astronomy

Peter J. Olver

Peter J. Olver is a astronomy 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 J. Olver rather than just read about it. In short: Peter John Olver (11 January 1952, Twickenham) is a British-American mathematician working in differential geometry. Education and career After moving to the USA in 1961, Olver obtained a bachelor's degree in Applied Mathematics at Brown University in 1973 and a PhD in Mathematics at Harvard University in 1976.

Key takeaways

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

Reference excerpt

Peter John Olver (11 January 1952, Twickenham) is a British-American mathematician working in differential geometry.

Education and career After moving to the USA in 1961, Olver obtained a bachelor's degree in Applied Mathematics at Brown University in 1973 and a PhD in Mathematics at Harvard University in 1976. His PhD thesis was entitled "Symmetry Groups of Partial Differential Equations" and was written under the supervision of Garrett Birkhoff. He worked as a L.E. Dickson Instructor in Mathematics at University of Chicago (1976-1978) and as a research fellow at University of Oxford (1978-1980). He then moved to University of Minnesota as assistant professor, and he became full professor in the same university in 1985. Between 1992 and 1993 he was professor at University of Maryland. Olver was member of the board of directors of Foundations of Computational Mathematics from 2002 to 2014. He was elected fellow of the American Mathematical Society in 2013 and of the Society for Industrial and Applied Mathematics in 2014, for "developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing." Olver is also member of International Society for the Interaction of Mechanics and Mathematics and an elected fellow of the Institute of Physics.

Research Olver's primary research fields are differential geometry and mathematical physics. His main interests involve the application of Lie groups and symmetries to the geometry of differential equations, as well as well the theories of moving frames and Cartan's equivalence method, differential invariants and pseudogroups. He has also contributed to various topics in applied mathematics, including image processing and computer vision, wave and fluid mechanics,, quasi-exact solvability and elasticity. He has written five books and over 150 research papers in peer-reviewed journals. In 2003, Olver was one of the top 234 most cited mathematicians in the world. He has supervised 23 PhD students.

Personal life Olver married Iranian mathematician Chehrzad Shakiban in 1976.

Books Olver, P. J. (1986), Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, vol. 107, Springer, doi:10.1007/978-1-4684-0274-2, ISBN 0387940073 Olver, Peter J.; Sattinger, David H., eds. (1990). Solitons in Physics, Mathematics, and Nonlinear Optics. New York, NY: Springer New York. ISBN 978-1-4613-9033-6. OCLC 852788413. Olver, P. J. (1995), Equivalence, Invariants and Symmetry, Cambridge University Press, doi:10.1017/CBO9780511609565, ISBN 0521101042 Olver, P. J. (1999), Classical Invariant Theory, Cambridge University Press, doi:10.1017/CBO9780511623660, ISBN 0521558212 Olver, Peter J.; Tannenbaum, Allen, eds. (2003). Mathematical methods in computer vision. New York: Springer. ISBN 0-387-00497-1. OCLC 51553365. Olver, P. J. (2014), Introduction to Partial Differential Equations, Undergraduate Texts in Mathematics, Springer, doi:10.1007/978-3-319-02099-0, ISBN 978-3319020983, S2CID 220617008 Olver, P. J.; Shakiban, C. (2018), Applied Linear Algebra, Springer, doi:10.1007/978-3-319-91041-3, ISBN 978-0131473829

References

Worked examples

Example 1 — a first encounter with Peter J. Olver

Start with the simplest possible case. Write down what Peter J. Olver claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 J. Olver 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 J. Olver 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 J. Olver

In research: Peter J. Olver appears in astronomy 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 J. Olver 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 J. Olver is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Peter J. Olver 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 Peter J. Olver in 20 minutes

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

Frequently asked questions

What is Peter J. Olver in simple terms?

Peter John Olver (11 January 1952, Twickenham) is a British-American mathematician working in differential geometry. Education and career After moving to the USA in 1961, Olver obtained a bachelor's degree in Applied Mathematics at Brown University in 1973 and a PhD in Mathematics at Harvard Univer…

Why does Peter J. Olver matter?

Because it connects several astronomy 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 J. Olver?

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 J. Olver.