mathematics

Mary Celine Fasenmyer

Mary Celine Fasenmyer 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 Mary Celine Fasenmyer rather than just read about it. In short: Mary Celine Fasenmyer, RSM (October 4, 1906, Crown, Pennsylvania – December 27, 1996, Erie, Pennsylvania) was an American mathematician and Catholic religious sister. She is most noted for her work on hypergeometric functions and linear algebra.

Key takeaways

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

Reference excerpt

Mary Celine Fasenmyer, RSM (October 4, 1906, Crown, Pennsylvania – December 27, 1996, Erie, Pennsylvania) was an American mathematician and Catholic religious sister. She is most noted for her work on hypergeometric functions and linear algebra.

Biography Fasenmyer grew up in Pennsylvania's oil country, and displayed mathematical talent in high school. For ten years after her graduation she taught and studied at Mercyhurst College in Erie, where she joined the Sisters of Mercy. She pursued her mathematical studies in Pittsburgh and the University of Michigan, obtaining her doctorate in 1946 under the direction of Earl Rainville, with a dissertation entitled Some Generalized Hypergeometric Polynomials. After earning her Ph.D., Fasenmyer published two papers which expanded on her doctorate work. These would be further elaborated by Doron Zeilberger and Herbert Wilf into "WZ theory", which allowed computerized proof of many combinatorial identities. After this, she returned to Mercyhurst to teach and did not engage in further research. Fasenmyer died in 1996.

"Sister Celine's" method Fasenmyer is most remembered for the method that bears her name, first described in her Ph.D. thesis concerning recurrence relations in hypergeometric series. The thesis demonstrated a purely algorithmic method to find recurrence relations satisfied by sums of terms of a hypergeometric polynomial, and requires only the series expansions of the polynomial. The beauty of her method is that it lends itself readily to computer automation. The work of Wilf and Zeilberger generalized the algorithm and established its correctness. The hypergeometric polynomials she studied are called Sister Celine's polynomials.

References

Publications Fasenmyer, Mary Celine (1947), "Some generalized hypergeometric polynomials", Bulletin of the American Mathematical Society, (1945 University of Michigan PhD thesis), 53 (8): 806–812, doi:10.1090/S0002-9904-1947-08893-5, ISSN 0002-9904, MR 0022276, Zbl 0032.15402 Fasenmyer, Mary Celine (1949), "A note on pure recurrence relations", The American Mathematical Monthly, 56 (1): 14–17, doi:10.1080/00029890.1949.11990232, ISSN 0002-9890, JSTOR 2305810, MR 0030044, Zbl 0032.41002

External links O'Connor, John J.; Robertson, Edmund F., "Mary Celine Fasenmyer", MacTutor History of Mathematics Archive, University of St Andrews "Sister Celine's Methods, Theorems, and Demonstrations" (PDF). Archived from the original (PDF) on 2010-06-01. (251 KB) Weisstein, Eric W. "Sister Celine's Method". MathWorld. Marko Petkovsek, Herbert Wilf and Doron Zeilberger (1996). A=B. AK Peters. pp. 57–58. ISBN 1-56881-063-6. Herbert Wilf and Lily Yen talk to Sister Celine (1993) Mary Celine Fasenmyer at the Mathematics Genealogy Project "Sister Mary Celine Fasenmyer", Biographies of Women Mathematicians, Agnes Scott College

Worked examples

Example 1 — a first encounter with Mary Celine Fasenmyer

Start with the simplest possible case. Write down what Mary Celine Fasenmyer 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 Mary Celine Fasenmyer 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 Mary Celine Fasenmyer 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 Mary Celine Fasenmyer

In research: Mary Celine Fasenmyer 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 Mary Celine Fasenmyer 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: Mary Celine Fasenmyer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1906 births, 1996 deaths, 20th-century American Roman Catholic nuns, so understanding it makes those chapters shorter.
In everyday life: Look for Mary Celine Fasenmyer 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Mary Celine Fasenmyer” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Mary Celine Fasenmyer in 20 minutes

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

Frequently asked questions

What is Mary Celine Fasenmyer in simple terms?

Why does Mary Celine Fasenmyer 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 Mary Celine Fasenmyer?

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 Mary Celine Fasenmyer.