mathematics

Peter Landweber

Peter Landweber 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 Peter Landweber rather than just read about it. In short: Peter Steven Landweber (born August 17, 1940, in Washington D. C.) is an American mathematician working in algebraic topology.

Key takeaways

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

Reference excerpt

Peter Steven Landweber (born August 17, 1940, in Washington D. C.) is an American mathematician working in algebraic topology. Landweber studied at the University of Iowa (B.S. 1960) and Harvard University (master's degree 1961), where he graduated in 1965 after studying under Raoul Bott (Künneth formulas for bordism theories). He was then Assistant Professor at the University of Virginia (from 1965) and at Yale University from 1968 to 1970. From 1967 to 1968 he was at the Institute for Advanced Study in Princeton, New Jersey. In 1970, he became Associate Professor at Rutgers University, where he taught from 1974 until his retirement in 2007. From 1974 to 1975 he was a NATO fellow at the University of Cambridge. Since 2007, he is a Professor Emeritus at Rutgers University. Landweber studied complex bordism in algebraic topology (introducing Landweber–Novikov algebra in the 1960s). In the beginning of the 1970s, he proved his exact functor theorem, which allows the construction of a homology theory from a formal group law. In 1986 he introduced elliptic cohomology with Douglas C. Ravenel and Robert E. Stong, which is a generalized cohomology theory with applications to modular forms and elliptic curves. From 1989 to 1992 he was Chairman of the Russian translation Committee of the American Mathematical Society. He is also a fellow of the society. Peter Landweber is the elder son of the engineer Louis Landweber and the father of the molecular biologist Laura Faye Landweber (born 1967) and of the mathematician Gregory David Landweber (born 1971).

Selected publications (Ed.): elliptic curves and modular forms in algebraic topology (= lecture notes in mathematics. ) issue 1326). Springer 1988 (proceedings of a Conference at the Institute for Advanced Study in 1986). Landweber: other elliptic and modular forms. PP. 55–86; Elliptic genera-of introductory overview. pg. 1–10.

References

External links Haynes Miller: A marriage of manifolds and algebra: The mathematical work of Peter Landweber Web page on his 60th birthday

Worked examples

Example 1 — a first encounter with Peter Landweber

Start with the simplest possible case. Write down what Peter Landweber 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 Peter Landweber 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 Peter Landweber 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 Peter Landweber

In research: Peter Landweber 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 Peter Landweber 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: Peter Landweber is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1940 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Landweber 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Peter Landweber” →

Affiliate

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

How to study Peter Landweber in 20 minutes

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

Frequently asked questions

What is Peter Landweber in simple terms?

Peter Steven Landweber (born August 17, 1940, in Washington D. C.) is an American mathematician working in algebraic topology.

Why does Peter Landweber 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 Peter Landweber?

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 Peter Landweber.