astronomy

Ronald Fintushel

Ronald Fintushel 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 Ronald Fintushel rather than just read about it. In short: Ronald Alan Fintushel (born 1945) is an American mathematician, specializing in low-dimensional geometric topology (specifically of 4-manifolds) and the mathematics of gauge theory. Education and career Fintushel studied mathematics at Columbia University with a bachelor's degree in 1967 and at the University of Illinois at Urbana–Champaign with a master's degree in 1969.

Key takeaways

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

Reference excerpt

Ronald Alan Fintushel (born 1945) is an American mathematician, specializing in low-dimensional geometric topology (specifically of 4-manifolds) and the mathematics of gauge theory.

Education and career Fintushel studied mathematics at Columbia University with a bachelor's degree in 1967 and at the University of Illinois at Urbana–Champaign with a master's degree in 1969. In 1975 he received his Ph.D. from the State University of New York at Binghamton with thesis Orbit maps of local S 1 {\displaystyle S^{1}} -actions on manifolds of dimension less than five under the supervision of Louis McAuley. Fintushel was a professor at Tulane University and is a professor at Michigan State University. His research deals with geometric topology, in particular of 4-manifolds (including the computation of Donaldson and Seiberg-Witten invariants) with links to gauge theory, knot theory, and symplectic geometry. He works closely with Ronald J. Stern. In 1998 he was an Invited Speaker, with Ronald J. Stern, with talk Construction of smooth 4-manifolds at the International Congress of Mathematicians in Berlin. In 1997 Fintushel received the Distinguished Faculty Award from Michigan State University. In 2016 a conference was held in his honor at Tulane University. He was elected a Fellow of the American Mathematical Society. Fintushel is a member of the editorial boards of Geometry & Topology and the Michigan Mathematical Journal.

Selected publications with Stern: Constructing lens spaces by surgery on knots, Mathematische Zeitschrift, vol. 175, 1980, pp. 33–51 with Stern: An exotic free involution of S 4 {\displaystyle S^{4}} , Annals of Mathematics, vol. 113, 1981, pp. 357–365 with Stern: Pseudofree orbifolds, Annals of Mathematics, vol. 122, 1985, pp. 335–364 with Stern: Instanton homology of Seifert fibred homology three spheres, Proceedings of the London Mathematical Society, vol. 61, 1990, pp. 109–137 with Stern: Immersed spheres in 4-manifolds and the immersed Thom conjecture, Turkish Journal of Mathematics, vol. 19, 1995, pp. 145–157 with Stern: Donaldson invariants of 4-manifolds with simple type, J. Diff. Geom., vol. 42, 1995, pp. 577–633 with Stern: The blowup formula for Donaldson invariants, Annals of Mathematics, vol. 143, 1996, pp. 529–546 arXiv with Stern: Rational blowdowns of smooth 4-manifolds, Journal of Differential Geometry, vol. 46, 1997, pp. 181–235 arXiv with Stern: Surfaces in 4-manifolds, Math. Res. Letters, vol. 4, 1997, pp. 907–914 arXiv with Stern: Knots, links, and 4-manifolds, Inventiones mathematicae, vol. 134, 1998, pp. 363–400, arXiv with Stern: Constructions of smooth 4-manifolds. Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 443–452 with Stern: Symplectic surfaces in a fixed homology class, J. Diff. Geom., vol. 52, 2000, pp. 203–222 with Stern: Families of simply connected 4-manifolds with the same Seiberg-Witten invariants, Topology, vol. 43, 2004, pp. 1449–1467 with Stern: Invariants for Lagrangian tori, Geom. Topol., vol. 8, 2004, pp., 947-968 arXiv with Stern: Tori in symplectic 4-manifolds, Geometry and Topology Monographs, vol. 7, 2004, Proceedings of the Casson Fest, pp. 311–333 with Stern, B. D. Park: Reverse engineering small 4-manifolds, Algebraic & Geometric Topology, vol. 7, 2007, pp. 2103–2116 arXiv with Stern: Six Lectures on Four 4-manifolds, Low dimensional topology, IAS/Park City Math. Ser. 15, Amer. Math. Soc., Providence, RI, 2009, pp. 265–315

Worked examples

Example 1 — a first encounter with Ronald Fintushel

Start with the simplest possible case. Write down what Ronald Fintushel 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 Ronald Fintushel 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 Ronald Fintushel 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 Ronald Fintushel

In research: Ronald Fintushel 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 Ronald Fintushel 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: Ronald Fintushel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1946 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ronald Fintushel 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 Ronald Fintushel in 20 minutes

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

Frequently asked questions

What is Ronald Fintushel in simple terms?

Ronald Alan Fintushel (born 1945) is an American mathematician, specializing in low-dimensional geometric topology (specifically of 4-manifolds) and the mathematics of gauge theory. Education and career Fintushel studied mathematics at Columbia University with a bachelor's degree in 1967 and at the…

Why does Ronald Fintushel 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 Ronald Fintushel?

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 Ronald Fintushel.