mathematics

Phyllis Nicolson

Phyllis Nicolson 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 Phyllis Nicolson rather than just read about it. In short: Phyllis Nicolson (21 September 1917 – 6 October 1968) was a British mathematician and physicist best known for her work on the Crank–Nicolson method together with John Crank. Early life and education Nicolson was born Phyllis Lockett in Macclesfield and went to Stockport High School for Girls.

Key takeaways

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

Reference excerpt

Phyllis Nicolson (21 September 1917 – 6 October 1968) was a British mathematician and physicist best known for her work on the Crank–Nicolson method together with John Crank.

Early life and education Nicolson was born Phyllis Lockett in Macclesfield and went to Stockport High School for Girls. She graduated from Manchester University with a B.Sc. in 1938, M.Sc. in 1939 and a Ph.D. on Three Problems in Theoretical Physics in 1946. Her Ph.D. thesis began with cosmic ray research conducted under Lajos Jánossy during 1939 and 1940.

Hartree Differential Analyser work Nicolson's Ph.D. was expected to be submitted in 1941 but was interrupted by wartime work with Douglas Hartree's research group at Manchester University from 1940 to 1945. During this time, Nicolson became a proficient numerical analyst and an expert user of Hartree's differential analyser. Nicolson, along with other members of the research group worked on defence-related problems for the Air Defence Research and Development Establishment (later the Radar Research and Development Establishment), both part of the Ministry of Supply. Nicolson's two significant bodies of wartime research, "Transient behaviour in the single anode magnetron" and "heat conduction", formed the basis of parts II and III of her 1946 PhD thesis Three Problems in Theoretical Physics. Nicolson's research on heat conduction related to solutions of the heat equation, and with her colleague John Crank she investigated the numerical stability of several solution techniques. The algorithm now known as the Crank–Nicolson method emerged from this work and was published in 1947.

Postwar life and work Nicolson was a research student in Cambridge from 1945 and completed her Ph.D. thesis completed at the Victoria University of Manchester (now Manchester University) in 1946. She was a Tucker-Price Research Fellow of Girton College, Cambridge from 1946 to 1949, working at the Cavendish Laboratory. Nicolson moved to Leeds around January 1950 with her husband Malcolm Nicolson, also a physicist, as he had been appointed to a lectureship in Physics at Leeds University. Phyllis Nicolson had married Malcolm in 1942 and they had two sons, Donald Macleod Nicolson (born 20 September 1947 in Cambridge) and Roderick Ian Nicolson (born 5 February 1950 in Leeds). Malcolm Nicolson, aged 33, died in a train accident in December 1951, and Phyllis was appointed to take over his lectureship. In 1955, Nicolson married physicist Malcolm McCaig, who had a son Ian McCaig (born February 1946) from a previous marriage. In May 1957, Nicolson and McCaig had a son together, Andrew Malcolm McCaig. All three of Nicolson's sons ended up getting PhDs – in mathematics, psychology, and geology. Nicolson died from breast cancer in 1968 in Sheffield.

Publications D. R. Hartree, P. Nicolson, N. Eyres. J. Howlett, and T. Pearcey. “Evaluation of the Solution of the Wave Equation for a Stratified Medium”, Air Defense Research & Development Establishment, Memorandum 47, May 1944. D. R. Hartree, P. Nicolson, N. Eyres. J. Howlett, and T. Pearcey. “Evaluation of the Solution of the Wave Equation for a Stratified Medium:Normalisation”, Radar Research and Development Establishment, RRDE Report No. 279, March 1945. Three Problems in Theoretical Physics. PhD Thesis, University of Manchester, 1946. The Sun's Magnetic Field and the Diurnal and Seasonal Variations in Cosmic Ray Intensity Janossy, L.; Lockett, P., Proc. of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1941, Vol. 178(972), pp. 52–60. Meson Formation and the Geomagnetic Effects. Janossy, L.; Nicolson, P., Proc. of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1947, Vol. 192(1028), pp. 99–114. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Crank, J.; Nicolson, P., Mathematical Proc. of the Cambridge Phil. Society, 1947, Vol. 43(1), pp. 50–67. A Theoretical Study of the Influence of Diffusion and Chemical Reaction Velocity on the Rate of Exchange of Carbon Monoxide and Oxygen between the Red Blood Corpuscle and the Surrounding Fluid, P. Nicolson and F. J. W. Roughton. Proc. of the Royal Society of London. Series B, Biological Sciences, Vol. 138, No. 891, 1951, pp. 241–264.

References

Worked examples

Example 1 — a first encounter with Phyllis Nicolson

Start with the simplest possible case. Write down what Phyllis Nicolson 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 Phyllis Nicolson 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 Phyllis Nicolson 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 Phyllis Nicolson

In research: Phyllis Nicolson 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 Phyllis Nicolson 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: Phyllis Nicolson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1917 births, 1968 deaths, 20th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Phyllis Nicolson 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 Phyllis Nicolson in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Phyllis Nicolson 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.
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Frequently asked questions

What is Phyllis Nicolson in simple terms?

Phyllis Nicolson (21 September 1917 – 6 October 1968) was a British mathematician and physicist best known for her work on the Crank–Nicolson method together with John Crank. Early life and education Nicolson was born Phyllis Lockett in Macclesfield and went to Stockport High School for Girls.

Why does Phyllis Nicolson 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 Phyllis Nicolson?

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 Phyllis Nicolson.