Series
AY 2007
Arts and Sciences

The World of Mathematics (Global Focus on Knowledge)

Produced by
#Mathematics
#Space & Physics
#AI & Information Science
#Economics & Finance
#数学
#数論
#解析学
#微分方程式
#物理学
#代数学
#暗号
#情報科学
#最適化
#情報技術
#経済
#データ分析
#金融
#幾何学
#Official UTokyo Courses (OCW)
#Arts and Sciences
Mathematics has the history of more than 2,000 years. It is the field still studied actively today, and developments are made rapidly in. Profound nature of numbers and figures, structures of functions and spaces are discovered one after another, and now, Fermat's last theorem, which had been the mystery of 350 years, or Poincare conjecture left pending for 100 years are solved. Recent proceedings of mathematics is quite spectacular. Also, since it allows free thinking and has a wide versatility, mathematics is applied to fundamental science, engineering, economics, sociology, and other disciplines as the common language of science. Sometimes, mathematics has the power to change all over the sociey, as it did when the principle of computer was discovered. Mathematics cannot be divided artificially. However, we are accustomed to, for the sake of convenience, separate it into four fields; algebra, geometry, analysis and applied mathematics. Plus, mathematical science includes mathematics for practical applications to analyze natural and social phenomena In this lecture series, themes characteristic to each fields are discussed by the experts working internationally. They navigate you for your further studies, by focusing mathematics from a wide perspective. Mathematics students learn in the first and second grade would be the basis of further studies. These lectures are expected to provide you with an outlook for the future.

Content List

Charms of Mathematics

1:33
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#1 The Wonder of Primes

大自然が持つ神秘は、数の世界に凝縮して現れ、数の世界の神秘は、素数の世界に凝縮して現れるように思われる。素数のふしぎさをめぐって、類体論を始めとして深い研究がなされてきたことを紹介する。1994年のフェルマーの最終定理の証明や2006年の佐藤テイト予想の証明が、類体論のさらなる進展によってなされたことも説明する。

Lecturer | Kazuya Kato
1:33
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Analyzing Phenomena

1:26
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#2 Mathematics of Phenomena

こちらの講義の概要をだいふくちゃん通信でもご紹介しています。 ⇒【駒場キャンパスで溢れかえるねずみ】微分方程式から現象の数理へ（だいふくちゃん通信）

Lecturer | Junkichi Satsuma
1:26
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1:33
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#3 The World of Non-Linear

こちらの講義の概要をだいふくちゃん通信でもご紹介しています。 ⇒【駒場キャンパスで溢れかえるねずみ】微分方程式から現象の数理へ（だいふくちゃん通信）

Lecturer | Junkichi Satsuma
1:33
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the World of Algebra -Number Theory and Its Application-

1:33
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#4 The World of Elementary Theory of Numbers and Finite Numbers

Lecturer | Toshiyuki Katsura
1:33
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1:22
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#5 Digital Mathematics, Mathematics for Security -Code and Cryptography-

Lecturer | Toshiyuki Katsura
1:22
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Mathematics of Optimization -Viewpoint of Applied Mathematics

1:22
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#6 Model and Data -Description-

Lecturer | Kazuo Murota
1:22
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1:30
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#7 Optimization -Planning-

Lecturer | Kazuo Murota
1:30
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1:22
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#8 Algorithm -Calculation-

Lecturer | Kazuo Murota
1:22
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Finance and Calculation

1:18
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#9 Practical Problems of Finance and Integral Calculation of Higher Dimensions

Lecturer | Shigeo Kusuoka
1:18
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1:32
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#10 Ito Analysis and Finance

Lecturer | Shigeo Kusuoka
1:32
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Activities of Geometry

1:28
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#11 Cognition and Activity in Geometry -Non-Euclidean Geometry and Space-Time-

Lecturer | Mikio Furuta
1:28
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1:32
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#12 Analysis and Multidiscipline in Geometry -Duality and Self in a Mirror-

Lecturer | Mikio Furuta
1:32
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1:37
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#13 Geometrical Mind and Its Changes -Focusing on Topology and Concept of Manifold-

Lecturer | Mikio Furuta
1:37
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