mathematics

Jerry Kazdan

Jerry Kazdan 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 Jerry Kazdan rather than just read about it. In short: Jerry Lawrence Kazdan (born 31 October 1937 in Detroit, Michigan) is an American mathematician noted for his work in differential geometry and the study of partial differential equations. His contributions include the Berger–Kazdan comparison theorem, which was a key step in the proof of the Blaschke conjecture and the classification of Wiedersehen manifolds.

Key takeaways

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

Reference excerpt

Jerry Lawrence Kazdan (born 31 October 1937 in Detroit, Michigan) is an American mathematician noted for his work in differential geometry and the study of partial differential equations. His contributions include the Berger–Kazdan comparison theorem, which was a key step in the proof of the Blaschke conjecture and the classification of Wiedersehen manifolds. His best-known work, done in collaboration with Frank Warner, dealt with the problem of prescribing the scalar curvature of a Riemannian metric.

Biography Kazdan received his bachelor's degree in 1959 from Rensselaer Polytechnic Institute and his master's degree in 1961 from NYU. He obtained his PhD in 1963 from the Courant Institute of Mathematical Sciences at New York University; his thesis was entitled A Boundary Value Problem Arising in the Theory of Univalent Functions and was supervised by Paul Garabedian. He then took a position as a Benjamin Peirce Instructor at Harvard University. Since 1966, he has been a Professor of Mathematics at the University of Pennsylvania. Dennis DeTurck was a student of his.

Honours In 1999 he received the Lester Randolph Ford Award for his expository article Solving equations, an elegant legacy. In 2012 he became a fellow of the American Mathematical Society.

Major publications DeTurck, Dennis M.; Kazdan, Jerry L. Some regularity theorems in Riemannian geometry. Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 3, 249–260. Kazdan, Jerry L.; Warner, F.W. Curvature functions for compact 2-manifolds. Ann. of Math. (2) 99 (1974), 14–47. Kazdan, Jerry L.; Warner, F.W. Remarks on some quasilinear elliptic equations. Comm. Pure Appl. Math. 28 (1975), no. 5, 567–597. Kazdan, Jerry L.; Warner, F.W. Scalar curvature and conformal deformation of Riemannian structure. Journal of Differential Geometry 10 (1975), 113–134. Kazdan, Jerry L.; Warner, F.W. Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures. Ann. of Math. (2) 101 (1975), 317–331.

Books Lectures on Complex Numbers and Infinite Series (1966) Calculus Two: Linear and Nonlinear Functions (1971, with Francis J. Flanigan) Intermediate Calculus And Linear Algebra (1975) Prescribing the Curvature of a Riemannian Manifold (1985)

See also Prescribed scalar curvature problem

References

External links Jerry Kazdan's homepage

Brief biography on the occasion of receiving the Lester R. Ford award

Illustrations

Worked examples

Example 1 — a first encounter with Jerry Kazdan

Start with the simplest possible case. Write down what Jerry Kazdan 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 Jerry Kazdan 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 Jerry Kazdan 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 Jerry Kazdan

In research: Jerry Kazdan 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 Jerry Kazdan 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: Jerry Kazdan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1937 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jerry Kazdan 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 Jerry Kazdan in 20 minutes

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

Frequently asked questions

What is Jerry Kazdan in simple terms?

Why does Jerry Kazdan 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 Jerry Kazdan?

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 Jerry Kazdan.