mathematics

Tevian Dray

Tevian Dray 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 Tevian Dray rather than just read about it. In short: Tevian Dray (born March 17, 1956) is an American mathematician who has worked in general relativity, mathematical physics, geometry, and both science and mathematics education. He was elected a Fellow of the American Physical Society in 2010.

Key takeaways

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

Reference excerpt

Tevian Dray (born March 17, 1956) is an American mathematician who has worked in general relativity, mathematical physics, geometry, and both science and mathematics education. He was elected a Fellow of the American Physical Society in 2010. He has primarily worked in the area of classical general relativity. His research results include confirmation of the existence of solutions of Einstein's equation containing gravitational radiation, the use of computer algebra to classify exact solutions of Einstein's equation, an analysis of a class of gravitational shock waves (including one of the few known exact 2-body solutions in general relativity), and the study of signature change, a possible model for the Big Bang. More recently, his work has focused on applications of the octonions to the theory of fundamental particles. He was a graduate student under Rainer K. Sachs at Berkeley, where he received his Ph.D. in 1981, although much of his dissertation research was done in collaboration with Abhay Ashtekar. The context of his dissertation, titled The Asymptotic Structure of a Family of Einstein-Maxwell Solutions focused on families of spacetimes which describe accelerating black holes, and which contain gravitational radiation. This demonstrated the existence of exact radiating solutions to the Einstein field equations. He is currently a professor of mathematics at Oregon State University. In addition to his ongoing work in mathematical physics, he has made significant contributions in science education, where he directs the Vector Calculus Bridge Project, an attempt to teach vector calculus the way it is used by scientists and engineers, and is part of the development team of the Paradigms Project, a complete restructuring of the undergraduate physics major around several core "paradigms". He has written a book on special relativity and a sequel on general relativity using differential forms, and is coauthor of The Geometry of the Octonions, released in 2015. In 2017 he received a Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics.

Bibliography Abhay Ashtekar & Tevian Dray (1981). "On the Existence of Solutions to Einstein's Equation with Non-Zero Bondi News". Commun. Math. Phys. 79 (4): 581–589. Bibcode:1981CMaPh..79..581A. doi:10.1007/BF01209313. S2CID 121427482. Tevian Dray & Gerard 't Hooft (1985). "The Effect of Spherical Shells of Matter on the Schwarzschild Black Hole". Commun. Math. Phys. 99 (4): 613–625. Bibcode:1985CMaPh..99..613D. doi:10.1007/BF01215912. hdl:1874/4753. S2CID 122717417. Paul C. W. Davies; Tevian Dray & Corinne A. Manogue (1996). "Detecting the Rotating Quantum Vacuum". Phys. Rev. D. 53 (8): 4382–4387. arXiv:gr-qc/9601034. Bibcode:1996PhRvD..53.4382D. doi:10.1103/PhysRevD.53.4382. PMID 10020436. S2CID 2114187. Tevian Dray; George Ellis; Charles Hellaby & Corinne A. Manogue (1997). "Gravity and Signature Change". Gen. Rel. Grav. 29 (5): 591–597. arXiv:gr-qc/9610063. Bibcode:1997GReGr..29..591D. doi:10.1023/A:1018895302693. S2CID 7617543. (2012) Tevian Dray, The Geometry of Special Relativity (A K Peters/CRC Press) ISBN 978-1466510470 (2014) Tevian Dray, Differential Forms and The Geometry of General Relativity (A K Peters/CRC Press) ISBN 978-1466510005 (2015) Tevian Dray and Corinne A. Manogue, The Geometry of the Octonions (World Scientific) ISBN 978-9814401814

References

External links Tevian Dray's home page Vector Calculus Bridge Project Paradigms Project

Worked examples

Example 1 — a first encounter with Tevian Dray

Start with the simplest possible case. Write down what Tevian Dray 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 Tevian Dray 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 Tevian Dray 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 Tevian Dray

In research: Tevian Dray 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 Tevian Dray 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: Tevian Dray is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1956 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Tevian Dray 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 Tevian Dray in 20 minutes

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

Frequently asked questions

What is Tevian Dray in simple terms?

Why does Tevian Dray 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 Tevian Dray?

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 Tevian Dray.