mathematics

Jane Piore Gilman

Jane Piore Gilman 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 Jane Piore Gilman rather than just read about it. In short: Jane Piore Gilman (born 1945) is an American mathematician, a distinguished professor of mathematics at Rutgers University. Her research concerns topology and group theory.

Key takeaways

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

Reference excerpt

Jane Piore Gilman (born 1945) is an American mathematician, a distinguished professor of mathematics at Rutgers University. Her research concerns topology and group theory.

Education and career Gilman is one of three children of physicist Emanuel R. Piore. She did her undergraduate studies at the University of Chicago, graduating in 1965, and received her Ph.D. from Columbia University in 1971. Her thesis, supervised by Lipman Bers, was entitled Relative Modular Groups in Teichmüller Spaces. She worked for a year as an instructor at Stony Brook University before joining Rutgers in 1972.

Books Gilman is the author of a monograph on the problem of testing whether pairs of elements of PSL(2,R) (the group of orientation-preserving isometries of the hyperbolic plane) generate a Fuchsian group (a discrete subgroup of PSL(2,R)). It is Two-generator Discrete Subgroups of PSL(2, R) (Memoirs of the American Mathematical Society 117, 1995). With Irwin Kra and Rubí E. Rodríguez she is the co-author of a graduate-level textbook on complex analysis, Complex Analysis: In the Spirit of Lipman Bers (Graduate Texts in Mathematics 245, Springer, 2007; 2nd ed., 2013).

Recognition In 2014, she was elected as a Fellow of the American Mathematical Society "for contributions to topology and group theory, and for service to her department and the larger community."

References

Worked examples

Example 1 — a first encounter with Jane Piore Gilman

Start with the simplest possible case. Write down what Jane Piore Gilman 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 Jane Piore Gilman 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 Jane Piore Gilman 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 Jane Piore Gilman

In research: Jane Piore Gilman 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 Jane Piore Gilman 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: Jane Piore Gilman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jane Piore Gilman 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 Jane Piore Gilman in 20 minutes

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

Frequently asked questions

What is Jane Piore Gilman in simple terms?

Jane Piore Gilman (born 1945) is an American mathematician, a distinguished professor of mathematics at Rutgers University. Her research concerns topology and group theory.

Why does Jane Piore Gilman 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 Jane Piore Gilman?

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 Jane Piore Gilman.