mathematics

Hitoshi Kumano-Go

Hitoshi Kumano-Go 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 Hitoshi Kumano-Go rather than just read about it. In short: Hitoshi Kumano-Go (4 October 1935 – 24 August 1982) was a Japanese mathematician who specialized in partial differential equations. He is especially recognized for his work on pseudo-differential operators and Fourier integral operators.

Key takeaways

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

Reference excerpt

Hitoshi Kumano-Go (4 October 1935 – 24 August 1982) was a Japanese mathematician who specialized in partial differential equations. He is especially recognized for his work on pseudo-differential operators and Fourier integral operators.

Life Hitoshi Kumano-go was born on 4 October 1935 in Arita, Wakayama Prefecture. After finishing high school in 1954, he studied mathematics and graduated from Osaka University in 1958. He started a doctoral work at the same university under the supervision of Mitio Nagumo. He received his PhD in 1963. He was promoted to associate professor in 1967 and to full professorship in 1971. From 1967 to 1969, Kumano-go had been a visiting member at the Courant Institute of Mathematical Sciences of New York University. In May 1981 he entered Osaka University Hospital where a brain tumor was discovered. Kumano-go died on 24 August 1982 in Osaka at the age of 46.

Work Kumano-Go first studied the local and global uniqueness of the solutions of the Cauchy problem for partial differential equations. While at the Courant Institute of Mathematical Sciences, Kumano-Go collaborated with Kurt Friedrichs, Peter Lax and Louis Nirenberg among others. He made major contributions to the theory of pseudo-differential operators. Its work contributed to the construction of the fundamental solution of a first order hyperbolic partial differential equation. His treatise on pseudo differential operators was first published in Japanese in 1974 and translated into English in 1981. Kumano-Go also made important contribution to the study of Fourier integral operators.

References

Worked examples

Example 1 — a first encounter with Hitoshi Kumano-Go

Start with the simplest possible case. Write down what Hitoshi Kumano-Go 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 Hitoshi Kumano-Go 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 Hitoshi Kumano-Go 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 Hitoshi Kumano-Go

In research: Hitoshi Kumano-Go 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 Hitoshi Kumano-Go 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: Hitoshi Kumano-Go is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1935 births, 1982 deaths, Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hitoshi Kumano-Go 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 Hitoshi Kumano-Go in 20 minutes

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

Frequently asked questions

What is Hitoshi Kumano-Go in simple terms?

Why does Hitoshi Kumano-Go 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 Hitoshi Kumano-Go?

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 Hitoshi Kumano-Go.