### 2016　Graduate Methodologies in Cognition, Mathematics and Information F1

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Graduate major in Social and Human Sciences
Instructor(s)
Murai Hajime  Kuriyama Naoko  Inohara Takehiro
Course component(s)
Lecture
Day/Period(Room No.)
Tue1-2(W9-707)
Group
-
Course number
SHS.M462
Credits
2
2016
Offered quarter
3-4Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

In this course, students study major methods of multivariate analysis such as regression analysis, quantification method, principal component analysis and also network analysis in order to deal with phenomenon mathematically based on practical examples. Moreover, students study how to select those methods properly against practical problems through exercises.

This course aims to cultivate the students’ abilities to: select a proper methodology from various mathematical methods in order to cooperate with real problems; decide what necessary data is; develop an effective research plan.

### Student learning outcomes

At the end of this course, students will be able to:
1) Understand characteristics and merits of various mathematical methods.
2) Select proper methods for practical complicated problem solving.
3) Develop mathematical research plan which is appropriate for objects and goals.

### Keywords

Multivariate analysis, Network analysis

### Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
-

### Class flow

In former part of a class, a lecture about characteristics of mathematical method is done based on an example of practical research. In latter half of a class, an exercise about actual social problems is done. Students consider about what data should be extracted from an object and what method should be applied and also what result will be obtained. At last, a research plan is developed based on result of consideration.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Guidance Investigate what methods are included in multivariate analysis, and network analysis.
Class 2 Hypothesis testing, analysis of variance Develop a research plan which utilizes hypothesis testing　or analysis of variance.
Class 3 Simple regression, multiple regression, mathematical quantification theory class I Develop a research plan which utilizes simple regression, multiple regression, or mathematical quantification theory class I.
Class 4 Factor analysis, principal component analysis Develop a research plan which utilizes factor analysis or principal component analysis.
Class 5 Mathematical quantification theory class III Develop a research plan which utilizes mathematical quantification theory class III.
Class 6 Covariance structure analysis Develop a research plan which utilizes covariance Structure Analysis
Class 7 Discriminant analysis, mathematical quantification theory class II Develop a research plan which utilizes discriminant analysis or mathematical quantification theory class II.
Class 8 Multi-dimensional scaling Develop a research plan which utilizes multi-dimensional scaling.
Class 9 Cluster analysis Develop a research plan which utilizes Cluster analysis.
Class 10 Basis of network Develop a research plan which utilizes network representation.
Class 11 Sub graph, creek Develop a research plan which utilizes concepts of sub graph or creek.
Class 12 Network centrality Develop a research plan which utilizes Network centrality.
Class 13 Structural analysis of network Develop a research plan which utilizes structural analysis of network.
Class 14 Network and randomness Develop a research plan which utilizes network which includes randomness.
Class 15 Small world and scale free Develop a research plan which utilizes large scale network.

### Textbook(s)

Nothing required.

### Reference books, course materials, etc.

Eric D. Kolaczyk, “Statistical Analysis of Network Data: Methods and Models”, Springer
T. W. Anderson, “An Introduction to Multivariate Statistical Analysis”, Wiley-Interscience

### Assessment criteria and methods

Feedback sheets are submitted in each class

### Related courses

• SHS.M441 ： Graduate Lecture in Cognition, Mathematics and Information S1A
• SHS.M442 ： Graduate Lecture in Cognition, Mathematics and Information S1B
• SHS.D463 ： Analyses and Modeling Techniques of Educational Data
• LAT.A401 ： Introduction to Psychological and Educational Measurement A
• LAT.A402 ： Introduction to Psychological and Educational Measurement B

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students should have successfully completed fundamental linear algebra.

### Other

This course consists of the content of science. 