2026年度 シラバス大学院 2026年度 シラバス大学院 2026年度 シラバス大学院
| 2026/03/01 現在 |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 1学期 ／First Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
劉 勇 |
| 担当教員名 ／Instructor |
劉 勇 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
PL02 C Programming PL03 JAVA Programming I PL04 C++ Programming FU01 Algorithms and Data Structures I |
| 更新日／Last updated on | 2026/02/05 |
|---|---|
| 授業の概要 ／Course outline |
An intelligent system must have at least the following means: 1) A means to access and acquire information. 2) A means to integrate, abstract, and be aware of the information. 3) A means to change and to adapt to the environment based on acquired information. The goal of neural network research is to realize an intelligent system using the human brain as a single model to realize all of the above means. There are many research topics in this area, for example 1) How to use neural networks to represent/acquire information/knowledge? 2) How to use neural networks to integrate, abstract, and be aware of the information? 3) How to change a neural network to adapt to the environment? This course introduces the basic models, learning algorithms, and some applications of neural networks. After this course, we should be able to know how to use neural networks for solving some practical problems such as pattern recognition, pattern classification, function approximation, data visualization, and so on. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
In this course, the students will study the following topics: 1) Basic neuron models: McCulloch-Pitts model, nearest neighbor model, radial basis function model, etc. 2) Basic neural network models: multilayer neural network, self-organizing neural network, associative memory, radial basis function neural network, support vector machine, neural network tree, etc. 3) Basic learning algorithms: delta learning rule, back propagation, winner take all, self-organizing feature map, learning vector quantization, etc. 4) Applications: character recognition, function approximation, data visualization, etc. |
| 授業スケジュール ／Class schedule |
1. Introduction - A brief introduction of this course. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 2. Fundamental concepts - Neuron models and the general learning rule. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 3. Multilayer neural networks - Structure and the back propagation learning algorithm for multilayer perceptron (MLP). [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 4. Team project - I - Learning of MLP for solving simple problems. [Preparation/Review] Discuss the MLP learning algorithms and simulation results: preparation (3 hours), review (3 hours). 5. Associative memory - Hopfield neural network, energy function, and convergence. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 6. Team project II - Application of Hopfield neural network to image restoration. [Preparation/Review] Discuss the learning in Hopfield neural network and simulation results: preparation (3 hours), review (3 hours). 7. Self-organizing neural networks - Kohonen neural network, pattern clustering, and the winner-take-all learning algorithm. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 8. Team project III - Pattern classification using self-organizing neural networks. [Preparation/Review] Discuss the learning in the self-organizing neural networks and simulation results: preparation (3 hours), review (3 hours). 9. Self-organizing feature map - Dimensionality reduction and data visualization based on the self-organizing feature map algorithm. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 10. Team project IV - Visualization of high dimensional patterns. [Preparation/Review] Discuss the self-organizing feature map learning and simulation results: preparation (3 hours), review (3 hours). 11. RBF neural networks - Radial basis neural network and support vector machines (SVM). [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 12. Team project V - Pattern recognition based on SVM. [Preparation/Review] Discuss SVM learning and simulation results: preparation (3 hours), review (3 hours). 13. Neural network trees - Hybridization of neural networks and the decision tree. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). 14. Presentation of team projects [Preparation/Review] Write presentation slides: preparation (2 hours), review (4 hours). |
| 教科書 ／Textbook(s) |
Lecture notes and reference materials will be available on the course page. |
| 成績評価の方法・基準 ／Grading method/criteria |
Projects: 75 (15 x 5) points Final presentation: 25 points |
| 履修上の留意点 ／Note for course registration |
Students are required to do 5 team projects for implementing the taught neural network models by using C, or C++, or Java languages. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
1) Ian Goodfellow and Yoshua Bengio and Aaron Courville, Deep Learning, MIT Press, 2016. 2) Jacek M. Zurada, Introduction to Artificial Neural Systems, PWS Publishing Company, 1995. 3) Simon Haykin, Neural Networks: A Comprehensive Foundation, Macmillan College Publishing Company, 1994. 4) Mohamad H. Hassoun, Foundamentals of Artificial Neural Networks,The MIT Press, 1995. 5) Laurene Fausett, Fundamentals of Neural Networks: Architectures, Algorithms, and Applications, Prentice Hall International, Inc., 1994. 6) B. D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press., 1996. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
劉 勇 |
| 担当教員名 ／Instructor |
劉 勇 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
CSA01 Neural Networks I: Fundamental Theory and Applications |
| 更新日／Last updated on | 2026/02/05 |
|---|---|
| 授業の概要 ／Course outline |
The course starts from an overview of evolutionary computation, and a simple example of evolutionary optimization so that the students could quickly grasp the basic ideas of nature-inspired techniques. In the following lectures, design examples in game, learning systems, and intelligent systems will be given. The aim of this course is to let students learn nature-inspired design by examples. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
1. To know what nature-inspired design techniques are and how they are applied to some real problems. 2. To understand the advantages and disadvantages of nature-inspired design techniques compared to other traditional design techniques. 3. To investigate potential applications of nature-inspired techniques to some real world problems. |
| 授業スケジュール ／Class schedule |
1. Introduction to Evolutionary Computation - An overview of evolutionary computation - Genetic algorithms, evolutionary programming, evolution strategies, and genetic programming [Preparation/Review] Study lecture notes and reference materials: preparation (3 hours), review (1 hour). 2. Evolutionary Programming - Global function optimization - Evolutionary programming with adaptation [Preparation/Review] Study lecture notes and reference papers: preparation (1 hour), review (1 hour). 3. Fast Evolutionary Programming - Fast evolutionary programming with Cauchy mutation - How to compare random search methods statistically [Preparation/Review] Study lecture notes and reference papers: preparation (2 hours), review (2 hours). 4. Evolutionary Game - How to learn a game without any teachers - How well the player can learn - How well the evolved strategies can generalize [Preparation/Review] Study lecture notes and reference papers: preparation (3 hours), review (2 hours). 5. Search Operators and Representations - Hybrid evolutionary algorithms with the mixed search operators and representations. [Preparation/Review] Study lecture notes and reference papers: preparation (2 hours), review (2 hours). 6. Team Project 1 on Evolutionary Optimization Students are required to work Team Project 1 on implementing evolutionary optimization for either numerical or combinatorial optimization problems. [Preparation/Review] Discuss the used evolutionary algorithms and the tested problems (4 hours), review the simulation results (2 hours). 7. Selection and Recombination - Different selection schemes - How to incorporate domain knowledge into search operators [Preparation/Review] Study lecture notes and reference materials: preparation (2 hour), review (1 hour). 8. Evolutionary Robots - An example of evolvable system design for a robot controller - Evolutionary algorithms for evolving programmable logic array [Preparation/Review] Study lecture notes and reference materials: preparation (2 hours), review (2 hours). 9. Evolutionary System with Reinforcement Learning - Real time evolvable system with reinforcement learning [Preparation/Review] Study lecture notes and reference materials: preparation (2 hours), review (2 hours). 10. Design of Neural Network Architecture - Architecture learning [Preparation/Review] Study lecture notes and reference materials: preparation (2 hour), review (1 hour). 11. Team Project 2 on Evolutionary Learning Students are required to work Team Project 2 on implementing evolutionary learning for some design problems. [Preparation/Review] Disscuss the used evolutionary learning and the design problems (3 hours), review the simulation results (3 hours). 12. Evolutionary Artificial Neural Networks - Direct encoding representations and indirect encoding representations - Hybrid learning [Preparation/Review] Study lecture notes and reference materials: preparation (2 hours), review (2 hours). 13. Evolutionary Neural Network Ensembles - Evolve a population of neural networks - Fitness sharing [Preparation/Review] Study lecture notes and reference materials: preparation (3 hours), review (2 hours). 14. Presentation of team projects [Preparation/Review] Write presentation slides: preparation (2 hours), review (4 hours). |
