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-[[数理解析分野>http://www-is.amp.i.kyoto-u.ac.jp/]]: 応用可積分系:可積分系によるアルゴリズム開発
-[[離散数理分野:http://www-or.amp.i.kyoto-u.ac.jp/index.html]]: 離散数学の問題の複雑さの解明とアルゴリズムの開発
-[[最適化数理分野:http://www-optima.amp.i.kyoto-u.ac.jp/index.html]]: 最適化は問題解決のキーワード
-[[制御システム論分野:http://www.bode.amp.i.kyoto-u.ac.jp/]]: 制御とモデリングへの数理的アプローチ
-[[物理統計学分野:http://amech.amp.i.kyoto-u.ac.jp/index.php]]: 多要素結合系におけるダイナミクスの数理と情報処理
-[[力学系理論分野:http://yang.amp.i.kyoto-u.ac.jp/]]: 力学系を通してシステムを考える
-数理ファイナンス(協力講座): 金融市場の数理モデルの構成・解析
-[[応用数理モデル分野:http://www.bode.amp.i.kyoto-u.ac.jp/amm/]](連携ユニット): 情報システムに知を吹きこむ

高度情報化社会とよばれる現代においては、大規模で複雑なシステムをモデル化し、解析、計画、制御し、そして運用するという状況がいたるところに現れます。そこでは、情報、電気、機械、化学など個々の専門知識を身に付けるだけでなく、一見異なるように見える様々な問題に共通する数理的な構造を解明し、さらに問題解決のための数理的な手法を開発することが非常に重要となります。このような観点に立ち、私たち数理工学専攻の8つの研究室では、 数理解析・離散数理・最適化数理・制御システム論・物理統計学・力学系理論・応用数理モデル(連携ユニット)・数理ファイナンス(協力講座) の最先端の研究を進めています。

Research and education in this Department deal with modeling, analysis, and control of complicated and large-scaled systems, not necessarily confined to artificial ones, and optimization of their performances together with basic methodologies such as discrete and applied mathematics, dynamical system theory, and statistical physics. The aim of the Department is to bring up scientists or engineers who can cope with various problems encountered in highly organized and informatized modern societies, based on flexible conception, sharp insight, and high competence for searching solutions, resulting from profound attainments in mathematics and mathematical physics and from a general background in computer sciences. 


The Department has 3 divisions, each with 2 or 3 sub-divisions, and consists of  7 chairs. 21 graduate students are accepted into the Master's Program annually and 7 into the Doctoral program.

