mathematics

Umesh Vazirani

Umesh Vazirani 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 Umesh Vazirani rather than just read about it. In short: Umesh Virkumar Vazirani is an Indian–American academic who is the Roger A. Strauch Professor of Electrical Engineering and Computer Science at the University of California, Berkeley, and the director of the Berkeley Quantum Computation Center.

Key takeaways

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

Reference excerpt

Umesh Virkumar Vazirani is an Indian–American academic who is the Roger A. Strauch Professor of Electrical Engineering and Computer Science at the University of California, Berkeley, and the director of the Berkeley Quantum Computation Center. His research interests lie primarily in quantum computing. He is also a co-author of a textbook on algorithms.

Biography Vazirani received a BS from MIT in 1981 and received his Ph.D. in 1986 from UC Berkeley under the supervision of Manuel Blum. He is the brother of University of California, Irvine professor Vijay Vazirani.

Research Vazirani is one of the founders of the field of quantum computing. His 1993 paper with his student Ethan Bernstein on quantum complexity theory defined a model of quantum Turing machines which was amenable to complexity based analysis. This paper also gave an algorithm for the quantum Fourier transform, which was then used by Peter Shor within a year in his celebrated quantum algorithm for factoring integers. With Charles Bennett, Ethan Bernstein, and Gilles Brassard, he showed that quantum computers cannot solve black-box search problems faster than O ( N ) {\displaystyle O({\sqrt {N}})} in the number of elements to be searched. This result shows that the Grover search algorithm is optimal. It also shows that quantum computers cannot solve NP-complete problems in polynomial time using only the certifier.

Awards and honors In 2005, both Vazirani and his brother Vijay Vazirani were inducted as Fellows of the Association for Computing Machinery, Umesh for "contributions to theoretical computer science and quantum computation" and Vijay for his work on approximation algorithms. Vazirani was awarded the Fulkerson Prize for 2012 for his work on improving the approximation ratio for graph separators and related problems (jointly with Satish Rao and Sanjeev Arora). In 2018, he was elected to the National Academy of Sciences.

Selected publications Mulmuley, Ketan; Vazirani, Umesh V.; Vazirani, Vijay V. (1987), "Matching is as easy as matrix inversion", Combinatorica, 7 (1): 105–113, CiteSeerX 10.1.1.70.2247, doi:10.1007/BF02579206, MR 0905157, S2CID 47370049 {{citation}}: Cite uses deprecated parameter |citeseerx= (help). A preliminary version of this paper was also published in STOC '87. Bernstein, Ethan; Vazirani, Umesh (1993), "Quantum complexity theory", Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC '93), pp. 11–20, CiteSeerX 10.1.1.655.1186, doi:10.1145/167088.167097, ISBN 978-0897915915, S2CID 676378 {{citation}}: Cite uses deprecated parameter |citeseerx= (help). Kearns, Michael J.; Vazirani, Umesh V. (1994), An Introduction to Computational Learning Theory, MIT Press, ISBN 9780262111935. Bennett, Charles H.; Bernstein, Ethan; Brassard, Gilles; Vazirani, Umesh (1997), "Strengths and weaknesses of quantum computing", SIAM Journal on Computing, 26 (5): 1510–1523, arXiv:quant-ph/9701001, Bibcode:1997quant.ph..1001B, doi:10.1137/S0097539796300933, MR 1471991, S2CID 13403194.

References

External links Umesh Vazirani at UC Berkeley

Worked examples

Example 1 — a first encounter with Umesh Vazirani

Start with the simplest possible case. Write down what Umesh Vazirani 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 Umesh Vazirani 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 Umesh Vazirani 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 Umesh Vazirani

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

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

Frequently asked questions

What is Umesh Vazirani in simple terms?

Why does Umesh Vazirani 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 Umesh Vazirani?

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 Umesh Vazirani.