mathematics

Rodica Simion

Rodica Simion 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 Rodica Simion rather than just read about it. In short: Rodica Eugenia Simion (January 18, 1955 – January 7, 2000) was a Romanian-American mathematician. She was the Columbian School Professor of Mathematics at George Washington University.

Key takeaways

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

Reference excerpt

Rodica Eugenia Simion (January 18, 1955 – January 7, 2000) was a Romanian-American mathematician. She was the Columbian School Professor of Mathematics at George Washington University. Her research concerned combinatorics: she was a pioneer in the study of permutation patterns, and an expert on noncrossing partitions.

Biography Simion was one of the top competitors in the Romanian national mathematical olympiads. She graduated from the University of Bucharest in 1974, and immigrated to the United States in 1976. She did her graduate studies at the University of Pennsylvania, earning a Ph.D. in 1981 under the supervision of Herbert Wilf. After teaching at Southern Illinois University and Bryn Mawr College, she moved to George Washington University in 1987, and became Columbian School Professor in 1997.

Recognition She is included in a deck of playing cards featuring notable women mathematicians published by the Association of Women in Mathematics.

Research contributions Simion's thesis research concerned the concavity and unimodality of certain combinatorially defined sequences, and included what Richard P. Stanley calls "a very influential result" that the zeros of certain polynomials are all real. Next, with Frank Schmidt, she was one of the first to study the combinatorics of sets of permutations defined by forbidden patterns; she found a bijective proof that the stack-sortable permutations and the permutations formed by interleaving two monotonic sequences are equinumerous, and found combinatorial enumerations of many permutation classes. The "simsun permutations" were named after her and Sheila Sundaram, after their initial studies of these objects; a simsun permutation is a permutation in which, for all k, the subsequence of the smallest k elements has no three consecutive elements in decreasing order. Simion also did extensive research on noncrossing partitions, and became "perhaps the world's leading authority" on them.

Other activities Simion was the main organizer of an exhibit about mathematics, Beyond Numbers, at the Maryland Science Center, based in part on her earlier experience organizing a similar exhibit at George Washington University. She was also a leader in George Washington University's annual Summer Program for Women in Mathematics. As well as being a mathematician, Simion was a poet and painter; her poem "Immigrant Complex" was published in a collection of mathematical poetry in 1979.

Selected publications Simion, Rodica (1984), "A multi-indexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences", Journal of Combinatorial Theory, Series A, 36 (1): 15–22, doi:10.1016/0097-3165(84)90075-X, MR 0728500. Simion, Rodica; Schmidt, Frank W. (1985), "Restricted permutations", European Journal of Combinatorics, 6 (4): 383–406, doi:10.1016/s0195-6698(85)80052-4, MR 0829358. Simion, Rodica; Ullman, Daniel (1991), "On the structure of the lattice of noncrossing partitions", Discrete Mathematics, 98 (3): 193–206, doi:10.1016/0012-365X(91)90376-D, MR 1144402. Simion, Rodica (2000), "Noncrossing partitions", Discrete Mathematics, 217 (1–3): 367–409, doi:10.1016/S0012-365X(99)00273-3, MR 1766277.

Worked examples

Example 1 — a first encounter with Rodica Simion

Start with the simplest possible case. Write down what Rodica Simion 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 Rodica Simion 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 Rodica Simion 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 Rodica Simion

In research: Rodica Simion 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 Rodica Simion 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: Rodica Simion is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, 2000 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Rodica Simion 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 Rodica Simion in 20 minutes

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

Frequently asked questions

What is Rodica Simion in simple terms?

Rodica Eugenia Simion (January 18, 1955 – January 7, 2000) was a Romanian-American mathematician. She was the Columbian School Professor of Mathematics at George Washington University.

Why does Rodica Simion 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 Rodica Simion?

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 Rodica Simion.