mathematics

Takeshi Saito (mathematician)

Takeshi Saito (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 Takeshi Saito (mathematician) rather than just read about it. In short: Takeshi Saito (斎藤毅 Saitō Takeshi, born 11 September 1961) is a Japanese mathematician, specializing in some areas of number theory and algebraic geometry. His thesis advisor was Kazuya Kato.

Key takeaways

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

Reference excerpt

Takeshi Saito (斎藤毅 Saitō Takeshi, born 11 September 1961) is a Japanese mathematician, specializing in some areas of number theory and algebraic geometry. His thesis advisor was Kazuya Kato. Saito was an invited speaker of the International Congress of Mathematicians in 2010.

Selected publications

Articles Saito, Takeshi (1987). "Vanishing Cycles and Geometry of Curves Over a Discrete Valuation Ring". American Journal of Mathematics. 109 (6): 1043–1085. doi:10.2307/2374585. ISSN 0002-9327. JSTOR 2374585. Saitō, Takeshi (1993). "Determinant representation, Jacobi sum and de Rham discriminant (Algebraic Number Theory : Recent Developments and Their Backgrounds)" (PDF). 数理解析研究所講究録 (Mathematical Analysis Workshop Proceedings) (844). Departmental Bulletin Paper, Kyoto University: 79–83. Saito, Takeshi (2004). "Log smooth extension of a family of curves and semi-stable reduction". Journal of Algebraic Geometry. 13 (2): 287–322. CiteSeerX 10.1.1.25.4186. doi:10.1090/S1056-3911-03-00338-2. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help) Saito, Takeshi (2014). "Characteristic cycle and the Euler number of a constructible sheaf on a surface". arXiv:1402.5720 [math.AG].

Books Kato, Kazuya; Kurokawa, Nobushige; Saito, Takeshi; Kurihara, Masato (2000). Number Theory 1: Fermat's Dream. Translations of Mathematical Monographs, vol. 186. American Mathematical Soc. ISBN 978-0-8218-0863-4. Kato, Kazuya; Kurokawa, Nobushige; Saitō, Takeshi; Kurihara, Masato (2000). Number Theory 2: Introduction to class field theory. Translations of Mathematical Monographs, vol. 240. American Mathematical Society. ISBN 978-0-8218-1355-3. Saito, Takeshi (2014-12-18). Fermat's Last Theorem: The Proof. Translations of Mathematical Monographs, vol. 245. American Mathematical Society. ISBN 978-0-8218-9849-9.

References

Worked examples

Example 1 — a first encounter with Takeshi Saito (mathematician)

Start with the simplest possible case. Write down what Takeshi Saito (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 Takeshi Saito (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 Takeshi Saito (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 Takeshi Saito (mathematician)

In research: Takeshi Saito (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 Takeshi Saito (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: Takeshi Saito (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1961 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Takeshi Saito (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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How to study Takeshi Saito (mathematician) in 20 minutes

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

Frequently asked questions

What is Takeshi Saito (mathematician) in simple terms?

Takeshi Saito (斎藤毅 Saitō Takeshi, born 11 September 1961) is a Japanese mathematician, specializing in some areas of number theory and algebraic geometry. His thesis advisor was Kazuya Kato.

Why does Takeshi Saito (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 Takeshi Saito (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 Takeshi Saito (mathematician).