| 教科書 ／Textbook(s) |
Lecture notes will be available on the course page. |
| 成績評価の方法・基準 ／Grading method/criteria |
Team projects: 60 (30x2, two projects) Final presentation: 40 |
| 履修上の留意点 ／Note for course registration |
Students are required to do 2 team projects for implementing both evolutionary optimization and evolutionary learning. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
1. Some references will be shown on course pages. 2. Ian Goodfellow and Yoshua Bengio and Aaron Courville, Deep Learning, MIT Press, 2016. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
森 和好 |
| 担当教員名 ／Instructor |
森 和好 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/04 |
|---|---|
| 授業の概要 ／Course outline |
本講義のシラバスは英語版を参照してください。 |
| 授業の目的と到達目標 ／Objectives and attainment goals |
This course is concerned with the multidimensional systems theory. This theory includes multidimensional control system and image processing, and so on. We will proceed precisely with mathematical descriptions. |
| 授業スケジュール ／Class schedule |
1. Scalar 2-D Input/Output Systems 2. Stability 3. Structural Stability 4. Multi-Input/Multi-Output Systems 5. Stabilization of Scalar Feedback Systems 6. Characterization of Stabilizers for Scalar Systems 7. Stabilization of Strictly Causal Transfer Matrices 8. Characterization of Stabilizers for MIMO Systems 9. Stabilization of Weakly Causal Systems 10. Stabilization of MIMO Weakly Causal Systems Pre-class and Post-class Learning (including homeworks) may be required (it is expected about 4hours). |
| 教科書 ／Textbook(s) |
To be distributed. |
| 成績評価の方法・基準 ／Grading method/criteria |
Final examination and/or Reports |
| 履修上の留意点 ／Note for course registration |
The language is English. If all students can understand Japanese, Japanese may be used in addtion. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
1. Multidimensional Systems Theory (2nd Ed). D.Reidel Publishing, 2003. (Reference) 2. Schaum's Outline of Theory and Problems of Signals and Systems 3rd Ed.(Schaum's Outlines) (Reference) |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 4学期 ／Fourth Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
ハマダ モハメド |
| 担当教員名 ／Instructor |
ハマダ モハメド |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
Automata and Langauges |
| 更新日／Last updated on | 2026/02/03 |
|---|---|
| 授業の概要 ／Course outline |
The models of computations will be introduced and the term rewriting systems (TRS), as a universal model of computation, and its major properties such as termination and confluence will be discussed. Term rewriting is a branch of theoretical computer science which combines elements of logic, universal algebra, automated theorem proving and functional programming. Its foundation is equational logic. TRS constitutes a Turing- complete computational model which is very close to functional programming. It has applications in Algebra, recursion theory, software engineering and programming languages. In general TRSs apply in any context where efficient methods for reasoning with equations are required. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
This course gives students the fundamental concepts of the computational models and the concept of rewriting systems and its applications in many areas of theoretical computer science. It also give the students more understanding of the major properties of term rewriting systems. |
| 授業スケジュール ／Class schedule |
1. Introduction to models of computation 2. Finite automata as a model of computation for formal languages 3. Turing machines as a powerful model of computation 4. Rewriting systems as a general-purpose model of computation 5. Term rewriting systems 6. Unification, most general unifier and unification algorithm 7. Midterm Report/Exam/presentation 8. Church-Rosser property, Confluence, and Local confluence 9. Critical pairs (CP) and CP algorithm 10. Termination of rewriting systems 11. Completion and Knuth-Bendix algorithm 12. Other rewriting systems 13. General review 14. Final report presentation/Exam |
| 教科書 ／Textbook(s) |
1. F. Baader and T. Nipkow, Term Rewriting and All That, Cambridge University Press, 1998. 2. Other materials related to the topics will be introduced in the class. Various materials will be prepared |
| 成績評価の方法・基準 ／Grading method/criteria |
1. Class activities: 14% 2. Exercise: 26% 3. Midterm exam/report: 20% 4. Final exam/report: 40% |
| 履修上の留意点 ／Note for course registration |
As this course is given to students who have not studied the fundamentals of term rewriting systems, there is no prerequisites. But we expect students have some basic courses such as discrete mathematics and/or algebra. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
Will be given during lectures. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 1学期 ／First Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
浅井 信吉 |
| 担当教員名 ／Instructor |
浅井 信吉 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
Linear Algebras I, II Numerical Analysis |
| 更新日／Last updated on | 2026/02/03 |
|---|---|
| 授業の概要 ／Course outline |
This is a topic course: several topics of matrix based numerical computation will be selected, especially properties of matrices from the view point of decomposition theorems are discussed. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
Give a summary of properties of matrices on matrix computations. |
| 授業スケジュール ／Class schedule |
1. Matrix operations
2. Vector space and linear transformation 3. Vector space and linear transformation 4. Matrix Decompositions 5. Equivalent Decomposition 6. LDU Decomposition 7. Determinant and Inner Product 8. QR Decomposition 9. QR Decomposition 10. Shur Decomposition 11. Shur Decomposition 12. Jordan Decomposition 13. Jordan Decomposition 14. Singular value Decomposition and CS Decomposition [Preparation/Review] Before each class, prepare by studying the lecture materials and the relevant textbook pages for the content indicated in the course plan. Also, complete any unfinished exercises (within the day of the class, or) until the next class. The typical preparation/review time per session (100 min.) is 3-5 hours. |
| 教科書 ／Textbook(s) |
池辺八洲彦、池辺淑子、浅井信吉、宮崎佳典、現代線形代数 -分解定理を中心として-、共立出版、２００９ G. H. Golub, C. F Van Loan, Matrix Computations, The Johns Hopkins University Press, 1996 |
| 成績評価の方法・基準 ／Grading method/criteria |
Class activity, quizzes, and/or reports |
| 履修上の留意点 ／Note for course registration |
Knowledge on the following classes are needed: Linear Algebras I, II Numerical Analysis |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
浅井 信吉 |
| 担当教員名 ／Instructor |
浅井 信吉 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
Linear Algebra 1,2 Numerical Analysis |
| 更新日／Last updated on | 2026/02/03 |
|---|---|
| 授業の概要 ／Course outline |
This is a topics course: several recent topics of numerical computation will be selected and discussed in detail. ・Elements of the Hilbert space. ・The eigenvalue problem for infinite matrices. ・Application to the special function computation. ・Visualization. ・Introduction to high-performance computing. Case studies include introduction to important software packages and the Internet usage. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
To study some application of functional analysis to numerical computation. |
| 授業スケジュール ／Class schedule |
1. Elements of the Hilbert space(1)
2. Elements of the Hilbert space(2)
3. The eigenvalue problem for infinite matrices(1)
4. The eigenvalue problem for infinite matrices(2)
5. The eigenvalue problem for infinite matrices(3)
6. The eigenvalue problem for infinite matrices(4)
7. Application to the special function computation(1)
8. Application to the special function computation(2)
9. Application to the special function computation(3)
10. Application to the special function computation(4)
11. Visualization(1)
12. Visualization(2)
13. Introduction to high-performance computing(1)
14. Introduction to high-performance computing(2) [Preparation/Review] Before each class, prepare by studying the lecture materials and the relevant textbook pages for the content indicated in the course plan. Also, complete any unfinished exercises (within the day of the class, or) until the next class. The typical preparation/review time per session (100 min.) is 3-5 hours. |
| 教科書 ／Textbook(s) |
A. E. Taylor, D. C. Lay, Introduction to Functional Analysis, Kriger Pub., 1980 G. F. Simmons, Introduction to Topology and Modern Analysis, Mc-Graw Hill, 1963 |
| 成績評価の方法・基準 ／Grading method/criteria |
Quizzes, activities and/or reports. |
| 履修上の留意点 ／Note for course registration |
Knowledge on the following classes are needed: Linear Algebras I, II Numerical Analysis |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
池辺八洲彦、池辺淑子、浅井信吉、宮崎佳典、現代線形代数 -分解定理を中心として-、共立出版、２００９ 池辺八洲彦、稲垣敏之、数値解析入門、昭晃堂、１９９４ |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
ハマダ モハメド |
| 担当教員名 ／Instructor |
ハマダ モハメド |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
Discrete Mathematics |
| 更新日／Last updated on | 2026/02/03 |
|---|---|
| 授業の概要 ／Course outline |
This course gives students advanced topics in the theory of automata and languages. The characterization of language classes, which is one of the most important themes in the formal language theory, will be introduced. Especially, the homomorphic characterizations of language classes will be discussed in detail. Moreover, some applications of formal language theory will be discussed. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
Students can be familiar to the automata and languages and recognize the importance of the theory of automata and languages, and have enough knowledge to read and understand advanced papers in this field completely. |
