mathematics

Jane Cronin Scanlon

Jane Cronin Scanlon 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 Cronin Scanlon rather than just read about it. In short: Jane Smiley Cronin Scanlon (July 17, 1922 – June 19, 2018) was an American mathematician and an emeritus professor of mathematics at Rutgers University. Her research concerned partial differential equations and mathematical biology.

Key takeaways

Jane Cronin Scanlon 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 Cronin Scanlon to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Jane Cronin Scanlon from memory before moving on to harder problems.

Reference excerpt

Jane Smiley Cronin Scanlon (July 17, 1922 – June 19, 2018) was an American mathematician and an emeritus professor of mathematics at Rutgers University. Her research concerned partial differential equations and mathematical biology.

Education and career Scanlon earned a bachelor's degree in mathematics from Wayne University (now Wayne State University). She completed her Ph.D. in mathematics at the University of Michigan in 1949, under the supervision of Erich Rothe. Her dissertation was Branch Points of Solutions of Equations in Banach Space. After working for the United States Air Force and the American Optical Company, she returned to academia as a lecturer at Wheaton College (Massachusetts) and then Stonehill College. She moved to the Polytechnic Institute of Brooklyn in 1957, and to Rutgers in 1965. In 1974 Scanlon was elected as an AMS Member at Large and held the position until 1976. She retired in 1991. During her twenty-six years at Rutgers, she supervised seven doctoral students. She died in June 2018 at the age of 95.

Recognition Scanlon was a Noether Lecturer in 1985, and Pi Mu Epsilon J. Sutherland Frame Lecturer in 1989. Her talks concerned "entrainment of frequency" and the application of this principle to mathematical models of the Purkinje fibers in the heart. In 2012, she became one of the inaugural fellows of the American Mathematical Society.

Personal life She married the physicist Joseph Scanlon in 1953. The two divorced in 1979. Upon her death, she was survived by four children and seven grandchildren.

Selected publications

Articles Cronin, Jane (1950). "The existence of multiple [sic] solutions of elliptic differential equations". Transactions of the American Mathematical Society. 68: 105–131. doi:10.1090/S0002-9947-1950-0032891-3. —— (1950). "Branch points of solutions of equations in Banach space". Transactions of the American Mathematical Society. 69 (2): 208–231. doi:10.1090/S0002-9947-1950-0040578-6. hdl:2027.42/182251. —— (1953). "Analytic Functional Mappings". Annals of Mathematics. 58 (1): 175–181. doi:10.2307/1969827. JSTOR 1969827. —— (1954). "Branch points of solutions of equations in Banach space. II". Transactions of the American Mathematical Society. 76 (2): 207–222. doi:10.1090/S0002-9947-1954-0062949-8. —— (1956). "Some mappings with topological degree zero". Proceedings of the American Mathematical Society. 7 (6): 1139–1145. doi:10.1090/S0002-9939-1956-0083724-1. —— (1961). "Families of solutions of a perturbation problem". Proceedings of the American Mathematical Society. 12: 84–91. doi:10.1090/S0002-9939-1961-0131017-8. ——; Richards, Paul B.; Russell, Lawrence H. (1964). "Some periodic solutions of a four-body problem". Icarus. 3 (5–6): 423–428. Bibcode:1964Icar....3..423C. doi:10.1016/0019-1035(64)90003-X. ——; McAuley, L. F. (1966). "Whyburn's conjecture for some differentiable maps". Proceedings of the National Academy of Sciences. 56 (2): 405–412. Bibcode:1966PNAS...56..405C. doi:10.1073/pnas.56.2.405. ISSN 0027-8424. PMC 224386. PMID 16591368. —— (1971). "Quasilinear systems with several periodic solutions". Proceedings of the American Mathematical Society. 30: 107–111. doi:10.1090/S0002-9939-1971-0280803-9. —— (1973). "Equations with bounded nonlinearities" (PDF). Journal of Differential Equations. 14 (3): 581–596. Bibcode:1973JDE....14..581C. doi:10.1016/0022-0396(73)90069-7. —— (1973). "Biomathematical model of aneurysm of the circle of Willis: A aqualitative analysis of the differential equation of Austin". Mathematical Biosciences. 16 (3–4): 209–225. doi:10.1016/0025-5564(73)90031-X. —— (1977). "Some Mathematics of Biological Oscillations". SIAM Review. 19: 100–138. doi:10.1137/1019007.

Books Advanced Calculus, Boston, Heath 1967 Differential equations: Introduction and Qualitative Theory, Dekker 1980, 2nd edition 1994, 3rd edition CRC/Chapman and Hall 2008 Fixed points and topological degrees in nonlinear analysis, American Mathematical Society 1964; 1995 pbk edition of 1972 reprint with corrections Mathematical aspects of the Hodgkin-Huxley neural theory, Cambridge University Press 1987 Mathematics of Cell Electrophysiology, Dekker 1981

as editor Cronin, Jane; O'Malley Jr., Robert E., eds. (1999). Analyzing Multiscale Phenomena Using Singular Perturbation Methods: American Mathematical Society Short Course, January 5-6, 1998, Baltimore, Maryland. American Mathematical Soc. ISBN 978-0-8218-0929-7.

References

External links Aboufadel, Edward F. (October 2019), "In Memoriam: Jane Smiley Cronin Scanlon" (PDF), Notices of the American Mathematical Society, 66 (9): 1448–1452, doi:10.1090/noti1948

Worked examples

Example 1 — a first encounter with Jane Cronin Scanlon

Start with the simplest possible case. Write down what Jane Cronin Scanlon 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 Cronin Scanlon 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 Cronin Scanlon 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 Cronin Scanlon

In research: Jane Cronin Scanlon 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 Cronin Scanlon 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 Cronin Scanlon is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1922 births, 2018 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jane Cronin Scanlon 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 Cronin Scanlon in 20 minutes

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

Frequently asked questions

What is Jane Cronin Scanlon in simple terms?

Why does Jane Cronin Scanlon 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 Cronin Scanlon?

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 Cronin Scanlon.