mathematics

Karl Rubin

Karl Rubin 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 Karl Rubin rather than just read about it. In short: Karl Cooper Rubin (born January 27, 1956) is an American mathematician at University of California, Irvine as Thorp Professor of Mathematics. Between 1997 and 2006, he was a professor at Stanford, and before that worked at Ohio State University between 1987 and 1999.

Key takeaways

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

Reference excerpt

Karl Cooper Rubin (born January 27, 1956) is an American mathematician at University of California, Irvine as Thorp Professor of Mathematics. Between 1997 and 2006, he was a professor at Stanford, and before that worked at Ohio State University between 1987 and 1999. His research interest is in elliptic curves. He was the first mathematician (1986) to show that some elliptic curves over the rationals have finite Tate–Shafarevich groups. It is widely believed that these groups are always finite.

Education and career Rubin graduated from Princeton University in 1976, and obtained his Ph.D. from Harvard in 1981. His thesis advisor was Andrew Wiles. He was a Putnam Fellow in 1974, and a Sloan Research Fellow in 1985. In 1988, Rubin received a National Science Foundation Presidential Young Investigator award, and in 1992 won the American Mathematical Society Cole Prize in number theory. In 2012 he became a fellow of the American Mathematical Society. Rubin's parents were mathematician Robert Joshua Rubin and astronomer Vera Rubin. Rubin is brother to astronomer and physicist Judith Young.

See also CEILIDH Torus-based cryptography Euler system Stark conjectures

References

External links Karl Cooper Rubin at the Mathematics Genealogy Project Karl Rubin's Home page

Illustrations

Worked examples

Example 1 — a first encounter with Karl Rubin

Start with the simplest possible case. Write down what Karl Rubin 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 Karl Rubin 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 Karl Rubin 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 Karl Rubin

In research: Karl Rubin 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 Karl Rubin 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: Karl Rubin 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 Karl Rubin 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 Karl Rubin in 20 minutes

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

Frequently asked questions

What is Karl Rubin in simple terms?

Why does Karl Rubin 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 Karl Rubin?

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 Karl Rubin.