| 授業スケジュール ／Class schedule |
1. Introduction and background 2. Review of the theory of automata and languages 3. Methods to describe infinite sets 4. Grammars as generating systems of infinite sets 5. Automata as recognizing systems of infinite sets 6. Chomsky hierarchy of language classes 7. Relation among grammars and automata 8. Midterm exam or report 9. Topics on the theory of automata and languages 10. Subclasses languages defined by automata with restrictions 11. Subclasses languages defined by grammars with restrictions 12. Operations on languages 13. Homomorphic characterization of language classes 14. Applications of the theory of automata and languages |
| 教科書 ／Textbook(s) |
We do not specify textbooks but introduce books related to the topics in the class. Various materials will be prepared. |
| 成績評価の方法・基準 ／Grading method/criteria |
1. Class activities: 14% 2. Exercise: 26% 3. Midterm exam/Report: 25% 4. Final exam: 35% |
| 履修上の留意点 ／Note for course registration |
Automata theory |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
There are so many good textbooks in this field. Some of them will be introduced in the class and some are given here for students' convenience. J. Hopcroft, J. Ullman: Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1979. A. Meduna: Automata and Languages, Theory and Applications, Springer, 1999. P. Linz: An Introduction to Formal Languages and Automata(3 ed.), Jones and Bartlett, 2001. J. L. Hein: Theory of Computation, An Introduction, Jones and Bartlett, 1996. M. Sipser: Introduction to the Theory of Computation, PWS Publishing Co., 1996. N. Pippenger: Theories of Computability, Cambridge Univ. Press, 1997. R. Greenlaw, H. J. Hoover: Fundamentals of the Theory of Computation, Principles and Proctice, Morgan Kaufmann Pub. Inc., 1998. A. Maruoka, Concise Guide to Computation Theory, Springer, 2011. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 1学期 ／First Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
渡部 繁 |
| 担当教員名 ／Instructor |
渡部 繁 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/08 |
|---|---|
| 授業の概要 ／Course outline |
学部レベルの数学（フーリエ解析, 複素関数論, 位相空間論）をよく理解している人 を対象にした, より進んだ解析学の授業. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
関数空間論への入門としてのフーリエ解析が理解できる. ヒルベルト空間論の基礎が理解できる. 直交多項式によるフーリエ展開が理解できる. |
| 授業スケジュール ／Class schedule |
１〜２ 学部で習った数学の復習 ３〜６ 関数空間論入門 ７〜１０ 関数解析入門 １１〜１４ 直交多項式によるフーリエ展開 |
| 教科書 ／Textbook(s) |
特になし |
| 成績評価の方法・基準 ／Grading method/criteria |
レポート １００％ |
| 履修上の留意点 ／Note for course registration |
フーリエ解析, 複素関数論, 位相空間論を履修していること. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
浅井 和人 |
| 担当教員名 ／Instructor |
浅井 和人 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/15 |
|---|---|
| 授業の概要 ／Course outline |
授業実施形態: 対面授業と遠隔授業の併用 本講においては，代数系および組合せ論におけるさまざまな topics の紹介を行う． 本年度は主に代数系に注目し，有限体の話題を取り上げたいと考えている．有限体 F_q は ガロアが初めに考えたとされるため，ガロア体とも呼ばれており，有限 (q) 個の元のなす体である． F_q の構造は元の個数 q によってただひとつに定まり，また q は素数のべきでなければならない． われわれは多項式環からはじめて，素体，有限多項式体，体の拡大，分解体，有限体の構造， 原始元，フローベニウスサイクル，円分多項式，有限体の間の関数などの話題について学びたい． 一般に数と言えば実数あるいは複素数であることを前提としてしまっているが， ここではより抽象的な『数』および『環』『体』などにふれることで，より抽象的，数学的な思考力を 育成することをひとつの目標にしている． このように有限体は純数学的な対象であり，数学の研究においては，通常の数における理論を 有限体の場合に拡張するといったことはひんぱんに行われているが，有限体はなにも純粋数学のみで 扱われるわけではない．むしろ実験計画，コーディング理論，論理回路等への応用面で極めて有用であり， 理学者，工学者にとって重要な対象であることを付け加えておく． |
| 授業の目的と到達目標 ／Objectives and attainment goals |
多項式環，素体，正標数，(準)同型写像，体の拡大，分解体，q元体の一意性，有限体の構造，原始元， フローベニウスサイクル，円分多項式． |
| 授業スケジュール ／Class schedule |
1. 多項式環． 2. 素体 F_p． 3. 準同型写像と同型写像． 4. 有限多項式体と体の拡大． 5--6. 有限体． 7--8. 有限体の構造． 9--10. 原始元． 11--12. フローベニウスサイクル． 13--14. 円分多項式． |
| 教科書 ／Textbook(s) |
1. ハンドアウト: Algebraic Systems and Combinatorics: -- Finite Fields --, by K. Asai 2. Introduction to Finite Fields and Their Applications, Revised ed. (1994), Cambridge University Press, by R. Lidl, H. Niederreiter 3. Finite Fields (Encyclopedia of Mathematics and its Applications) (1997), Cambridge University Press, by R. Lidl, H. Niederreiter 4. 組合せ理論とその応用 (1979)，岩波全書316，高橋磐郎 |
| 成績評価の方法・基準 ／Grading method/criteria |
レポート:80％ プレゼンテーション:20% |
| 履修上の留意点 ／Note for course registration |
重要な関連科目：応用代数，線形代数 I,II． |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
授業用ホームページ: http://web-ext.u-aizu.ac.jp/~k-asai/classes/class-texts.html |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
本間 道雄 |
| 担当教員名 ／Instructor |
本間 道雄 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/15 |
|---|---|
| 授業の概要 ／Course outline |
This course deals with several basic problems in natural sciences in order to show how the information theory and various computational methods are utilized in the analysis of practical systems. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
At the end of the course the students should be able to: (1) explain the importance and advantages of various numerical methods in the analysis of physical systems. (2) design a suitable model and write a program for solving practical problems. |
| 授業スケジュール ／Class schedule |
(1) Introduction - Numerical derivative, integral, and root finding - Exercise 1 (2) Differential equation 1 - Initial value problem - Exercise 2 (3) Differential equation 2 - Boundary value problem - Exercise 3 (4) Matrix manipulation 1 - Matrix inversion - Exercise 4 (5) Matrix manipulation 2 - Eigenvalue problem - Exercise 5 (6) Monte Carlo method 1 Random numbers and sampling of random variables - Exercise 6 (7) Monte Carlo method 2 Monte Carlo integrals and simulations - Exercise 7 |
| 教科書 ／Textbook(s) |
Lecture materials will be provided on the LMS. |
| 成績評価の方法・基準 ／Grading method/criteria |
Reports (100%) Students should submit a report on the problem given in each exercise class. |
| 履修上の留意点 ／Note for course registration |
Prerequisites: Students should have some experience and knowledge of basic physics (classical mechanics, electricity and magnetism, quantum mechanics, statistical mechanics) and programming. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
(1) An introduction to computer simulation methods : applications to physical systems 2nd ed. Harvey Gould and Jan Tobochnik Addison-Wesley, c1996 (2) Computational physics : FORTRAN version Steven E. Koonin and Dawn C. Meredith Addison-Wesley, c1990 |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
藤津 明 |
| 担当教員名 ／Instructor |
藤津 明 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/10 |
|---|---|
| 授業の概要 ／Course outline |
This course provides fundamental comcepts in high energy particle physics. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
At the end of the course the students should: 1. have basic knowledge of high energy physics 2. know how to use computer to study theory of high energy physics |
| 授業スケジュール ／Class schedule |
Lecture schedule 1. Elementary particle physics 2. Special relativity 3. General relativity 4. Quantum mechanics 5. Quantum field theory 6. Planck mass and Hawking radiation 7. DIrac equation for spinors 8. Dirac equation and Pauli's principle 9. Supersymmetry 10. Gauge symmetry and BRST quantiztion 11. Bosonic string 12. Bosonic string and Virasoro algebra 13. Superstring and Super Virasoro algebra 14. Superstring models for elemntary particles |
| 教科書 ／Textbook(s) |
Handout will be provided in LMS. |
| 成績評価の方法・基準 ／Grading method/criteria |
Students must submit a report for every lecture. They should write questions in their reports. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
Office hour: Monday, Thursday 1,2,3,4 period |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
成瀬 継太郎 |
| 担当教員名 ／Instructor |
成瀬 継太郎, 土屋 貴裕 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/06 |
|---|---|
| 授業の概要 ／Course outline |
This is a graduate school course on stochastic processes and applications. We focus on several classes of elementary stochastic processes which are often used in various applications: random walks, branching processes, discrete Markov chains and, time permitting, the Poisson process and Brownian motion. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
The student will get acquainted with mathematical tools and techniques, as well as the probabilistic intuition necessary for understanding and successful use of stochastic models in a variety of applications within mathematics and in science, engineering, economics, etc. He/she will also learn how to build new models, in yet-unencountered situations and novel frameworks. |
| 授業スケジュール ／Class schedule |
Each class will be conducted in lecture format. 1 Probability Review 2 Stochastic Processes 3 Simple Random Walk: Theory 4 Simple Random Walk: Implementation 5 Random Walks - Advanced Methods 6 Kalman Filter 7 Branching Processes 8 Markov Chains: Theory 9 Markov Chains: Implementation 10 Classification of States 11 Absorption and reward 12 Stationary and Limiting Distributions 13 Robotic applications 14 Wrap up [Preparation/Review] Preparation: Before each class, prepare by studying the lecture materials as well as implementing sample codes for the content indicated in the course plan. Review: Complete any unfinished exercises until the next class, as well as extra probelms and analysis shown in classes. The typical preparation/review time per session is 4–5 hours. |
| 教科書 ／Textbook(s) |
None, lecture notes will be delivered in classes. |
| 成績評価の方法・基準 ／Grading method/criteria |
By assignments. |
| 履修上の留意点 ／Note for course registration |
None. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
LMS. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
イエン ニール ユーウェン |
| 担当教員名 ／Instructor |
イエン ニール ユーウェン, 裴 岩 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/02 |
|---|---|
| 授業の概要 ／Course outline |