**&size(21){Applied Mathematical Analysis};   &size(12){ - Developing algorithms from integrable systems };[#sc84cb37]
We carry out research in the areas of contemporary soliton research
and integrable system research, not only regarding the applied analysis of
orthogonal polynomials and special functions that are closely associated
with integrable systems, but also regarding the application of the mathematical
methods developed by integrable system studies to the solution of
various problems hitherto thought to be unrelated to integrable systems
(such as numerical calculation and algorithm development). Our Group is
a pioneer in this research field, and conducts studies into the applied
analysis of integrable systems in the development of algorithms and other
new branches of mathematics from the perspective of computer science.&br;
(Professor: Yoshimasa NAKAMURA, Associate Professor: Satoshi TSUJIMOTO,  
Assistant Professor: Shuhei KAMIOKA, Hiroto SEKIDO)
**&size(21){Discrete Mathematics};   &size(12){ -Exploring the complexity of discrete mathematics problems and developing algorithms}; [#w71aad75]
Topics in discrete mathematics, such as the graphs and network used
to represent systems, schedules to enhance the efficiency of production,
and the logical analysis of large volumes of data, are closely related to
applications of research results. We explore the complexity of the calculations
used to solve these problems; design logical approximation algorithms;
develop taboo search algorithms, genetic algorithms and other
metaheuristic algorithms; and apply them to solving actual problems.
(Professor: Hiroshi NAGAMOCHI, Assistant Professor: Aleksandar SHURBEVSKI)
**&size(21){System Optimization};   &size(12){ - Optimization is the keyword for solving problems}; [#ab315b65]
We conduct education and research regarding the theory and methodology
of system optimization, which plays an important role as a mathematical
approach that is used to resolve many different kinds of practical
problems. In particular, we develop efficient mathematical optimization
approaches to actual large-scale systems, complex nonlinear systems, and
systems with uncertainty, as well as basic research regarding mathematical
(Professor: Nobuo YAMASHITA, Assistant Professor: Ellen Hidemi FUKUDA)
**&size(21){Control Systems Theory};   &size(12){ - Mathematical approaches to modeling and control }; [#o9515ff3]
We carry out teaching and research regarding the mathematical
methodologies of modeling, analysis and design of control systems, and
their application with the aim of developing practical and expansive control
theories. Our main research themes are robust control, control systems
with input/output constraints, networked control systems, algebraic
system theory, mathematical optimization in control, stochastic realization
and system identification.
(Professor: Yoshito OHTA, Associate Professor: Kenji KASHIMA, 
Assistant Professor: Kentaro OHKI)
**&size(21){Physical Statistics}; &size(12){ - The mathematical studies on dynamics of coupled multi-element systems and information processing}; [#p5eb59df]
We aim to gain a mathematical and unified understanding of the complex
and diverse phenomena that arise out of the intense mutual interactions
of multiple elements (units) in a system and apply this understanding
to information processing. For example, we will use stochastic process theory,
statistical physics, computer simulations, dynamical system theory,
agent models, and large-scale data processing techniques to analyze information
processing in simple threshold systems, neurons, and their networks;
the structure of the Internet and other complex networks, and the
propagation of information within them; and the dynamical properties of
price change, stock markets and other economic phenomena.
(Professor: Ken UMENO, Associate Professor: Aki-Hiro SATO)
**&size(20){Dynamical Systems};   &size(12){ - Looking into systems through dynamical systems theory }; [#j17f08be]
Our research purpose is that we analyze complicated phenomena such as chaos and bifurcations in various systems appearing in science, engineering and other disciplines using dynamical systems approaches, and apply them to develop novel engineering technologies. For this purpose, we not only use standard approaches but also establish new innovative theories in dynamical systems. Moreover, we utilize numerical approaches such as verifiable computation and large-scale numerical simulation, and study nonintegrability of dynamical systems and differential equations, nonlinear waves in partial differential equations, periodic motions in the n-body problem of classical mechanics and kinetic theory of many-body systems, design of spacecraft transfer trajectories and dynamics and control of flying objects such as quadrocopters.
(Professor: Kazuyuki YAGASAKI, Associate Professor: Mitsuru SHIBAYAMA, Assistant Professor: Yoshiyuki YAMAGUCHI)
**&size(21){Applied Mathematical Modeling Adjunct Unit}; (in collaboration with Hitachi, Ltd.)   &size(12){ -  Infusing information systems with intelligence}; [#ca90345d]
To make information systems useful to our day-to-day lives and
industry at large, we need to be able to mathematically model both the
behavior of people and the movements of objects that these systems deal
with. The form of these models ranges from the conceptual to the numerically
precise. We will examine case studies from industry in our research
of modeling technology, including methods of using human knowledge
(structural modeling) and methods using actual data (multivariate analysis).
(Professor: Yoichi NONAKA  (Hitachi, Ltd.), Associate Professor: Tatsuhiro SATO (Hitachi, Ltd.)

**&size(21){数理解析分野};   &size(12){ - 応用可積分系:可積分系によるアルゴリズム開発 };[#sc84cb37]

従来からアルゴリズムは主にコンピュータサイエンスの対象でしたが、 1990年代になって様々のアルゴリズムに共通して可積分系の構造が見いだされるようになりました。「応用可積分系」として、可積分系とそのアルゴリズムへの応用、とりわけ、高速高精度な行列特異値分解、可積分系の離散化の手法、直交多項式や特殊関数など可積分系の古典解析学を研究しています。

**&size(21){離散数理分野};   &size(12){ - 離散数学の問題の複雑さの解明とアルゴリズムの開発 }; [#w71aad75]


**&size(21){最適化数理分野};   &size(12){ - 最適化は問題解決のキーワード }; [#ab315b65]


**&size(21){制御システム論分野};   &size(12){ - 制御とモデリングへの数理的アプローチ }; [#o9515ff3]


**&size(21){物理統計学分野};   &size(12){ - 多要素結合系におけるダイナミクスの数理と情報処理 }; [#md7b67b7]


**&size(21){力学系理論分野};   &size(12){ - 力学系を通してシステムを考察する }; [#j17f08be]


**&size(21){数理ファイナンス}; (協力講座)   &size(12){ - 金融市場の数理モデルの構成・解析 }; [#m9a45de9]

金融市場の数理モデルを構成し、その解析を通して金融市場の現象の説明や意思決定のための指標を与えることを試みます。その際重要な武器になるのは、確率微分・積分(方程式)といった確率解析(stochastic calculus; 伊藤解析とも呼ばれる)の諸概念・道具です。

**&size(21){応用数理モデル分野}; (連携ユニット)   &size(12){ -  情報システムに知を吹きこむ }; [#ca90345d]