebraic geometry. The prize committee specifically cited her papers "Tight closure of parameter ideals" (Inventiones Mathematicae 1994), "F-rational rings have rational singularities" (American J. Math. 1997, and, with Gennady Lyubeznik, "Weak and strong F-regularity are equivalent in graded rings" (American J. Math., 1999). In addition to the Satter Prize, Smith was the recipient of a 1997 Sloan Research Fellowship, a Fulbright award, and a University of Michigan Faculty Recognition Award for outstanding contributions as a teacher, scholar and member of the University community. In 1996, Smith was the first recipient of the Etta Z. Falconer Award, where she presented the lecture "Calclulus mod p." Smith was selected to give the 2015 Earle Raymond Hedrick Lectures at the Mathematical Association of America's MathFest. Smith was chosen to give the Association for Women in Mathematics-American Mathematical Society 2016 Noether Lecture at the Joint Mathematics Meetings. In 2015 she was elected as a fellow of the American Mathematical Society "for contributions to commutative algebra and algebraic geometry." She was named MSRI Clay Senior Scholar for 2012-2013. In 2019, she was elected to the National Academy of Sciences. The Association for Women in Mathematics has included her in the 2020 class of AWM Fellows for "her tireless support of women in mathematics; throughout her career, she has officially and unofficially mentored numerous female mathematicians at every level from undergraduate to full professor; she continues to be an incredibly strong role model for women everywhere". She was elected to the American Academy of Arts and Sciences in 2021.

Books An Invitation to Algebraic Geometry (with Lauri Kahanpää, Pekka Kekäläinen, and William Traves, Universitext, Springer, 2000 and 2004). Rational and Nearly Rational Varieties (with János Kollár and Alessio Corti, Cambridge Studies in Advanced Mathematics 92, Cambridge University Press, 2004).

References

External links

Home page

Worked examples

Example 1 — a first encounter with Karen E. Smith

Start with the simplest possible case. Write down what Karen E. Smith 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 Karen E. Smith 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 Karen E. Smith 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 Karen E. Smith

In research: Karen E. Smith 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 Karen E. Smith 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: Karen E. Smith is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1965 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Karen E. Smith 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 Karen E. Smith in 20 minutes

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

Frequently asked questions

What is Karen E. Smith in simple terms?

Why does Karen E. Smith 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 Karen E. Smith?

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 Karen E. Smith.