Human-centered computing (HCC) is the science of decoding human behavior. It discusses a computational approaches to understand human behavior all aspects of human beings. However, the complexity of this new domain necessitates alterations to common data collection and modeling techniques. This course covers the techniques that underlie the state-of-the-art systems in this emerging field. Students will develop a critical understanding of human-centered computing including fundamentals, approaches and applications/services. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
This course aims at instructing our students (especially master students) the fundamentals of human-centered computing. Through this course, students are expected to: 1) cultivate interdisplinary thinking skills; 2) be able to build systems that combine technologies with organizational designs; 3) understand the human, and translate the human needs to real-world systems. |
| 授業スケジュール ／Class schedule |
This course will give an introduction that covers a wide range of theories, techniques, applications to the well-designed human-computer systems. Examples and academic papers on HCC researches (to each topics above) will be distributed to students who are enrolled in this class. Students will be grouped and make presentation on distributed research papers, and trained to ask questions and provide personal opinions on specific studies. The schedule may be adjusted according to actual conditions. In that case, we will contact you separately. Remote / Online course may be conducted if necessary. |
| 教科書 ／Textbook(s) |
No specific textbook will be used for this course. Slides and handouts will be prepared by instructors, according to the references (see below), and available on the course website for download. Papers, news, and videos related to the theme will be selected from top-rank academic publications (e.g., IEEE/ACM/IEICE Transactions and SCI-indexed peer-reviewed journals), and the Internet (e.g., with copyright permission) will be taught during the classes. |
| 成績評価の方法・基準 ／Grading method/criteria |
Presentation: 30% Report: 70% Please note that the proportion of above grading criteria may be adjusted according to actual conditions. |
| 履修上の留意点 ／Note for course registration |
All the topics will be taught through the reading of past high quality studies. Students are expected to cultivate independent reading ability. The reports and the attendance are also considered very important factors to evaluate the learning performance. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
Witold Pedrycz, Fernando Gomide (2007). Fuzzy Systems Engineering: Toward Human-Centric Computing Wiebe Bijker, Of Bicycles, Bakelites, and Bulbs: Toward a Theory of Sociotechnical Change (Inside Technology) Clifford Geertz, The Interpretation Of Cultures (Basic Books Classics) The Presentation of Self in Everyday Life Victor Kaptelinin and Bonnie Nardi, Acting with Technology: Activity Theory and Interaction Design Guy A. Boy (2011). The Handbook of Human-machine Interaction: A Human-centered Design Approach |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
ハミード サジ |
| 担当教員名 ／Instructor |
ハミード サジ, 中里 直人 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/28 |
|---|---|
| 授業の概要 ／Course outline |
This course provides an introduction to parallel computing including parallel architectures and parallel programming techniques. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
The students will learn the basic parallel programming models including shared memory and distributed memory models. Parallel programming using MPI a will be a main focus. The course will heavily involve coding projects and weekly assignments. |
| 授業スケジュール ／Class schedule |
1. Introduction to Parallel Architecture 2. Introduction to Parallel Programming 3. Performance considerations 4. Programming in MPI 5. Programming in OpenMP |
| 教科書 ／Textbook(s) |
Numerical Analysis for Engineers and Scientists, G. Miller, Cambridge University Press Parallel Programming with MPI, P.S. Pachebo, Morgan Kaufmann Publishers Parallel Programming in C with MPI and OpenMP, M. J. Quinn, McGraw-Hill |
| 成績評価の方法・基準 ／Grading method/criteria |
Assignments = 30%, Project = 20%, Exam = 50% |
| 履修上の留意点 ／Note for course registration |
Computer architecture, mathematics, algorithms and programming Students are expected to have good skills in C or Fortran programming to take this course. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
http://pages.tacc.utexas.edu/~eijkhout/istc/istc.html |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
ラゲ ウダイ キラン |
| 担当教員名 ／Instructor |
ラゲ ウダイ キラン |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/10 |
|---|---|
| 授業の概要 ／Course outline |
This course provides an in-depth study of advanced pattern mining techniques for extracting meaningful knowledge from large, complex, and heterogeneous datasets. Pattern mining plays a central role in data science, big data analytics, and knowledge discovery, enabling the identification of regularities, trends, and relationships hidden in data. The course goes beyond classical frequent pattern mining and focuses on advanced and emerging topics, including maximal and closed pattern mining, periodic and temporal patterns, uncertain and fuzzy pattern mining, high-utility pattern mining, sequence and graph patterns, and scalable pattern mining for big data environments. Emphasis is placed on both theoretical foundations (formal definitions, properties, and complexity issues) and practical algorithm design, enabling students to understand how state-of-the-art pattern mining algorithms are developed, optimized, and applied to real-world datasets. A “Learn by Doing” approach is adopted. Each topic is introduced through conceptual explanations and algorithmic analysis, followed by hands-on exercises involving implementation, experimentation, and evaluation on real or benchmark datasets. Each class consists of one lecture period and two exercise/seminar periods, promoting active learning, discussion, and research-oriented thinking. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
Objectives Modern applications generate massive volumes of transactional, temporal, and uncertain data. Classical pattern mining techniques often fail to handle scalability, redundancy, and complexity issues arising in such data. Advanced pattern mining techniques have emerged to address these challenges. This course aims to equip students with advanced analytical and algorithmic skills required to design, analyze, and apply modern pattern mining methods in research and industrial settings. Attainment Goals By the end of this course, students will be able to: Formally define and analyze different types of patterns and pattern constraints Design and evaluate advanced frequent, closed, and maximal pattern mining algorithms Mine patterns from temporal, sequential, and uncertain datasets Apply fuzzy and high-utility pattern mining techniques Analyze algorithmic complexity and scalability issues Implement and experimentally evaluate pattern mining algorithms Critically read and present recent research papers in pattern mining |
| 授業スケジュール ／Class schedule |
Course Content and Methods Each session includes a lecture focusing on theoretical foundations and algorithms, followed by exercise and seminar sessions involving algorithm implementation, experimentation, paper discussion, or case studies. Exercises are conducted individually or in small groups. Selected sessions involve student-led paper presentations. Schedule (14 Sessions) Session 1 Lecture: Introduction to pattern mining and knowledge discovery Exercise: Review of classical frequent pattern mining algorithms Session 2 Lecture: Pattern types, measures, and constraints Exercise: Constraint-based pattern mining examples Session 3 Lecture: Closed and maximal pattern mining Exercise: Implementation and comparison of closed vs maximal mining Session 4 Lecture: Redundancy reduction and pattern condensation Exercise: Experimental evaluation of pattern reduction techniques Session 5 Lecture: Periodic and cyclic pattern mining Exercise: Mining periodic patterns from temporal data Session 6 Lecture: Sequential pattern mining Exercise: Sequence pattern extraction and analysis Session 7 Lecture: Temporal and interval-based pattern mining Exercise: Mining patterns from time-interval data Session 8 Lecture: Uncertain data and probabilistic pattern mining Exercise: Mining patterns from uncertain databases Session 9 Lecture: Fuzzy pattern mining Exercise: Design and evaluation of fuzzy frequent patterns Session 10 Lecture: High-utility pattern mining Exercise: Utility-based pattern extraction Session 11 Lecture: Pattern mining in big data environments Exercise: Scalability analysis and optimization strategies Session 12 Lecture: Pattern mining in data streams and dynamic data Exercise: Incremental and online pattern mining Session 13 Lecture: Recent research trends in pattern mining Exercise: Student paper presentations and discussions Session 14 Lecture: Integrated case studies and open research problems Exercise: Project discussion and future research directions Pre-class and Post-class Learning Students are expected to read assigned research papers or textbook chapters before each session and complete implementation or analysis tasks after class. Typical out-of-class study time per session: 5–7 hours, including reading, coding, experimentation, and report preparation. |
| 教科書 ／Textbook(s) |
Data Mining: Concepts and Techniques, Jiawei Han, Micheline Kamber, Jian Pei Frequent Pattern Mining, Charu C. Aggarwal Mining of Massive Datasets, Anand Rajaraman, Jeffrey Ullman, Jure Leskovec |
| 成績評価の方法・基準 ／Grading method/criteria |
