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James Harkness (mathematician)

James Harkness (mathematician) 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 James Harkness (mathematician) rather than just read about it. In short: James Harkness (1864–1923) was a Canadian mathematician, born in Derby, England, and educated at Trinity College, Cambridge with a B.A. in 1885 and an M.A. in 1889. Coming early to the United States, he was connected with Bryn Mawr College from 1888 to 1903, for the last seven years as professor of mathematics.

Key takeaways

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

Reference excerpt

James Harkness (1864–1923) was a Canadian mathematician, born in Derby, England, and educated at Trinity College, Cambridge with a B.A. in 1885 and an M.A. in 1889. Coming early to the United States, he was connected with Bryn Mawr College from 1888 to 1903, for the last seven years as professor of mathematics.

The study of the Theory of Functions received a new impetus in America through the arrival of James Harkness (1864–1923), a man who from his boyhood had shown unusual ability in the field of mathematics. At the age of eight he mastered the first book of Euclid's Elements without any help. He studied under Dr. E. J. Routh at Trinity College, Cambridge, graduating as eighth wrangler in 1885. Harkness complemented Scott with a course on "Abelian Integrals and Functions" that also drew on the latest literature in German — the work of Alfred Clebsch and Paul Gordan, Bernhard Riemann, Hermann Amandus Schwarz and others — and "aimed to prepare the students for the recent Memoirs of Felix Klein in the Mathematische Annalen". In 1903, he was appointed Peter Redpath professor of pure mathematics at McGill University, Montreal, Quebec. Harkness was for a time a vice president of the American Mathematical Society and associate editor of its Transactions, was elected a member of the London Mathematical Society and in 1908 became a fellow of the Royal Society of Canada. He published, with Professor Frank Morley, two treatises on the Theory of Functions and collaborated on the article "Elliptic Functions", in the German Encyclopædia of Mathematics (1914–15).

References

External links Frank Morley and James Harkness A treatise on the theory of functions (New York: Macmillan, 1893) Frank Morley and James Harkness Introduction To The Theory of Analytic Functions (G.E.Stechert And Company, 1898)

Worked examples

Example 1 — a first encounter with James Harkness (mathematician)

Start with the simplest possible case. Write down what James Harkness (mathematician) 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 James Harkness (mathematician) 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 James Harkness (mathematician) 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 James Harkness (mathematician)

In research
James Harkness (mathematician) 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 James Harkness (mathematician) 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
James Harkness (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1864 births, 1923 deaths, Academic staff of McGill University, so understanding it makes those chapters shorter.
In everyday life
Look for James Harkness (mathematician) 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 James Harkness (mathematician) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what James Harkness (mathematician) 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 James Harkness (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is James Harkness (mathematician) in simple terms?

James Harkness (1864–1923) was a Canadian mathematician, born in Derby, England, and educated at Trinity College, Cambridge with a B.A. in 1885 and an M.A. in 1889. Coming early to the United States, he was connected with Bryn Mawr College from 1888 to 1903, for the last seven years as professor of…

Why does James Harkness (mathematician) 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 James Harkness (mathematician)?

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 James Harkness (mathematician).

Tags

  • 1864 births
  • 1923 deaths
  • Academic staff of McGill University
  • Alumni of Trinity College, Cambridge
  • British emigrants to the United States
  • Bryn Mawr College faculty
  • Canadian mathematicians
  • Canadian science writers
  • Fellows of the Royal Society of Canada
  • Immigrants to Canada
  • People from Derby

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