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Karl H. Hofmann

Karl H. Hofmann 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 Karl H. Hofmann rather than just read about it. In short: Karl Heinrich Hofmann (born 3 October 1932), known professionally as Karl H. Hofmann is a German mathematician and illustrator who is professor emeritus at the Technical University of Darmstadt (TU Darmstadt).

Karl H. Hofmann — main illustration
Karl H. Hofmann — illustration

Key takeaways

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

Reference excerpt

Karl Heinrich Hofmann (born 3 October 1932), known professionally as Karl H. Hofmann is a German mathematician and illustrator who is professor emeritus at the Technical University of Darmstadt (TU Darmstadt). His research is primarily focused on topological algebra and functional analysis.

Education Hofmann began his first mathematics degree at the University of Hamburg but transferred to the University of Tübingen and completed it there. He remained in Tübingen for his master's degree and Ph.D. which was completed in 1958 under supervisor Hellmuth Kneser.

Career Most of Hofmann's work is in lie theory and topological analysis. His book with Sidney Morris, The Structure of Compact Groups, has been printed in four editions and is a standard reference for the subject. The University of Tübingen hired Hofmann as an assistant professor following the completion of his Ph.D. in 1958. He remained at Tübingen until 1963 where he became an associate professor at Tulane University. He became a full professor two years later an in 1979 the university appointed him as W. R. Irby Professor of Mathematics. Hofmann supervised 37 doctoral students throughout his fifty-year career. In 2013, Hofmann was inducted as a fellow of the American Mathematical Society. Alongside his academic career, Hofmann worked as an illustrator. He illustrated multiple books, including Proofs from THE BOOK, a Leroy P. Steele Prize winner. He has also created posters for TU Darmstadt's colloquiums since 1983.

Selected publications Hofmann, Karl H. (2020). The Structure of Compact Groups: A Primer for the Student - a Handbook for the Expert (4th ed.). Berlin/Boston: Walter de Gruyter GmbH. doi:10.1515/9783110695991. ISBN 9783110695991. Gierz, Gerhard; Hofmann, Karl Heinrich; Keimel, Klaus; Lawson, Jimmie D.; Mislove, Michael W.; Scott, Dana S. (1980). A Compendium of Continuous Lattices. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-67678-9. ISBN 978-3-642-67680-2. Aigner, Martin; Ziegler, Günter M. (2018). Proofs from THE BOOK (6 ed.). Springer. pp. i–viii. doi:10.1007/978-3-662-57265-8. ISBN 978-3-662-57265-8. Illustrated by Karl H. Hofmann.{{cite book}}: CS1 maint: postscript (link)

References

External links Karl H. Hofmann's homepage Karl H. Hofmann at the Mathematics Genealogy Project

Illustrations

Karl H. Hofmann illustration

Worked examples

Example 1 — a first encounter with Karl H. Hofmann

Start with the simplest possible case. Write down what Karl H. Hofmann 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 Karl H. Hofmann 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 Karl H. Hofmann 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 Karl H. Hofmann

In research
Karl H. Hofmann 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 Karl H. Hofmann 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
Karl H. Hofmann is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1932 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Karl H. Hofmann 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 Karl H. Hofmann in 20 minutes

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

Frequently asked questions

What is Karl H. Hofmann in simple terms?

Karl Heinrich Hofmann (born 3 October 1932), known professionally as Karl H. Hofmann is a German mathematician and illustrator who is professor emeritus at the Technical University of Darmstadt (TU Darmstadt).

Why does Karl H. Hofmann 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 Karl H. Hofmann?

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 Karl H. Hofmann.

Tags

  • 1932 births
  • 20th-century German mathematicians
  • 21st-century German mathematicians
  • Fellows of the American Mathematical Society
  • Living people
  • People from Heilbronn
  • Tulane University faculty
  • University of Hamburg alumni
  • University of Tübingen alumni

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