mathematics

Wolf Barth

Wolf Barth 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 Wolf Barth rather than just read about it. In short: Wolf Paul Barth (20 October 1942, in Wernigerode – 30 December 2016, in Nuremberg) was a German mathematician who discovered Barth surfaces and whose work on vector bundles has been important for the ADHM construction. Until 2011, Barth was working in the Department of Mathematics at the University of Erlangen-Nuremberg in Germany.

Key takeaways

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

Reference excerpt

Wolf Paul Barth (20 October 1942, in Wernigerode – 30 December 2016, in Nuremberg) was a German mathematician who discovered Barth surfaces and whose work on vector bundles has been important for the ADHM construction. Until 2011, Barth was working in the Department of Mathematics at the University of Erlangen-Nuremberg in Germany. Barth received a PhD degree in 1967 from the University of Göttingen. His dissertation, written under the direction of Reinhold Remmert and Hans Grauert, was entitled Einige Eigenschaften analytischer Mengen in kompakten komplexen Mannigfaltigkeiten (Some properties of analytic sets in compact, complex manifolds).

Publications Barth, Wolf (1977). "Moduli of vector bundles on the projective plane". Inventiones Mathematicae. 42 (1): 63–91. Bibcode:1977InMat..42...63B. doi:10.1007/bf01389784. MR 0460330. S2CID 121360092. Barth, Wolf (1977). "Some properties of stable rank-2 vector bundles on Pn". Mathematische Annalen. 226 (2): 125–150. doi:10.1007/bf01360864. MR 0429896. S2CID 121286408. Barth, Wolf (1996). "Two projective surfaces with many nodes, admitting the symmetries of the icosahedron". Journal of Algebraic Geometry. 5 (1): 173–186. MR 1358040.

See also Barth surfaces Barth–Nieto quintic

References

External links "Author profile". At zbMATH.

Illustrations

Wolf Barth: Wolf Barth at Dortmund in 1980(photo from MFO) — Wolf Barth at Dortmund in 1980(photo from MFO)

Worked examples

Example 1 — a first encounter with Wolf Barth

Start with the simplest possible case. Write down what Wolf Barth 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 Wolf Barth 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 Wolf Barth 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 Wolf Barth

In research: Wolf Barth 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 Wolf Barth 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: Wolf Barth is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, 2016 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Wolf Barth 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Wolf Barth in 20 minutes

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

Frequently asked questions

What is Wolf Barth in simple terms?

Why does Wolf Barth 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 Wolf Barth?

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 Wolf Barth.