Student performance is evaluated based on: Quizzes and short tests: 20% Programming assignments / experiments: 30% Paper presentation and seminar participation: 20% Final project or examination: 30% Attendance is not included in grading criteria. |
| 履修上の留意点 ／Note for course registration |
Attendance is mandatory. Students must maintain at least 75% attendance to be eligible for course completion. Failure to satisfy the attendance requirement will result in failure of the course, regardless of academic performance. Prior knowledge of Data Mining, Algorithms, and Database Systems is strongly recommended. Familiarity with Python or Java is desirable. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 4学期 ／Fourth Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
蘇 春華 |
| 担当教員名 ／Instructor |
蘇 春華, 可知 靖之 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
MA01–2 線形代数 I, II (本学・学部課程), MA03–4 微積分 I, II (本学・学部課程) またはそれに対応する他大学でのコース. |
| 更新日／Last updated on | 2026/02/06 |
|---|---|
| 授業の概要 ／Course outline |
暗号学者と純粋数学者が共同で教える非常にユニークな授業です。前半は可知（数学者）、後半は蘇（暗号学者）が教えます。 数学的な面では、純粋数学の中でも、ポスト量子暗号への応用を視野に入れ、（他の総合大の院の数学専攻に匹敵するような）質の高いトピックを厳選しています。ヤコビ和は、大きな整数の素数判定（Adleman-Pomerance-Rumely）に応用できることが示されました。後者は、耐量子「以前」の時代の公開鍵アルゴリズムではあるが、RSA (Rivest–Shamir–Adleman) の文脈で依然として重要性は失われていません。また、ヤコビ和の理論を再吟味することで、とりわけ「耐量子」の文脈で重要な暗号アルゴリズムを生成できる可能性が期待できます。このような立場で、離散フーリエ解析の考えをも一部取入れ、整数論的に意味のある 1 の冪根の和（ガウス和、ヤコビ和）の理論を概観します。 また、暗号学の分野では、ポスト量子暗号を目指した講義を行います。暗号技術入門（暗号、セキュリティ、公開鍵暗号、計算複雑性）、ポスト量子暗号入門、q線型暗号方式、多変数2次暗号方式、格子型暗号方式、アイソジェニー型暗号方式、量子フーリエ解析など多岐に亘り解説します。 |
| 授業の目的と到達目標 ／Objectives and attainment goals |
1. 数学と暗号学は、ともに純粋に理論的で、演繹的推論に基づくという点で異なる学問分野であることを理解すること。暗号学が純粋数学の原理を最も基本的な形で用いていることを理解すること。 2. 1 の冪根とその和の基本を理解する。不変式論を取入れた枠組みを理解する。3. 耐量子暗号の存在意義について理解する（量子コンピュータの登場と不可分）。4. 耐量子暗号の基本を理解し、最先端レベルの暗号分野で何が研究すべきテーマ/問題になっているのかを理解する。 |
| 授業スケジュール ／Class schedule |
第1部 1. はじめに -基本的な数論と公開鍵暗号方式 2. フーリエ変換等（古典的フーリエ解析）のクラッシュコース。 -フーリエ変換の枠組みで微分の公理的定義を再検討し、分数階微分を視野に入れる。 -多項式環に作用する一般的な線形群。 多項式環に作用する一般的な線形群 -有限群作用による多項式環の不変部分環 -Galois理論に関する若干の小技。 -テンソル表現（クロネッカーのテンソル積）。 -アフィン空間の有限 abelian cover 、ガウス-ヤコビ和の理論と相性の良いガロア群から生じるもの。 3. 量子コンピュータ - 量子コンピュータの基礎 - Shorのアルゴリズム - 有限体演算 - Karatsuba と数論的変換に基づく乗算 - Montgomery modular 乗算 第II部 4. 格子暗号 - 格子暗号の基礎知識 - NewHope, Kyber, Saber (NISTのポスト量子候補) - NTRU、NTRU Prime - デジタル署名アルゴリズム Dilithium、Falcon 5. コードベース暗号 - クラシックマッケイリス - HQC 6. 同種写像暗号 - 超重合同型鍵交換(SIKE) - 等質性に基づくデジタル署名アルゴリズム |
| 教科書 ／Textbook(s) |
Post-Quantum Cryptography by Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen https://link.springer.com/book/10.1007/978-3-540-88702-7 |
| 成績評価の方法・基準 ／Grading method/criteria |
成績評価は、レポート（50％）と最終発表（50％）に基づいて行われます。 |
| 履修上の留意点 ／Note for course registration |
前提条件 MA01-2 線形代数I, II（学部）, MA03-4 微積分I, II（学部）, または同等。 |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
参考 : https://pqcrypto.org |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 4学期 ／Fourth Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
ヴィリエッタ ジョヴァンニ |
| 担当教員名 ／Instructor |
ヴィリエッタ ジョヴァンニ |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
Prerequisites: FU01 Algorithms and Data Structures I (undergraduate), or equivalent. FU03 Discrete Systems (undergraduate), or equivalent. Optional: FU09 Algorithms and Data Structures II (undergraduate), or equivalent. SEA01 Parallel Distributed & Internet Computing (graduate), or equivalent. |
| 更新日／Last updated on | 2026/01/19 |
|---|---|
| 授業の概要 ／Course outline |
This course provides an introduction to modern algorithmic aspects of distributed systems, with a special focus on decentralized networks. In such networks, resources and data are distributed across multiple devices that collaborate towards a common goal. Examples include peer-to-peer networks of smartphones, wireless sensor networks, or blockchain networks. We will define an abstract model of communication network and study the design and analysis of general algorithmic solutions to common problems, such as Leader Election and Consensus. The course begins with basic scenarios and solutions, progressively tackling more complex situations, including networks with dynamic topologies, anonymous agents, congested channels, and corrupt messages. Building on classical algorithms, the course gradually incorporates cutting-edge techniques and data structures, with particular emphasis on history trees. This course serves as a valuable complement to offerings in the field of Computer Network Systems by focusing specifically on the theory of distributed computing, rather than delving into software engineering aspects. Although it is designed to be self-contained, students who have completed SEA01 Parallel Distributed & Internet Computing (or equivalent courses) will find that this course develops the subject from systems with shared memory to general distributed systems. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
We cover fundamental aspects of the theory of distributed computing, with emphasis on anonymous dynamic networks and the history tree data structure. Goals: 1. Learn basic network models and paradigms, as well as their relationships with real-world distributed systems. 2. Master traditional algorithmic techniques for static networks, and learn how to analyze simple distributed algorithms in various network scenarios. 3. Learn advanced data structures such as history trees, and understand how to apply them to complex distributed systems such as anonymous, dynamic, and congested networks. |
| 授業スケジュール ／Class schedule |
1. Introduction to distributed algorithms and basic network models. 2. Computation in simple static networks such as rings and trees. 3. Basic algorithms for anonymous static networks. 4. History trees: definition and fundamental properties. 5. Basic applications of history trees to anonymous dynamic networks. 6. Applications of history trees to directed networks. 7. Streaming algorithms, port awareness, and disconnected networks. 8. Examples, counterexamples, and lower bounds. 9. Basic termination detection techniques in dynamic networks. 10. Termination in dynamic networks with multiple leaders. 11. Self-stabilization and fault tolerance. 12. Finite-state stabilization. 13. Universal computation in congested networks. 14. New frontiers and open research problems. |
| 教科書 ／Textbook(s) |
N. Santoro, "Design and Analysis of Distributed Algorithms". John Wiley & Sons, 2007. |
| 成績評価の方法・基準 ／Grading method/criteria |
Final Exam. |
| 履修上の留意点 ／Note for course registration |
Students are expected to have a strong familiarity with elementary graph theory and discrete mathematics, algorithm design and analysis, and basic data structures. Some knowledge of network algorithms and parallel and distributed computing is preferred but not required. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
[1] N. Santoro, "Design and Analysis of Distributed Algorithms". John Wiley & Sons, 2007. [2] Computing in Anonymous Dynamic Networks Is Linear Giuseppe A. Di Luna and Giovanni Viglietta, FOCS 2022 https://giovanniviglietta.com/papers/anonymity.pdf [3] History Trees and Their Applications Giovanni Viglietta, SIROCCO 2024 https://giovanniviglietta.com/papers/historytree.pdf [4] Lecture notes provided by the instructor. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
中村 章人 |
| 担当教員名 ／Instructor |
中村 章人, 渡邊 曜大, 蘇 春華 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/03 |
|---|---|
| 授業の概要 ／Course outline |
Today's computing environment encompasses a wide range of devices, including smartphones, portable/desktop PCs, server computers, IoT devices, and virtual machines on cloud computing platforms. Information security technology is essential to leverage these capabilities while preventing accidents and cyberattacks, enabling the secure processing and communication of diverse data types. This course covers the fundamental concepts and technologies of information security. It also introduces cutting-edge technologies and mechanisms. [keywords] authentication, vulnerability, cyberattack, OS and IoT, public key encryption |
| 授業の目的と到達目標 ／Objectives and attainment goals |
[Objectives] To maximize the functionality and performance of information systems and prevent accidents and cyberattacks, knowledge of information security is essential. This course covers fundamental and advanced knowledge of information security. [Attainment Goals] - Students will acquire fundamental and advanced knowledge of information security concepts and technologies, enabling them to apply this knowledge to software and system design and implementation. - Students will understand the principles of information security management and apply them to practical tasks such as system operations. |
| 授業スケジュール ／Class schedule |
Each class session will be conducted in a lecture format. During class, students will occasionally present quiz answers orally for discussion and solve practice problems to deepen their understanding of the course content. 1, 2. Fundamentals - Goal of information security - Risk, threat, vulnerability, and control - Confidentiality, integrity, availability (C-I-A) triad - Attack paradigm and protection paradigm - Authentication and password 3, 4. Vulnerability - Classes of vulnerabilities - Trends of vulnerability - Vulnerability management - Open standards for vulnerability management 5, 6. Cyberattacks and Controls - DoS and DDoS attacks - Password cracking - Risks of Web applications 7, 8. Security Notions for Public Key Encryption Schemes - Definition of public key encryption schemes - Security goals: Semantic security (SS), Indistinguishability (IND), Non-malleability (NM) - Attacking models: Chosen plaintext attack (CPA), Chosen ciphertext attack (CCA1, CCA2) 9, 10. Relation among Security Notions - Equivalence between SS and IND - NM implies IND, IND-CCA2 implies NM-CCA2 11, 12. Cryptography for IoT Security and Privacy - Cryptography for IoT - Side channel attacks - Authentication by IoT 13, 14. System Security - OS security - Password and access control - FinTech security [Preparation/Review] To maximize learning effectiveness, students should review the relevant sections of the lecture and reference materials and complete preparatory work on the content outlined in the class schedule before attending class. Additionally, students should use the materials or resources they have obtained themselves to review the class content. The recommended time for preparation and review per session is 3 to 5 hours. |
