mathematics

Nathan Dunfield

Nathan Dunfield 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 Nathan Dunfield rather than just read about it. In short: Nathan Michael Dunfield (born 1975) is an American mathematician, specializing in Topology. Career Dunfield did his undergraduate studies at Oregon State University, obtaining a B.S. in mathematics in 1994.

Key takeaways

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

Reference excerpt

Nathan Michael Dunfield (born 1975) is an American mathematician, specializing in Topology.

Career Dunfield did his undergraduate studies at Oregon State University, obtaining a B.S. in mathematics in 1994. For his graduate studies, he went to the University of Chicago, obtaining his Ph.D. in 1999, with a thesis on Cyclic Surgery, Degrees of Maps of Character Curves, and Volume Rigidity for Hyperbolic Manifolds written under the supervision of Peter Shalen and Melvin Rothenberg. He then was a Benjamin Peirce Assistant Professor at Harvard University (1999–2003) and an associate professor at the California Institute of Technology (2003–2007), after which he moved to the University of Illinois at Urbana–Champaign, where he was promoted to professor in 2018.

Work Dunfield is an expert in group theory, low-dimensional topology, three-manifolds, and computational aspects of these fields. He is also, with Marc Culler, one of the key developers of the program SnapPy, the modern version of Jeffrey Weeks' program SnapPea. Dunfield is an editor for the New York Journal of Mathematics.

Selected publications Dunfield, Nathan; Gukov, Sergei; Rasmussen, Jake; The superpolynomial for knot homologies. Experimental Mathematics 15 (2006), 129–159. math.GT/0505662. Dunfield, Nathan; Calegari, Danny; Laminations and groups of homeomorphisms of the circle. Inventiones Mathematicae 152 (2003) 149–207. math.GT/0203192. Dunfield, Nathan; Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds. Inventiones Mathematicae 136 (1999) 3, 623–657. math.GT/9802022.

References

External links "Publications of Nathan Dunfield". "Dunfield's home page at UIUC".

Worked examples

Example 1 — a first encounter with Nathan Dunfield

Start with the simplest possible case. Write down what Nathan Dunfield 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 Nathan Dunfield 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 Nathan Dunfield 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 Nathan Dunfield

In research: Nathan Dunfield 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 Nathan Dunfield 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: Nathan Dunfield is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1975 births, 21st-century American mathematicians, American topologists, so understanding it makes those chapters shorter.
In everyday life: Look for Nathan Dunfield 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 Nathan Dunfield in 20 minutes

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

Frequently asked questions

What is Nathan Dunfield in simple terms?

Nathan Michael Dunfield (born 1975) is an American mathematician, specializing in Topology. Career Dunfield did his undergraduate studies at Oregon State University, obtaining a B.S. in mathematics in 1994.

Why does Nathan Dunfield 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 Nathan Dunfield?

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 Nathan Dunfield.