mathematics

Israel Michael Sigal

Israel Michael Sigal 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 Israel Michael Sigal rather than just read about it. In short: Israel Michael Sigal (born 31 August 1945 in Kiev, Ukrainian SSR) is an Israeli, Canadian mathematician specializing in mathematical physics. He is a professor at the University of Toronto Department of Mathematics.

Key takeaways

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

Reference excerpt

Israel Michael Sigal (born 31 August 1945 in Kiev, Ukrainian SSR) is an Israeli, Canadian mathematician specializing in mathematical physics. He is a professor at the University of Toronto Department of Mathematics. He was an invited speaker at International Congress of Mathematicians, Kyoto—1990 and in International Congress on Mathematical Physics, Lausanne—1979, W. Berlin—1981, Marseille—1986.

Education Born in Kiev, Ukrainian SSR, Sigal obtained his bachelor's degree at Gorky University and his Ph.D. at Tel-Aviv University

Research interests Partial differential equation of quantum physics, Quantum mechanics and quantum information theory, Quantum field theory, Statistical mechanics, Non-linear equations, Mathematical biology, Pattern recognition

Awards The Jeffrey-Williams Lectureship, CMS Summer Meeting, 1992. John L. Synge Award, 1993. Fellow of the Royal Society of Canada, 1993. University Professor, 1997. Norman Stuart Robertson Chair in Applied Mathematics, 1998. CRM-Fields-PIMS prize, 2000. Fellow of the American Mathematical Society, 2012.

Selected works Mathematical foundations of quantum scattering theory for multiparticle systems. Mem. Amer. Math. Soc. 1978. MR 0508478. Sigal, I. M. (1982). "Mathematical theory of single channel systems. Analyticity of scattering matrix". Trans. Amer. Math. Soc. 270 (2): 409–437. doi:10.1090/s0002-9947-1982-0645323-x. MR 0645323. Scattering theory for many body quantum-mechanical systems: rigorous results. Lecture Notes in Mathematics 1011. Springer Verlag. 1983. Bach, V.; Fröhlich, J.; Sigal, I. M. (1995). "Mathematical theory of nonrelativistic matter and radiation". Lett. Math. Phys. 34 (3): 183–201. Bibcode:1995LMaPh..34..183B. CiteSeerX 10.1.1.52.2248. doi:10.1007/bf01872776. S2CID 17664339. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help) with Peter D. Hislop: Introduction to spectral theory: with applications to Schrödinger operators. Springer Verlag. 1996. with F. Ting: Sigal, I. M.; Ting, F. (2005). "Pinning of magnetic vortices by an external potential". St. Petersburg Math. J. 16 (1): 211–236. doi:10.1090/s1061-0022-04-00848-9. MR 2069485. with Stephen J. Gustafson: Mathematical concepts of quantum mechanics (2nd ed.). Springer Verlag. 2011.

References

External links Israel Michael Sigal at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Israel Michael Sigal

Start with the simplest possible case. Write down what Israel Michael Sigal 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 Israel Michael Sigal 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 Israel Michael Sigal 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 Israel Michael Sigal

In research: Israel Michael Sigal 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 Israel Michael Sigal 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: Israel Michael Sigal is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, Academic staff of the University of Toronto Faculty of Arts and Science, Canadian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Israel Michael Sigal 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 Israel Michael Sigal in 20 minutes

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

Frequently asked questions

What is Israel Michael Sigal in simple terms?

Why does Israel Michael Sigal 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 Israel Michael Sigal?

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 Israel Michael Sigal.