| 教科書 ／Textbook(s) |
No textbook. |
| 成績評価の方法・基準 ／Grading method/criteria |
Method: assignments (reports) 100% Criteria: - Correctness for computational problems - Relevance, quality, presentation, and originality of essays |
| 履修上の留意点 ／Note for course registration |
- Lecture materials will be distributed via the LMS and the university's internal web server. - Late submission of reports will result in point deductions. - The course assumes a basic knowledge of mathematical logic and probability. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
- Office hours: Accepted individually via email, etc., and handled on a case-by-case basis. - The course instructor, Akihito Nakamura, has practical experience: He worked at AIST (National Institute of Advanced Industrial Science and Technology) for 20 years, where he was involved in R&D in information security and cloud computing. Based on his experience, he equips students with the advanced technical knowledge of information security. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 4学期 ／Fourth Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
李 想 |
| 担当教員名 ／Instructor |
李 想, 蘇 春華 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/26 |
|---|---|
| 授業の概要 ／Course outline |
信号処理は、現代の情報システムの構築における基本的な理論および技術です。過去半世紀にわたり、この分野では多くの理論や手法が提案され、広く研究されてきました。本コアコースでは、まず離散時間信号およびシステムの基礎を復習します。主なトピックには、離散時間信号の概念と分類、時間領域・周波数領域・Z領域・離散周波数領域における信号の表現、システムの表現、解析、およびフィルタ設計が含まれます。その後、コースは確定的信号およびシステムを超えて、確率的信号およびシステムに焦点を移します。これらの内容は、学部レベルの「信号処理と線形システム」コースで学習した内容を発展させるものです。具体的には、推定理論、ランダム信号モデリング、確率的信号およびシステムの特性解析、ノンパラメトリック推定、適応信号処理、およびカルマンフィルタリングなどのトピックを扱います。 |
| 授業の目的と到達目標 ／Objectives and attainment goals |
このコースは、情報システムのあらゆる分野の大学院生を対象とした基礎的なコアコースとして設計されています。基本的な信号処理の包括的な方法論を提供し、特に信号の統計的特性とそれを高度な処理技術に応用する方法に重点を置きながら、より発展的なトピックを紹介します。さらに、本コースでは、信号処理手法のコンピュータープログラミングによる実装についても取り扱います。最後に、ノイズキャンセリング、システム同定、カルマンフィルタリングなどの実際の応用についても学びます。 |
| 授業スケジュール ／Class schedule |
1) 導入（イントロダクション） 2) 線形時不変（LTI）システム、インパルス応答、および畳み込み和 3) フーリエ変換、周波数応答、およびサンプリング定理 4) Z変換とその特性、逆Z変換 5) 微分方程式、伝達関数、システムの安定性 6) 離散フーリエ変換（DFT）、高速フーリエ変換（FFT） 7) 有限インパルス応答（FIR）フィルターと無限インパルス応答（IIR）フィルター 8) 離散時間信号処理の基礎 9) 確率変数、系列、および確率過程 10) スペクトル推定 11) 最適線形フィルター、ウィーナーフィルター 12) 最小二乗フィルタリングと予測、自適応フィルター 13) 最適線形フィルターのアルゴリズムと構造 14) カルマンフィルター |
| 教科書 ／Textbook(s) |
[1] 担当講師が作成した講義ノート [2] Applied Digital Signal Processing: Theory and Practice. Dimitris G Manolakis and Vinay K. Ingle. Cambridge University Press, 2011, ISBN: 9780521110020. [3] Signals and Systems (2nd Edition), Alan V. Oppenheim, Alan S. Willsky and S. Hamid, Pearson, 1997, ISBN: 0138147574. |
| 成績評価の方法・基準 ／Grading method/criteria |
課題（35%） クイズ（15%） 期末レポート（50%） |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
[1] Applied Digital Signal Processing: Theory and Practice. Dimitris G Manolakis and Vinay K. Ingle. Cambridge University Press, 2011, ISBN: 9780521110020. [2] Signals and Systems (2nd Edition), Alan V. Oppenheim, Alan S. Willsky and S. Hamid, Pearson, 1997, ISBN: 0138147574. [3] Statistical and Adaptive Signal Processing, Dimitris G. Manolakis et al. Boston: McGraw-Hill, 2000, ISBN: 163081203X. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 3学期 ／Third Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
土屋 貴裕 |
| 担当教員名 ／Instructor |
土屋 貴裕, 橋本 康弘, 渡邊 曜大 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/29 |
|---|---|
| 授業の概要 ／Course outline |
This course provides advanced contents of applied statistics. Most important statistical methods are explained with many examples of data. At the same time, their mathematical foundations are given. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
Students can understand basic applied statistics such as estimation, test, regression, and analysis of variance by using Gaussian, t, F, and chi-square distributions. Moreover, they can learn knowledge on stochastic processes. |
| 授業スケジュール ／Class schedule |
The course contains following topics with 3-4 hours for each including lecture and practical exercises. Module 0: Measure-Theoretic Toolkit for Learning: - A fundamental set theory - Improper integral - linear algebra Module 1: Probability Spaces and Random Variables - The intuitive meaning of Probability model; Sample space, point of omega, Event as measurable set, the probability of an event. - measurable and sigma algebra - measure theory and probability triple - Random variables - Distribution functions; pmfs, pdfs - A first transformation rule for pdfs Module 2: Expectation as a Linear Functional - Expectation \$ |mathbb $\{E\} \$$ - Variance and Covariance - Integrable space $ L^ p $ - Correlation coefficient, MSE - Variance of a sum Module 3: Sample Means and the Central Limit Theorem - Red and white balls - sample space, prior probabilities likelihood - Bayes' theorem - Red and White ball example again*. - Independence - Law of large numbers - Unbiased Estimator of Sample Variance. - Using the sample median quantiles in statistics - Strong Law of Large Numbers - Empirical Distribution Function Module 4: Linear Models and Ordinary Least Squares - An application: Regression - Linear least squares: ordinary least squares - The true coefficient via Central limit theorem Module 5: Case Study Module 6: High-Dimensional Statistics for Learning - Covariance, - Shrinkage - L2-norm Ridge and L1-norm Lasso |
| 教科書 ／Textbook(s) |
Class materials will be distributed. |
| 成績評価の方法・基準 ／Grading method/criteria |
Reports 50％, Quiz 50%. |
| 履修上の留意点 ／Note for course registration |
Courses preferred to be learned prior to this course : Calculus, Linear algebra, Probability, Information theory. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
Weighing the Odds: A Course in Probability and Statistics (English Edition) W. Feller, An Introduction to Probability Theory, Vol.1, (Wiley) |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 1学期 ／First Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
山上 雅之 |
| 担当教員名 ／Instructor |
山上 雅之, 浅井 信吉 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/08 |
|---|---|
| 授業の概要 ／Course outline |
This course provides basic knowledge of quantum information and quantum computations for graduate students who want to learn modern information and computational models. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
At the end of the course, students can acquire 1) Basin knowledge of quantum mechanics for quantum information theory 2) Algorithms of quantum computers 3) Quantum cryptography. |
| 授業スケジュール ／Class schedule |
[Class Format] This course will be conducted in a lecture-based format in every class. [Preparation/Review] Before each class, please review the lecture materials distributed in advance, based on the course schedule. To check your understanding, a short quiz will be assigned in every class. Please be sure to submit the quiz by the next class. The expected study time for preparation and review for each class is approximately 3–5 hours. [First part (Prof. YAMAGAMI Masayuki)] 1: Introduction: Purpose of quantum information 2: Review of quantum mechanics 1 (Quantum systems) 3: Review of quantum mechanics 2 (Interference of quantum states) 4: Definition of quantum computer 5: Elementary quantum algorithm 1 (Deutsch-Jozsa algorithm) 6: Elementary quantum algorithm 2 (Grover's algorithm) 7: Summary and guidance for further study [Second part (Prof. ASAI Nobuyoshi)] 8: Quantum state and vector expression 9: Quantum operation and Matrix Expression 10: Superposition, entanglement, and measurement 11: Quantum Fourier transform 12: Phase Estimation 13: Harrow-Hassidim-Lloyd(HHL) algorithm 14: Summary |
| 教科書 ／Textbook(s) |
No specific textbooks are designated, but the following are usefull books for beginners. 1. Fundamentals of Quantum Information(H. Sagawa and N. Yoshida, World Scientific) 2. Quantum Computing for Everyone (Chris Bernhardt, The MIT Pres) 3. 量子コンピュータ ― 超並列計算のからくり(竹内 繁樹、講談社) [2の日本語版] 量子情報理論(佐川弘幸 / 吉田宣章, 丸善出版, 日本語版 [3の日本語版] みんなの量子コンピュータ （クリス バーンハルト [(翻訳) 湊 雄一郎, 中田 真秀] 、翔泳社） |
| 成績評価の方法・基準 ／Grading method/criteria |
Reports: 50 points (first part) and 50 points (second part) |
| 履修上の留意点 ／Note for course registration |
A basic proficiency in linear algebra is desired. It is recommended to have basic knowledge of quantum mechanics. However, the course will accept students who do not have any knowledge of quantum mechanics but have strong desire to learn new knowledge. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 1学期 ／First Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
鈴木 大郎 |
| 担当教員名 ／Instructor |
鈴木 大郎, 渡邊 曜大 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/06 |
|---|---|
| 授業の概要 ／Course outline |
計算は計算機科学において最も重要な概念である。計算機の能力に限界があるという、計算機科学と計算機工学に関わる者が必須の事柄も、計算の概念によって示すことができる。 計算の概念によって、我々が計算機に解かせたい問題は計算可能と計算不能なものという２つのクラスに分類される。後者はけして計算機で解くことはできない。 この授業では、計算の厳密な概念である計算モデルとそれらの間の等価性、および計算不能な問題の存在とその具体例について学ぶ。 |
| 授業の目的と到達目標 ／Objectives and attainment goals |
この授業を履修した学生は、チューリング機械、レジスタ機械、帰納的関数のような種々の計算モデルについての知識を得ることができる。さらに、計算機の限界、すなわり計算機で解くことのできない問題が存在することを理解し、計算機で解くことのできない問題にはどのようなものがあるかを述べることができる。 |
