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Ralph Duncan James

Ralph Duncan James 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 Ralph Duncan James rather than just read about it. In short: Ralph Duncan James (8 February 1909 – 19 May 1979) was a Canadian mathematician working on number theory and mathematical analysis. Born in Liverpool, England, James moved with his parents to Vancouver, British Columbia when he was 10 years old.

Key takeaways

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

Reference excerpt

Ralph Duncan James (8 February 1909 – 19 May 1979) was a Canadian mathematician working on number theory and mathematical analysis. Born in Liverpool, England, James moved with his parents to Vancouver, British Columbia when he was 10 years old. After graduating from high school, James attended University of British Columbia. After graduating, he continued in mathematics, writing a master’s thesis on Tangential Coordinates. Proceeding to University of Chicago, he studied number theory and Waring's problem under L. E. Dickson. In 1932 he was a awarded a Ph.D. on the strength of his dissertation Analytical Investigations of Waring's Theorem. He continued post-graduate study, first with E. T. Bell at California Institute of Technology, then in 1934 with G. H. Hardy at Cambridge University. He published in the Transactions of the American Mathematical Society and extended some work of Viggo Brun in 1938. James was a professor of mathematics at University of California, Berkeley from 1934 to 1939. He was then called to University of Saskatchewan where he became head of the mathematics department. In 1943 he began his long tenure at University of British Columbia, becoming head of the department in 1948. James made contributions to the theory of the Perron integral and to solution of Goldbach's conjecture. When the International Congress of Mathematicians convened in Vancouver in 1974, the four volumes of the Proceedings of the congress were edited by Ralph D. James. He died on 19 May 1979 on Salt Spring Island in British Columbia. Since 1978, the Canadian Mathematical Society have awarded the Coxeter–James Prize in his honor.

Papers Ralph Duncan James published the following papers in the course of his career:

1934: Mathematische Annalen "On the representation of integers as sums of pyramidal numbers" 1934: Transactions of the American Mathematical Society 36(2):395–444 "The value of the number g(k) in Waring's problem" MR 1501751 1938: Transactions of the American Mathematical Society 43(2):296–302 "A problem in additive number theory" MR 1501944 1939: Duke Mathematical Journal 5:948–62 "Integers which are not represented by certain ternary quadratic forms" MR 0001230 1942: (with Hermann Weyl ) American Journal of Mathematics 64:539–52 "Elementary note on prime number problems of Vinogradoff’s type" MR 0006745 1943: Bulletin of the American Mathematical Society 49:422–32 "On the sieve method of Viggo Brun" MR 0008229 1946: (with Walter Gage ) Transactions of the Royal Society of Canada Section III(3) 40:25–35 "A generalized integral" MR 0021081 1949: Bulletin of the AMS 55:246–60 "Recent progress on the Goldbach problem" MR 0028893 1950: Canadian Journal of Mathematics 2:297–306 "A generalized integral II" MR 0036344 1954: (with Ivan Niven) Proceedings of the American Mathematical Society 5:834–8 "Unique factorization in multiplicative systems" MR 0060002 1955: Bulletin of the AMS 61:1–15 "Integrals and summable trigonometric series" MR 0067228 1956: Pacific Journal of Mathematics 6:99–110 "Summable trigonometric series" MR 0078474 1968: Canadian Mathematical Bulletin 11:733–5 "The factors of a square-free integer" MR 0240038 1970: American Mathematical Monthly 77(1):94 "Review: Studies in Number Theory"

References

Ralph James dies suddenly at Salt Spring Island home from Gulf Islands Driftwood, May 23, 1979, page 3. O'Connor, John J.; Robertson, Edmund F., "Ralph Duncan James", MacTutor History of Mathematics Archive, University of St Andrews Ralph Duncan James at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Ralph Duncan James

Start with the simplest possible case. Write down what Ralph Duncan James 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 Ralph Duncan James 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 Ralph Duncan James 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 Ralph Duncan James

In research
Ralph Duncan James 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 Ralph Duncan James 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
Ralph Duncan James is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1909 births, 1979 deaths, 20th-century Canadian mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Ralph Duncan James 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 Ralph Duncan James in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Ralph Duncan James means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Ralph Duncan James out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ralph Duncan James in simple terms?

Ralph Duncan James (8 February 1909 – 19 May 1979) was a Canadian mathematician working on number theory and mathematical analysis. Born in Liverpool, England, James moved with his parents to Vancouver, British Columbia when he was 10 years old.

Why does Ralph Duncan James 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 Ralph Duncan James?

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 Ralph Duncan James.

Tags

  • 1909 births
  • 1979 deaths
  • 20th-century Canadian mathematicians
  • British emigrants to Canada
  • Number theorists
  • Presidents of the Canadian Mathematical Society
  • The American Mathematical Monthly editors

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