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mathematics

Takeo Nakasawa

Takeo Nakasawa 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 Takeo Nakasawa rather than just read about it. In short: Takeo Nakasawa (Japanese: 中澤武雄, February 5, 1913, Kōchi prefecture, Japan – June 20, 1946, Khabarovsk, Soviet Union) was a Japanese mathematician who independently invented the theory of matroids, though his work was forgotten for many years. He published four papers (in German) of which the first three introduce the subject of matroid theory during 1935–1938, when he worked as an assistant in the Tokyo University o…

Key takeaways

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

Reference excerpt

Takeo Nakasawa (Japanese: 中澤武雄, February 5, 1913, Kōchi prefecture, Japan – June 20, 1946, Khabarovsk, Soviet Union) was a Japanese mathematician who independently invented the theory of matroids, though his work was forgotten for many years. He published four papers (in German) of which the first three introduce the subject of matroid theory during 1935–1938, when he worked as an assistant in the Tokyo University of Arts and Sciences (now University of Tsukuba). After his last paper was published, he left for Manchuria at the age of 25 in 1938, then ruled by Japan, and worked as a bureaucrat there. With the defeat of Japan in 1945, the Soviets took control of Manchuria and Nakasawa was carted off to Siberia. He died of dystrophia at the age of 33 in Khabarovsk in the Soviet Union in 1946.

References

Nishimura, Hirokazu; Kuroda, Susumu, eds. (2009), A lost mathematician, Takeo Nakasawa. The forgotten father of matroid theory, Basel: Birkhäuser Verlag, doi:10.1007/978-3-7643-8573-6, ISBN 978-3-7643-8572-9, MR 2516551

Worked examples

Example 1 — a first encounter with Takeo Nakasawa

Start with the simplest possible case. Write down what Takeo Nakasawa 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 Takeo Nakasawa 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 Takeo Nakasawa 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 Takeo Nakasawa

In research
Takeo Nakasawa 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 Takeo Nakasawa 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
Takeo Nakasawa is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1913 births, 1946 deaths, 20th-century Japanese inventors, so understanding it makes those chapters shorter.
In everyday life
Look for Takeo Nakasawa 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 Takeo Nakasawa in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Takeo Nakasawa means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Takeo Nakasawa out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Takeo Nakasawa in simple terms?

Takeo Nakasawa (Japanese: 中澤武雄, February 5, 1913, Kōchi prefecture, Japan – June 20, 1946, Khabarovsk, Soviet Union) was a Japanese mathematician who independently invented the theory of matroids, though his work was forgotten for many years. He published four papers (in German) of which the first…

Why does Takeo Nakasawa 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 Takeo Nakasawa?

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 Takeo Nakasawa.

Tags

  • 1913 births
  • 1946 deaths
  • 20th-century Japanese inventors
  • 20th-century Japanese mathematicians
  • Asian mathematician stubs
  • Japanese scientist stubs
  • Scientists from Kōchi Prefecture

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