| 授業スケジュール ／Class schedule |
各回の授業は講義と演習を組み合わせて行われる。講義は事前にLMSで配布されるハンドアウトと補足資料にしたがう。演習は講義の合間に実施される。 授業スケジュールは以下のとおりである。 第1回 1. 計算可能性と計算モデルの概要 第2回から第7回 2. 計算モデル 2.1 チューリング機械モデル 2.2 ランダムアクセスモデル (RAM) 2.3 帰納的関数モデル 2.4 Whileプログラムモデル 第8回から第10回 3. チャーチチューリングの提唱 3.1 計算モデルの等価性 3.2 チャーチチューリングの提唱 3.3 自然数以外のデータ型での計算 第11回と第12回 4. 万能プログラム 4.1 プログラムのコード化 4.2 万能プログラムの構成 第13回と第14回 5. 計算不能な問題 5.1 停止問題 5.2 帰着可能性 各回の授業とその内容との対応は、授業の進み具合により変更になることがある。 各回の授業に臨むにあたり、授業スケジュールにしたがってハンドアウトと補足資料の予習をしておくこと。また、授業後にハンドアウト、補足資料、演習問題の復讐を行うこと。毎回の予習・復習の目安は3～5時間である。 |
| 教科書 ／Textbook(s) |
教科書は指定しない。授業の中で配布するハンドアウトに沿って授業を進める。 |
| 成績評価の方法・基準 ／Grading method/criteria |
評価は最後の授業終了後メールで配布される最終課題の提出による。履修者は最終課題の解答を指定された期日までに返信しなければならない。 また、授業中に演習問題を数問解いてもらう。演習問題は成績評価には含まれないが、解かなければ最終課題に解答することが難しくなるので、演習問題を授業中に必ず解かなければならない。 |
| 履修上の留意点 ／Note for course registration |
この授業を履修する学生は、学部の授業である F3 離散系論、F1 アルゴリズムとデータ構造I、F8 オートマトンと言語理論、M9 数理論理学で学ぶ内容を知っていることが望ましい。 |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
R. Sommerhalder, S.C. van Westrhenen. The theory of computability : programs, machines, effectiveness and feasibility. Addison-Wesley. 1988. Martin D. Davis, Ron Sigal, Elaine J. Weyuker. Computability, complexity, and languages : fundamentals of theoretical computer science. Academic Press. 1994. Douglas S. Bridges. Computability : a mathematical sketchbook. Springer. 1994. Carl H. Smith. A recursive introduction to the theory of computation. Springer. 1994. Tom Stuart. Understanding computation : from simple machines to impossible programs. O'Reilly. 2013. (Tom Stuart著; 笹井崇司訳. アンダースタンディングコンピュテーション: 単純な機械から不可能なプログラムまで. オライリー・ジャパン. 2014) Chris Hankin. Lambda calculi: a guide for computer scientists. Oxford University Press. 1994. A.クフォーリ, R.モル, M.アービブ共著; 甘利俊一, 金谷健一, 川端勉共訳. プログラミングによる計算可能性理論. サイエンス社. 1987. 高橋正子著. 計算論 : 計算可能性とラムダ計算. 近代科学社. 1991. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
劉 勇 |
| 担当教員名 ／Instructor |
劉 勇, 橋本 康弘 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
Artificial intelligence (under graduate course) |
| 更新日／Last updated on | 2026/02/05 |
|---|---|
| 授業の概要 ／Course outline |
Most engineering problems can be formulated as optimization problems. Even machine learning (e.g. training of a neural network, finding the best architecture of a deep neural network for image classification) is a special case of optimization. To solve optimization problems, different methods have been studied in mathematical programming, operations research, and so on. Conventional methods, however, are usually not efficient enough when the problem space is large and complex. Many problems faced in artificial intelligence are combinatorial optimization problems. These problems are NP-hard, and we may never find polynomial time solutions. To solve these problems efficiently, different heuristics have been used to search for sub-optimal solutions. Heuristics are search methods produced based on human intuition and creative thinking, or inspired by some natural phenomena. They are often useful for finding good local solutions quickly in a restricted area. Meta-heuristics are multi-level heuristics that can control the whole process of search, so that global optimal solutions can be obtained systematically and efficiently. Although meta-heuristics cannot always guarantee to obtain the true global optimal solution, they can provide very good results for many practical problems. Usually, meta-heuristics can enhance the computing power of a computer system greatly without increasing the hardware cost. So far, many meta-heuristics have been proposed in the literature. In this course, we classify meta-heuristics into two categories. The first one is "single-point" (SP) search, and the second one is "multi-point" (MP) search. For the former, we study tabu search, simulated annealing, iterated local search, and so on. For the latter, we study evolutionary algorithms, including genetic algorithms, genetic programming, evolutionary strategy, and memetic algorithm; ant colony optimization, and particle swarm optimization. Although the efficiency and efficacy of these methods have been proved through experiments, because they were proposed based on human intuition, the theoretic foundation is still weak. Therefore, in this course, we will mainly introduce the basic idea of each method, and try to explain the physical meaning clearly. Mathematical proofs will be introduced very briefly when necessary. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
In this course, we will study the following topics: (1) Examples of important optimization problems. (2) Conventional optimization methods. (3) Single-point (SP) search methods: * Tabu search. * Simulated annealing. * Iterated local search. * Guided local search. (4) Multi-point (MP) search methods * Genetic algorithm (GA). * Genetic programming (GP). * Evolutionary programming (EP). * Memetic algorithm (MA). * Differential evolution (DE). * Particle swarm optimization (PSO) and ant colony optimization (ACO). After this course, students should be able to (1) Understand the basic ideas of each meta-heuristics algorithm; (2) know how to use meta-heuristics for solving different problems; and (3) become more interested in developing new algorithms. |
| 授業スケジュール ／Class schedule |
Session 1: An Introduction to Optimization - Classification and case study. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 2: Search Algorithms - An brief review of conventional search algorithms. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 3: Tabu Search - List, intensification, and diversification. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 4: Simulated Annealing - Find the global optimum without remembering search history. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 5: Iterated Local Search and Guided Local Search - Strategies for repeated search. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 6: Team Work I - Solving problems using single point search algorithms. [Preparation/Review] Discuss the used single point search algorithms and simulation results: preparation (3 hours), review (3 hours). Session7: Presentation of Team Work I. [Preparation/Review] Write presentation slides: preparation (2 hours), review (4 hours). Session 8: Genetic Algorithm - Basic components and steps of GA. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 9: Other Evolutionary Algorithms - Evolution strategies, evolutionary programming, and genetic programming. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 10: Differential Evolution - Evolve more efficiently, but why? [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 11: Memetic Algorithms - Meme, memotype, memeplex, and memetic evolution. - Combination of memetic algorithm and genetic algorithm. [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 12: Swarm Intelligence - Ant colony optimization - Particle swarm optimization [Preparation/Review] Study lecture notes: preparation (2 hours), review (1 hour). Session 13: Team Work II - Solving problems using multi-point search algorithms [Preparation/Review] Discuss the used multi-point search algorithms and simulation results: preparation (3 hours), review (3 hours). Session 14: Presentation of Team Work II. [Preparation/Review] Write presentation slides: preparation (2 hours), review (4 hours). |
| 教科書 ／Textbook(s) |
Lecture notes will be available on the course page. |
| 成績評価の方法・基準 ／Grading method/criteria |
- Team works: 70 (35 x 2) points. - Team presentation: 30 points. - Active Participation will also be considered in evaluation. |
| 履修上の留意点 ／Note for course registration |
This course is related to optimization problems. If you are interested in knowing how to find (search for) the "best" solution for any given problems, efficiently and effectively, please take this course. Note that designing deep neural networks, electronic devices, and so on, are all "special cases" of optimization problems. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
1) M. Gendreau and J. Y. Potvin, Handbook of metaheuristics, 2nd Edition, Springer, 2010. 2) C. Cotta, M. Sevaux, and K. Sorensen, Adaptive and multilevel metaheuristics, Springer, 2010. |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
浅井 和人 |
| 担当教員名 ／Instructor |
浅井 和人, 橋本 康弘, 可知 靖之, 土屋 貴裕, 渡邊 曜大 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/01/15 |
|---|---|
| 授業の概要 ／Course outline |
Course implementation methods: Remote classes A graph, composed of vertices and edges, is one of the most fundamental objects in mathematics. In spite of its simple definition, tons of notions concerning graphs are introduced, and it is sometimes very laborious to perform complete introduction of graph theory. In this class, we first overview graph theory terminology to moderate extent, then we change the focus to carefully selected important topics, and advance our knowledge in that area. For example, we focus on vertex/edge connectivity, and introduce Menger's theorem and Mader's theorem; also focus on spanning trees and Kirchhoff's theorem, etc. Graph theory, as a branch of mathematics, growing its branches like a tree, and even at present, contains many difficult open problems. As another aspect, it has a lot of applications to several areas. Graphs can be used to model many types of relations and processes in physical, biological, social and information systems. This is a reason why graph theory is important for many people in wide areas. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
