mathematics

Noga Alon

Noga Alon 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 Noga Alon rather than just read about it. In short: Noga M. Alon (Hebrew: נוגה אלון; born 1956) is an Israeli mathematician.

Key takeaways

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

Reference excerpt

Noga M. Alon (Hebrew: נוגה אלון; born 1956) is an Israeli mathematician. He is professor emeritus at Tel Aviv University and a professor of mathematics at Princeton University noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of papers.

Education and career Alon was born in 1956 in Haifa, where he graduated from the Hebrew Reali School in 1974. He graduated summa cum laude from the Technion – Israel Institute of Technology in 1979, earned a master's degree in mathematics in 1980 from Tel Aviv University, and received his Ph.D. in Mathematics at the Hebrew University of Jerusalem in 1983 with the dissertation Extremal Problems in Combinatorics supervised by Micha Perles. After postdoctoral research at the Massachusetts Institute of Technology, Alon returned to Tel Aviv University as a senior lecturer in 1985, obtained a permanent position as an associate professor there in 1986, and was promoted to full professor in 1988. He was head of the School of Mathematical Science from 1999 to 2001, and was awarded the Florence and Ted Baumritter Combinatorics and Computer Science Chair. He retired as professor emeritus from Tel Aviv and became a professor at Princeton University in 2018. He was editor-in-chief of the journal Random Structures and Algorithms from 2008 through 2023.

Research Alon has published more than five hundred research papers, mostly in combinatorics and in theoretical computer science, and one book, on the probabilistic method. He has also published under the pseudonym "A. Nilli", based on the name of his daughter Nilli Alon. His research contributions include the combinatorial Nullstellensatz, an algebraic tool with applications in combinatorics; color-coding, a technique for fixed-parameter tractability of pattern-matching algorithms in graphs; and the Alon–Boppana bound in spectral graph theory.

Selected works

Book The Probabilistic Method, with Joel Spencer, Wiley, 1992. 2nd ed., 2000; 3rd ed., 2008; 4th ed., 2016.

Research articles Alon, N. (1986). "Eigenvalues and expanders". Combinatorica. 6 (2): 83–96. doi:10.1007/BF02579166. MR 0875835. S2CID 41083612. Alon, N.; Boppana, R. B. (1987). "The monotone circuit complexity of Boolean functions". Combinatorica. 7 (1): 1–22. doi:10.1007/BF02579196. MR 0905147. S2CID 17397273. Alon, Noga (1987). "Splitting necklaces". Advances in Mathematics. 63 (3): 247–253. doi:10.1016/0001-8708(87)90055-7. MR 0877785. Alon, Noga; Kleitman, Daniel J (1992). "Piercing convex sets and the Hadwiger–Debrunner (p, q)-problem". Advances in Mathematics. 96 (1): 103–112. doi:10.1016/0001-8708(92)90052-M. MR 1185788. Alon, Noga; Yuster, Raphael; Zwick, Uri (1995). "Color-coding". Journal of the ACM. 42 (4): 844–856. doi:10.1145/210332.210337. MR 1411787. S2CID 208936467. Alon, Noga; Matias, Yossi; Szegedy, Mario (1999). "The space complexity of approximating the frequency moments". Journal of Computer and System Sciences. 58 (1, part 2): 137–147. doi:10.1006/jcss.1997.1545. MR 1688610. Previously in the ACM Symposium on Theory of Computing (STOC), 1996. Alon, Noga (1999). "Combinatorial Nullstellensatz". Combinatorics, Probability and Computing. 8 (1–2): 7–29. doi:10.1017/S0963548398003411. MR 1684621. S2CID 209877602.

Awards Alon has received a number of awards, including the following:

1989 – Erdős Prize; 2000 – George Pólya Prize in Applied Combinatorics of the Society for Industrial and Applied Mathematics 2001 – Michael Bruno Memorial Award of the Israel Institute for Advanced Studies; 2005 – Gödel Prize, with Yossi Matias and Mario Szegedy, for their paper "The space complexity of approximating the frequency moments" on streaming algorithms 2008 – Israel Prize, for mathematics. 2011 – EMET Prize, with Saharon Shelah, for mathematics. 2019 – Paris Kanellakis Award, with Phillip Gibbons, Yossi Matias and Mario Szegedy, "for foundational work on streaming algorithms and their application to large scale data analytics" 2021 – Leroy P. Steele Prize for Mathematical Exposition, with Joel Spencer, for The Probabilistic Method 2022 – Shaw Prize in Mathematical Sciences, with Ehud Hrushovski, "for their remarkable contributions to discrete mathematics and model theory with interaction notably with algebraic geometry, topology and computer sciences" 2022 – Knuth Prize, "for foundational contributions in combinatorics and graph theory and applications to fundamental topics in computer science" 2024 – Wolf Prize in Mathematics "for his fundamental contributions to Combinatorics and Theoretical Computer Science”. Alon gave plenary addresses at the 1996 European Congress of Mathematics, at the 2002 International Congress of Mathematicians, at the 2009 Turán Memorial Lectures, and a lecture in the 1990 International Congress of Mathematicians. In 2015 he gave the Łojasiewicz Lecture (on the "Signrank and its applications in combinatorics and complexity") at the Jagiellonian University in Kraków. He was given an honorary doctorate by ETH Zurich in 2013 and by the University of Waterloo in 2015. In addition, Alon has been a member of the Israel Academy of Sciences and Humanities since 1997. He was elected to the Academia Europaea in 2008. In 2015 he was elected as a fellow of the American Mathematical Society. In 2017 he became a Fellow of the Association for Computing Machinery. In 2019 he was named an honorary member of the Hungarian Academy of Sciences. In 2024, Alon gave the opening plenary talk on "Distance problems for typical norms" at the 33rd Cumberland Conference on Combinatorics, Graph Theory, and Computing at Mississippi State University.

See also Necklace splitting problem List of Israel Prize recipients

References

External links Noga Alon's home page Author profile in the database zbMATH Noga Alon publications indexed by Google Scholar

Illustrations

Worked examples

Example 1 — a first encounter with Noga Alon

Start with the simplest possible case. Write down what Noga Alon 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 Noga Alon 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 Noga Alon 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 Noga Alon

In research: Noga Alon 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 Noga Alon 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: Noga Alon is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1956 births, 20th-century Israeli mathematicians, 21st-century Israeli mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Noga Alon 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 Noga Alon in 20 minutes

Read the reference excerpt below once, without taking notes.
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Frequently asked questions

What is Noga Alon in simple terms?

Noga M. Alon (Hebrew: נוגה אלון; born 1956) is an Israeli mathematician.

Why does Noga Alon 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 Noga Alon?

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 Noga Alon.