mathematics

John H. Walter

John H. Walter 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 John H. Walter rather than just read about it. In short: John Harris Walter (14 December 1927 – 20 September 2021) was an American mathematician known for proving the Walter theorem in the theory of finite groups. Born in Los Angeles, Walter received from California Institute of Technology his bachelor's degree in 1951.

Key takeaways

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

Reference excerpt

John Harris Walter (14 December 1927 – 20 September 2021) was an American mathematician known for proving the Walter theorem in the theory of finite groups. Born in Los Angeles, Walter received from California Institute of Technology his bachelor's degree in 1951. He received from the University of Michigan his master's degree in 1953 and his Ph.D. in 1954 with thesis Automorphisms of the Projective Unitary Groups under the supervision of Leonard Tornheim. Walter was a visiting professor in 1960/61 and 1965/66 at the University of Chicago, 1967/68 at Harvard University, and 1972/73 at the University of Cambridge, UK. He was a professor emeritus of mathematics at the University of Illinois at Urbana–Champaign, where he became an associate professor in 1961 and a full professor in 1966. In 2012 he was elected a fellow of the American Mathematical Society. He died at the age of 93 in 2021.

Selected publications with Daniel Gorenstein: Gorenstein, Daniel; Walter, John H. (1962). "On finite groups with dihedral Sylow 2-subgroups". Illinois J. Math. 6 (4): 553–593. doi:10.1215/ijm/1255632706. MR 0142619. with Daniel Gorenstein: "The characterization of finite groups with dihedral Sylow 2-subgroups, Parts I, II, III". J. Algebra. 2. 1964. pages 85-151, doi:10.1016/0021-8693(65)90027-X; 217–270, doi:10.1016/0021-8693(65)90019-0; 354–393, doi:10.1016/0021-8693(65)90015-3. Walter, John H. (1967). "Finite groups with abelian Sylow 2-subgroups of order 8". Inventiones Mathematicae. 2 (5): 332–376. Bibcode:1967InMat...2..332W. doi:10.1007/BF01428899. S2CID 121324944. Walter, John H. (1969). "The characterization of finite groups with abelian Sylow 2-subgroups". Annals of Mathematics. 89 (3): 405–514. doi:10.2307/1970648. JSTOR 1970648.

References

Worked examples

Example 1 — a first encounter with John H. Walter

Start with the simplest possible case. Write down what John H. Walter 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 John H. Walter 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 John H. Walter 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 John H. Walter

In research: John H. Walter 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 John H. Walter 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: John H. Walter is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1927 births, 2021 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John H. Walter 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 John H. Walter in 20 minutes

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

Frequently asked questions

What is John H. Walter in simple terms?

Why does John H. Walter 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 John H. Walter?

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 John H. Walter.