Graphs, Subgraphs, Isomorphic graphs, Degrees of vertices, Walks, Trails, Paths, Distance, Diameter, Coloring, Special graphs, Multigraphs and matrices, Eulerian/Hamiltonian multigraphs, Connectivity, Menger's theorem, Mader's theorem, Planarity (optional), Trees, Spanning trees, Kirchhoff's theorem, Deletion-contraction method, Cayley's formula, Minimum spanning trees, Decompositions of graphs. |
| 授業スケジュール ／Class schedule |
1--2. Definition and basics 3. Walks, trails, paths; Connectivity 4. Distance and diameter; Coloring 5. Special graphs, matrices 6. Eulerian/Hamiltonian multigraphs 7. Connectivity (revisited) 8. Menger's theorem, Mader's theorem 9. Trees, Spanning trees and Kirchhoff's theorem 10. Deletion-contraction method 11. Prufer's bijective proof of Cayley's formula 12. Minimum spanning trees 13. Decomposition of graphs 14. Gyarfas tree packing conjecture |
| 教科書 ／Textbook(s) |
1. Handout: A Graduate Text for the Core Course: -- Graph Theory --, by K. Asai 2. Graph Theory (Graduate Texts in Mathematics, Vol. 173) (2012), Springer, by R. Diestel 3. Pearls in Graph Theory: A Comprehensive Introduction (Dover Books on Mathematics) (2003), Dover Publications, by N. Hartsfield, G. Ringel |
| 成績評価の方法・基準 ／Grading method/criteria |
Report:80％ Presentation:20% |
| 履修上の留意点 ／Note for course registration |
Related courses: Discrete Systems, Algorithms and Data Structures |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
Home page for the class: http://web-ext.u-aizu.ac.jp/~k-asai/classes/class-texts.html |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 4学期 ／Fourth Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
中里 直人 |
| 担当教員名 ／Instructor |
中里 直人, 浅井 信吉, 藤本 裕輔 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/03 |
|---|---|
| 授業の概要 ／Course outline |
This course mainly introduces 1. Ordinary and partial differential equations appear in science or engineering 2. Schemes to discretize the differential equations 3. Computational techniques to get numerical solutions. 4. Use of programming language and numerical libraries for solving differential equations and visualizing the results of simulation; main attention is focused on the use of C, Java, Python, or similar languages. This course starts with the theory and mathematics of differential equations followed by hands-on style exercises as well as computer-related exercises on numerical techniques to solve various differential equations. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
The main goal of this course is to introduce the basic theory of differential equations and several most important numerical techniques and schemes to get solutions to those equations. To program numerical solutions in exercise, we encourage students to use 1. Python for obtaining preliminary results with its efficient visualization and 2. C or Java languages for high-performance programs 3. Or other programming languages as you choose. |
| 授業スケジュール ／Class schedule |
week 1 Floating-point arithmetic operations (N.Nakasato) week 2 Introduction to Ordinary Differential Equations (N.Nakasato) week 3 Introduction to Partial Differential Equations (N.Nakasato & N.Asai) week 4 Topics in Partial Differential Equations (1) (N.Nakasato, N.Asai & Y.Fujimoto) week 5 Topics in Partial Differential Equations (2) (N.Nakasato, N.Asai & Y.Fujimoto) week 6 Practical Applications of Numerical Modeling and Simulations (N.Asai) week 7 Practical Applications of Numerical Modeling and Simulations (Y.Fujimoto) Every week, one lecture (2 periods) will be given followed by an exercise class (2 periods). Before the opening of the course : Review the undergraduate classes on "Linear Algebra", "Integration", and related courses for roughly 20 hr. Pre-class Learning : Review the lecture slide for 1 - 2 hr. If the learning material is given, review the material for 2 hr. Post-class Learning : Continue to solve exercise problems and submit reports for 3 - 4 hr. |
| 教科書 ／Textbook(s) |
The lecture slides will be available in the LMS. Part of the course is based on the following textbooks. Modeling with Differential Equations, by D.Burghes & M.Borrie, Ellis Horwood Ltd , 1981 Partial Differential Equations for Scientists and Engineers, Stanley J. Farlow, Dover Publications, 1993 |
| 成績評価の方法・基準 ／Grading method/criteria |
Homework&Reports (100 points) |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 4学期 ／Fourth Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
可知 靖之 |
| 担当教員名 ／Instructor |
可知 靖之, ヴィリエッタ ジョヴァンニ |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
【必修要件】MA01–2 線形代数 I & II (学部 1 年生向け) 、MA03–4 微積分 I & II (学部 1 年生向け) 、或いはそれと同等の単位と認定されるもの。MA05 フーリエ解析 (学部 2 年生向け) はいわゆる必修要件ではないが、受講歴があると望ましい。そうでなくとも、同科目についてある程度知識があれば理想的である。 |
| 更新日／Last updated on | 2026/02/06 |
|---|---|
| 授業の概要 ／Course outline |
このコースでは測度理論とルベーグ積分の初歩に焦点を当てます。 大学院生のみなさんは積分について詳しい筈ですが、そのみなさんの知っている積分は正確には「リーマン積分」と呼ばれます。 「ルベーグ積分」はリーマン積分を精密化したものです。 何の役に立つのか、ということを手短かに述べると、学部の『フーリエ解析』(MA05) の講義ではリーマン積分に基礎を置きつつ教えています (正当な理由があるため) が、実は、フーリエ解析の全体像はルベーグ積分に基礎を置いた理論展開により初めて開けてくるのです。数学的には、フーリエ解析の主な研究対象である二乗可積分函数の空間は、完備な無限次元ベクトル空間、いわゆるヒルベルト空間になります。 、ルベーグ測度に関して。 実は、数学の中の解析方面で使われる多くの定理・公式などは、最終的にはその事実に帰着します。 フーリエ解析はデータ サイエンス (信号処理、画像解析など) に必須の知識でもあるため、本講義内容は、データ・サイエンティストだけでなく、より広範にコンピュータ理工学関連分野に携わるすべての人にとって役立つと信じます 。 本講義は、全国の数学および理工系の学部・大学院を持つほとんどの大学で標準カリキュラムの一部として教えられている内容と一致しています。 |
| 授業の目的と到達目標 ／Objectives and attainment goals |
L^1 空間と L^2 空間の完備性に重点を置き、測度理論とルベーグ積分の初歩を取り上げる。 【目標】 1. 19 世紀に測度論とルベーグ積分の概念が姿を現したことが数学史における大きなパラダイム転換であったことを理解する。 今日、測定理論とルベーグ積分がコンピュータ理工学に浸透していることを理解する。 2. 測度理論の基礎を理解する : ボレルの σ 代数、σ 加法性 (σ 加法関数)、R^n のルベーグ測度、測度零集合。 3. ルベーグ積分の基礎を理解する。 L^1 空間の完備性がルベーグ積分の概念の存在意義を高めること。 同様に、二乗可積分性の概念と L^2 空間 (ヒルベルト空間) の完備性を理解する。 |
| 授業スケジュール ／Class schedule |
1. 長さ・面積・極限の概念の再検討。 一次元の間隔。 2. カントール集合。 σ-加法性 Part I. ペアノ・ジョルダン測度。 3. ルベーグの外測度・内測度。 測度零集合。 4.カラテオドリ/ルベーグ・スティルチェスの外測度。 可測集合。 ボレル σ-代数。 5. σ-加加性 Part II. 完備性。測度空間、ファトウの補題。 6. R^n のルベーグ測度。 R^n 内のボレル集合。 可測な cover/kernel 。 7. 連続函数 f に対する区間 I の逆像 f^−1 (I)。 ボレルの正規数。単函数。 8. 可測函数。 それらの和・積・積分。 エゴロフの定理。 9. ルベーグ積分、定義と基本性質。 ルベーグの支配収束定理。 10. ルーディンの定理。 L^p 空間。 リースの定理。 ハーン・ジョーダン分解。 11. ラドン・ニコディムの定理。 ヴィターリの補題。 σ-加法函数の微分。 12. フビニの定理。 ハウスドルフ測度/ハウスドルフ次元。 13. フーリエ解析への応用 I． 14. フーリエ解析への応用 II． |
| 教科書 ／Textbook(s) |
講義ノートを用いる。 参考書 : 志賀浩二 『ルベーグ積分 30 講』数学 30 講シリーズ 9 朝倉書店 伊藤清三 『ルベーグ積分入門』 裳華房 |
| 成績評価の方法・基準 ／Grading method/criteria |
試験と宿題。 |
| 履修上の留意点 ／Note for course registration |
【必修要件】 MA01–2 線形代数 I & II (学部 1 年生向け) 、MA03–4 微積分 I & II (学部 1 年生向け) 、或いはそれと同等の単位と認定されるもの。MA05 フーリエ解析 (学部 2 年生向け) はいわゆる必修要件ではないが、受講歴があると望ましい。そうでなくとも、同科目についてある程度知識があれば理想的である。 |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
参考書 : 志賀浩二 『ルベーグ積分 30 講』数学 30 講シリーズ 9 朝倉書店 伊藤清三 『ルベーグ積分入門』 裳華房 |
| コンピテンシーコード表を開く 科目一覧へ戻る |
| 開講学期 ／Semester |
2026年度／Academic Year 2学期 ／Second Quarter |
|---|---|
| 対象学年 ／Course for; |
1年 , 2年 |
| 単位数 ／Credits |
2.0 |
| 責任者 ／Coordinator |
渡部 有隆 |
| 担当教員名 ／Instructor |
渡部 有隆, 西舘 陽平 |
| 推奨トラック ／Recommended track |
－ |
| 先修科目 ／Essential courses |
－ |
| 更新日／Last updated on | 2026/02/06 |
|---|---|
| 授業の概要 ／Course outline |
Data structures play a key role in computer science and engineering. They are essential components to implement many efficient algorithms. This graduate-level course covers advanced topics not studied in introductory courses on algorithms and data structures. This course focuses on not only theory but also on practice to implement the advanced data structures and algorithms. The lectures and exercises will be given online according to the situation. |
| 授業の目的と到達目標 ／Objectives and attainment goals |
The core course covers several advanced data structures related to balanced search trees, range queries, sets and persistent data structures as well as advanced algorithms for graphs, string, computational geometry and artificial intelligence. Students should seek to develop a solid understanding of common and practical data structures as well as techniques used in their implementation to solve real world problems. |
| 授業スケジュール ／Class schedule |
1. Introduction: Review of fundamental data structures and algorithms as well as theory and techniques to analyze algorithms. 2. Balanced Tree: Basic Binary Search Trees, Treap, Red-Black Trees, AVL Trees, etc. 3. Range Query: Segment Trees, Range Minimum Query, Lazy Evaluation, Heavy-Light Decomposition, etc. 4. Sets: Union Find Trees, Merge Techniques, Persistent Data Structures, etc. 5. Algorithms on String: KMP, BM, Suffix Arrays and Trees, Rolling Hash, Trie, etc. 6. Graph Algorithms: Bridges, Articulation Points, Strongly Connected Components, Max-Flow, Min-Cost-Flow, Bipartite Matching, etc. 7. Computational Geometry. Closest Pairs, Minimum Enclosing Circle, Range Search, Sweep Algorithms, etc. It is subject to change, so some of these topics may be omitted and additional topics can be selected depending on the progress. Each week is divided into two parts: the first half consists of lecture-style sessions, and the second half is dedicated to practical exercises where students work on specific assignments. Before each class, students must review the lecture materials regarding the keywords listed in the schedule. Any assignments not completed during the exercise periods must be finished by the designated deadline. Approximately 5 hours of combined preparation and review per session. |
| 教科書 ／Textbook(s) |
1. Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2. Algorithm Design Manual, Steven S Skiena. 3. Algorithm Design, J. Kleinberg, E. Tardos |
| 成績評価の方法・基準 ／Grading method/criteria |
Assignments 50 % Examinations 50 % |
| 履修上の留意点 ／Note for course registration |
• Reviewing undergraduate courses Algorithms and Dada Structures I and II is expected. • The students should have basic skill of programming in C++ or Java. |
| 参考(授業ホームページ、図書など) ／Reference (course website, literature, etc.) |
https://onlinejudge.u-aizu.ac.jp/ |