mathematics

Louis Auslander

Louis Auslander 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 Louis Auslander rather than just read about it. In short: Louis Auslander (July 12, 1928 – February 25, 1997) was a Jewish American mathematician. He had wide-ranging interests both in pure and applied mathematics and worked on Finsler geometry, geometry of solvmanifolds and nilmanifolds, locally affine spaces, many aspects of harmonic analysis, representation theory of solvable Lie groups, and multidimensional Fourier transforms and the design of signal sets for communica…

Key takeaways

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

Reference excerpt

Louis Auslander (July 12, 1928 – February 25, 1997) was a Jewish American mathematician. He had wide-ranging interests both in pure and applied mathematics and worked on Finsler geometry, geometry of solvmanifolds and nilmanifolds, locally affine spaces, many aspects of harmonic analysis, representation theory of solvable Lie groups, and multidimensional Fourier transforms and the design of signal sets for communications and radar. He is the author of more than one hundred papers and ten books.

Education and career Auslander received his Ph.D. at the University of Chicago in 1955 under Shiing-Shen Chern. He was a visiting scholar at the Institute for Advanced Study in 1955-57 and again in 1971-72. After holding a variety of faculty positions at US universities, in 1965 Auslander joined the faculty at Graduate Center of the City University of New York and since 1971 he had been a Distinguished Professor of Mathematics and Computer Science there.

Personal life Louis Auslander was married twice, first for over 25 years to Elinor Newstadt Auslander, with whom he had three children (Nathan, Rose, and Daniel), and later to Fernande Couturier Auslander. His brother Maurice Auslander was also a mathematician.

Selected publications

Articles Auslander, Louis & Kostant, Bertram (1971). "Polarization and unitary representations of solvable Lie groups". Inventiones Mathematicae. 14 (4): 255–354. Bibcode:1971InMat..14..255A. doi:10.1007/bf01389744. S2CID 122009744. Auslander, L.; Tolimieri, R. (1979). "Is computing the finite Fourier transform pure or applied mathematics?". Bulletin of the American Mathematical Society. New Series. 1: 847–897. doi:10.1090/s0273-0979-1979-14686-x.

Books with L. Markus: Flat Lorentz 3-Manifolds, AMS 1957 with Robert MacKenzie: Introduction to differentiable Manifolds, McGraw Hill 1963 with Leon W. Green and Frank J. Hahn: Flows on homogeneous spaces, Princeton University Press 1963 (with the assistance of Lawrence Markus and William S. Massey and an appendix by L. Greenberg) with Calvin C. Moore: Unitary representations of solvable Lie groups, AMS 1966 Abelian Harmonic Analysis, Theta Functions and Function Algebras on a Nilmanifold, Springer, 1975 Lecture Notes on Nil-Theta Functions, CBMS lectures, American Mathematical Society, 1977 Minimal flows and their extensions, North-Holland 1988 as editor: Signal processing theory, 2 volumes, Springer 1990

References

Sources O'Connor, J.J.; Robertson, E.F. (2015a). "Louis Auslander". MacTutor. Retrieved 23 November 2023. O'Connor, J.J.; Robertson, E.F. (2015b). "Maurice Auslander". MacTutor. Retrieved 23 November 2023. Shiing-Shen Chern, Thomas Kailath, Bertram Kostant, Calvin C. Moore, Anna Tsao, Louis Auslander (1928–1997), Notices of the American Mathematical Society, volume 45, number 3, March 1998

External links Louis Auslander at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Louis Auslander

Start with the simplest possible case. Write down what Louis Auslander 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 Louis Auslander 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 Louis Auslander 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 Louis Auslander

In research: Louis Auslander 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 Louis Auslander 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: Louis Auslander is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1928 births, 1997 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Louis Auslander 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 Louis Auslander in 20 minutes

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

Frequently asked questions

What is Louis Auslander in simple terms?

Why does Louis Auslander 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 Louis Auslander?

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 Louis Auslander.