mathematics

Tadashi Nakayama (mathematician)

Tadashi Nakayama (mathematician) 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 Tadashi Nakayama (mathematician) rather than just read about it. In short: Tadashi Nakayama (中山正, Nakayama Tadashi; July 26, 1912, Tokyo Prefecture – June 5, 1964, Nagoya) was a mathematician who made important contributions to representation theory. Career He received his degrees from the University of Tokyo and the University of Osaka and held permanent positions at the University of Osaka and Nagoya University.

Key takeaways

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Reference excerpt

Tadashi Nakayama (中山正, Nakayama Tadashi; July 26, 1912, Tokyo Prefecture – June 5, 1964, Nagoya) was a mathematician who made important contributions to representation theory.

Career He received his degrees from the University of Tokyo and the University of Osaka and held permanent positions at the University of Osaka and Nagoya University. He had visiting positions at Princeton University, University of Illinois, and the University of Hamburg. Nakayama's lemma, Nakayama algebras, Nakayama's conjecture, and the Murnaghan–Nakayama rule are named after him.

Selected works

Nakayama, Tadasi (1939), "On Frobeniusean algebras. I", Annals of Mathematics, Second Series, 40 (3): 611–633, Bibcode:1939AnMat..40..611N, doi:10.2307/1968946, JSTOR 1968946, MR 0000016 Nakayama, Tadasi (1941), "On Frobeniusean algebras. II" (PDF), Annals of Mathematics, Second Series, 42 (1): 1–21, doi:10.2307/1968984, JSTOR 1968984, MR 0004237 Tadasi Nakayama. A note on the elementary divisor theory in non-commutative domains. Bull. Amer. Math. Soc. 44 (1938) 719–723. MR 1563855 doi:10.1090/S0002-9904-1938-06850-4 Tadasi Nakayama. A remark on representations of groups. Bull. Amer. Math. Soc. 44 (1938) 233–235. MR 1563716 doi:10.1090/S0002-9904-1938-06723-7 Tadasi Nakayama. A remark on the sum and the intersection of two normal ideals in an algebra. Bull. Amer. Math. Soc. 46 (1940) 469–472. MR 0001967 doi:10.1090/S0002-9904-1940-07235-0 Tadasi Nakayama and Junji Hashimoto. On a problem of G. Birkhoff. Proc. Amer. Math. Soc. 1 (1950) 141–142. MR 0035279 doi:10.1090/S0002-9939-1950-0035279-X Tadasi Nakayama. Remark on the duality for noncommutative compact groups. Proc. Amer. Math. Soc. 2 (1951) 849–854. MR 0045131 doi:10.1090/S0002-9939-1951-0045131-2 Tadasi Nakayama. Orthogonality relation for Frobenius- and quasi-Frobenius-algebras . Proc. Amer. Math. Soc. 3 (1952) 183–195. MR 0049876 doi:10.2307/2032255 Tadasi Nakayama. Galois theory of simple rings. Trans. Amer. Math. Soc. 73 (1952) 276–292. MR 0049875 doi:10.1090/S0002-9947-1952-0049875-3 Masatosi Ikeda and Tadasi Nakayama. On some characteristic properties of quasi-Frobenius and regular rings. Proc. Amer. Math. Soc. 5 (1954) 15–19. MR 0060489 doi:10.1090/S0002-9939-1954-0060489-9

References "Obituary: Tadasi Nakayama", Nagoya Mathematical Journal, 27: i–vii. (1 plate), 1966, ISSN 0027-7630, MR 0191789

External links O'Connor, John J.; Robertson, Edmund F., "Tadashi Nakayama", MacTutor History of Mathematics Archive, University of St Andrews Tadasi Nakayama at the Mathematics Genealogy Project https://www.math.uni-bielefeld.de/~sek/collect/nakayama.html

Worked examples

Example 1 — a first encounter with Tadashi Nakayama (mathematician)

Start with the simplest possible case. Write down what Tadashi Nakayama (mathematician) 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 Tadashi Nakayama (mathematician) 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 Tadashi Nakayama (mathematician) 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 Tadashi Nakayama (mathematician)

In research: Tadashi Nakayama (mathematician) 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 Tadashi Nakayama (mathematician) 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: Tadashi Nakayama (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1912 births, 1964 deaths, 20th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Tadashi Nakayama (mathematician) 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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Frequently asked questions

What is Tadashi Nakayama (mathematician) in simple terms?

Tadashi Nakayama (中山正, Nakayama Tadashi; July 26, 1912, Tokyo Prefecture – June 5, 1964, Nagoya) was a mathematician who made important contributions to representation theory. Career He received his degrees from the University of Tokyo and the University of Osaka and held permanent positions at th…

Why does Tadashi Nakayama (mathematician) 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 Tadashi Nakayama (mathematician)?

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 Tadashi Nakayama (mathematician).