mathematics

Theophil Henry Hildebrandt

Theophil Henry Hildebrandt 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 Theophil Henry Hildebrandt rather than just read about it. In short: Theophil Henry Hildebrandt (24 July 1888 – 9 October 1980) was an American mathematician who did research on functional analysis and integration theory. Hildebrandt was born in Dover, Ohio, graduated from high school at age 14 and at age 17 in 1905 received his bachelor's degree from the University of Illinois.

Key takeaways

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

Reference excerpt

Theophil Henry Hildebrandt (24 July 1888 – 9 October 1980) was an American mathematician who did research on functional analysis and integration theory. Hildebrandt was born in Dover, Ohio, graduated from high school at age 14 and at age 17 in 1905 received his bachelor's degree from the University of Illinois. As a graduate student at the University of Chicago he earned his master's degree in 1906 and his PhD in 1910, with thesis A Contribution to the Foundations of Fréchet's Calcul Fonctionnel written under the direction of E. H. Moore. He became an instructor at the University of Michigan in 1909 and then a full professor in 1923, serving as chair of the mathematics department from 1934 until his retirement in 1957. His doctoral students include Ralph S. Phillips, Charles Earl Rickart, and John V. Wehausen. In 1929 Hildebrandt received the Chauvenet Prize for his 1926 expository article The Borel theorem and its generalizations. He served two years, 1945 and 1946, as president of the American Mathematical Society. The U. of Michigan established in 1962 in his honor the T. H. Hildebrandt Research Instructorships, which were changed in 1974 to assistant professorships. Hildebrandt, as an instructor at the U. of Michigan, enrolled in the School of Music and earned a degree in music with a major in organ. He played the organ in his local church. He married Dora E. Ware in 1921, and they had four children. He died, aged 92, in Ann Arbor, Michigan.

Selected publications T. H. Hildebrandt (1923). "On uniform limitedness of sets of functional operations". Bulletin of the American Mathematical Society. 29 (7): 309–315. doi:10.1090/s0002-9904-1923-03730-0. MR 1560736. T. H. Hildebrandt (1928). "Über vollstetige linear Transformationen". Acta Mathematica. 51 (1): 311–318. doi:10.1007/bf02545664. MR 1555265.

References

External links Theophil Henry Hildebrandt at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Theophil Henry Hildebrandt

Start with the simplest possible case. Write down what Theophil Henry Hildebrandt 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 Theophil Henry Hildebrandt 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 Theophil Henry Hildebrandt 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 Theophil Henry Hildebrandt

In research: Theophil Henry Hildebrandt 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 Theophil Henry Hildebrandt 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: Theophil Henry Hildebrandt is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1888 births, 1980 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Theophil Henry Hildebrandt 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 Theophil Henry Hildebrandt in 20 minutes

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

Frequently asked questions

What is Theophil Henry Hildebrandt in simple terms?

Why does Theophil Henry Hildebrandt 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 Theophil Henry Hildebrandt?

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 Theophil Henry Hildebrandt.