mathematics

Louise Duffield Cummings

Louise Duffield Cummings 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 Louise Duffield Cummings rather than just read about it. In short: Louise Duffield Cummings (21 November 1870 – 9 May 1947) was a Canadian-born American mathematician. She was born in Hamilton, Ontario.

Key takeaways

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

Reference excerpt

Louise Duffield Cummings (21 November 1870 – 9 May 1947) was a Canadian-born American mathematician. She was born in Hamilton, Ontario.

Education and career As a young child, Louise Duffield Cummings studied at the public schools and Collegiate Institute at Hamilton. Cummings received her B.A. in 1895 from the University of Toronto. She studied mathematics at the graduate level in 1895–1896 under the Professor DeLury at University of Toronto, in 1896–1897 at the University of Pennsylvania where she held a fellowship, in 1897–1898 at the University of Chicago, and in 1898–1900 at Bryn Mawr College. During 1900–1901 she taught at the Ontario Normal College and, while completing her A.M. at the University of Toronto, she taught at St. Margaret's College during 1901–1902. she worked with Henry White and Charlotte Scott was her supervisor. She returned to Bryn Mawr College in 1905 and 1912–1913. Cummings joined the faculty of Vassar in 1902 as an instructor; she worked with Henry White and Charlotte Scott was her supervisor. She finally received her Ph.D. from Bryn Mawr in 1914 with a thesis "On a Method of Comparison for Triple-Systems," published in the Transactions of the American Mathematical Society, Vol 15 (July 1914) . Her major subject was Pure Mathematics, and her minors were Applied Mathematics and Physics. before her retirement in 1936. She was promoted to assistant professor in 1915, to associate professor in 1919, and to full professor in 1927. She was an invited speaker at the International Congress of Mathematicians in 1924 at Toronto and again in 1932 at Zürich.

Selected publications Cummings, L. D. (1913). "A note on the groups for triple-systems". Bull. Amer. Math. Soc. 19 (7): 355–356. doi:10.1090/s0002-9904-1913-02369-3. MR 1559362. Cummings, Louise D. (1914). "On a method of comparison for triple systems". Trans. Amer. Math. Soc. 15 (3): 311–327. doi:10.1090/s0002-9947-1914-1500982-1. hdl:2027/mdp.39015068190779. MR 1500982. (Ph.D. dissertation) with H. S. White: Cummings, Louise D.; White, H. S. (1915). "Groupless triad systems on fifteen elements". Bull. Amer. Math. Soc. 22: 12–16. doi:10.1090/s0002-9904-1915-02710-2. MR 1559701. Cummings, Louise D. (1918). "An undervalued Kirkman paper". Bull. Amer. Math. Soc. 24 (7): 336–339. doi:10.1090/s0002-9904-1918-03086-3. MR 1560081. Cummings, Louise D. (1919). "The trains for the 36 groupless triad systems on 15 elements". Bull. Amer. Math. Soc. 25 (7): 321–324. doi:10.1090/s0002-9904-1919-03192-9. MR 1560192. Cummings, Louise D. (1925). "A new type of double sextette closed under a binary (3,3) correspondence". Bull. Amer. Math. Soc. 31 (5): 266–274. doi:10.1090/s0002-9904-1925-04049-5. MR 1561036. Cummings, Louise D. (1932). "Hexagonal systems of seven lines in a plane". Bull. Amer. Math. Soc. 38 (2): 105–110. doi:10.1090/s0002-9904-1932-05337-x. MR 1562336. Cummings, Louise D. (1932). "Heptagonal systems of eight lines in a plane". Bull. Amer. Math. Soc. 38 (10): 700–702. doi:10.1090/s0002-9904-1932-05502-1. MR 1562491. Cummings, Louise D. (1933). "On a method of comparison for straight-line nets". Bull. Amer. Math. Soc. 39 (6): 411–416. doi:10.1090/s0002-9904-1933-05649-5. MR 1562638.

References

External links Works by or about Louise Duffield Cummings at the Internet Archive Media related to Louise Duffield Cummings (mathematician) at Wikimedia Commons

Illustrations

Worked examples

Example 1 — a first encounter with Louise Duffield Cummings

Start with the simplest possible case. Write down what Louise Duffield Cummings 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 Louise Duffield Cummings 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 Louise Duffield Cummings 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 Louise Duffield Cummings

In research: Louise Duffield Cummings 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 Louise Duffield Cummings 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: Louise Duffield Cummings is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1870 births, 1947 deaths, 19th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Louise Duffield Cummings 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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Frequently asked questions

What is Louise Duffield Cummings in simple terms?

Louise Duffield Cummings (21 November 1870 – 9 May 1947) was a Canadian-born American mathematician. She was born in Hamilton, Ontario.

Why does Louise Duffield Cummings 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 Louise Duffield Cummings?

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 Louise Duffield Cummings.