mathematics

Leonid Vaserstein

Leonid Vaserstein 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 Leonid Vaserstein rather than just read about it. In short: Leonid Nisonovich Vaserstein (Russian: Леонид Нисонович Васерштейн) is a Russian-American mathematician, currently Professor of Mathematics at Penn State University. His research is focused on algebra and dynamical systems.

Key takeaways

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

Reference excerpt

Leonid Nisonovich Vaserstein (Russian: Леонид Нисонович Васерштейн) is a Russian-American mathematician, currently Professor of Mathematics at Penn State University. His research is focused on algebra and dynamical systems. He is well known for providing a simple proof of the Quillen–Suslin theorem, a result in commutative algebra, first conjectured by Jean-Pierre Serre in 1955, and then proved by Daniel Quillen and Andrei Suslin in 1976. Leonid Vaserstein got his Master's degree and doctorate in Moscow State University, where he was until 1978. He then moved to Europe and the United States. Alternate forms of the last name: Vaseršteĭn, Vasershtein, Wasserstein. The Wasserstein metric was named after him by R.L. Dobrushin in 1970.

Biography Leonid Vaserstein grew up in the Soviet Union. In secondary school he won the second prize in the All-Russian High School Mathematical Olympiad. Vaserstein got his undergraduate, masters (1966), and doctoral degrees (1969) in mathematics from Moscow State University, where he worked as a lecturer concurrently with his doctoral research. After his doctoral graduation he worked for the Moscow State University-associated "Informelectro" Institute, a Federal State Unitary Enterprise focused on ways to develop industries in Russia with emphases on electrical engineering, energy efficiency, and environmental technologies like greenhouse gas mitigation. He started as a senior researcher for Informelectro and continued working there until 1978, eventually becoming head of his department. In 1978 and 1979 he made his way to the United States of America by way of Europe, taking a series of visiting professor positions at Bielefeld University, Institut des Hautes Études Scientifiques, University of Chicago, and Cornell University. In 1979, Vaserstein took a full-time position as a professor in the Department of Mathematics at Penn State University. Vaserstein's research interests extend across the areas of topology, algebra, and number theory, and the applications of these areas, including classical groups over rings, algebraic K-theory, systems with local interactions, and optimization and planning. Additionally, Vaserstein maintains the Penn State University Math Department's website on Algebra and Number Theory.

Selected publications Vaserstein, Leonid N. (1969). "Markov processes over denumerable products of spaces describing large systems of automata". Problemy Peredači Informacii. 5 (3): 64–72. Vaserstein, Leonid N. (1986). "On normal subgroups of Chevalley groups over commutative rings". Tohoku Math. J. 38 (2): 219–230. doi:10.2748/tmj/1178228489. Vaserstein, Leonid N. (1986). "Vector bundles and projective modules". Trans. Amer. Math. Soc. 294 (2): 749–755. doi:10.1090/s0002-9947-1986-0825734-3. MR 0825734. Vaserstein, L. N. (1986). "Normal subgroups of the general linear groups over von Neumann regular rings". Proc. Amer. Math. Soc. 96 (2): 209–214. doi:10.1090/s0002-9939-1986-0818445-7. MR 0818445. Vaserstein, L. N. (1986). "An answer to a question of M. Newman on matrix completion". Proc. Amer. Math. Soc. 97 (2): 189–196. doi:10.1090/s0002-9939-1986-0835863-1. MR 0835863. Vaserstein, L. N. (1988). "Reduction of a matrix depending on parameters to a diagonal form by addition operations". Proc. Amer. Math. Soc. 103 (3): 741–746. doi:10.1090/s0002-9939-1988-0947649-x. MR 0947649. Vaserstein, L. N. (1988). "Normal subgroups of orthogonal groups over commutative rings". Amer. J. Math. 110 (5): 955–973. doi:10.2307/2374699. JSTOR 2374699. Vaserstein, L. N. (1991). "Sums of cubes in polynomial rings". Math. Comp. 56 (193): 349–357. Bibcode:1991MaCom..56..349V. doi:10.1090/s0025-5718-1991-1052104-3. MR 1052104.

Worked examples

Example 1 — a first encounter with Leonid Vaserstein

Start with the simplest possible case. Write down what Leonid Vaserstein 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 Leonid Vaserstein 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 Leonid Vaserstein 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 Leonid Vaserstein

In research: Leonid Vaserstein 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 Leonid Vaserstein 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: Leonid Vaserstein is common in secondary-school and first-year university syllabi. It links to neighbouring topics Living people, Moscow State University alumni, Pennsylvania State University faculty, so understanding it makes those chapters shorter.
In everyday life: Look for Leonid Vaserstein 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 Leonid Vaserstein in 20 minutes

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

Frequently asked questions

What is Leonid Vaserstein in simple terms?

Why does Leonid Vaserstein 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 Leonid Vaserstein?

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 Leonid Vaserstein.