Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Informatics and Data Science Program
Lecture Code WSN21901 Subject Classification Specialized Education
Subject Name Analysis in Information Science
Subject Name
アナリシス イン インフォーメーション サイエンス
Subject Name in
Analysis in Information Science
シマ タダシ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Thur1-2,Fri1-2
Lesson Style Lecture Lesson Style
(More Details)
My teaching style in this class is heavily depend on a blackboard. 
Credits 2.0 Class Hours/Week   Language of Instruction E : English
Course Level 5 : Graduate Basic
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords graph, Markov chain, random walk, harmonic function. 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
Class Objectives
/Class Outline
The aim of this course is to introduce some basic concepts of the theory of stochastic processes and to show the application of them through the relationship between random walks on graphs and electrical circuits.
Class Schedule In this course, I want to show an aspect of the relation between the theory of stochastic processes and potential theory through random walks on graphs.  

In my plan, the lecture starts from the very beginning of the probability theory. That is introducing the concepts of probability space and conditional probabilities.
We then treat one of the most important stochastic processes called Markov processes.
The important concepts, transition matrices, Markov properties, stopping times are introduced.
The harmonic functions are treated in connection with the absorption probability.
We then consider the Dirichlet problems on graphs.
Solutions of the Dirichlet problems are constructed by using the idea of stochastic processes.
We will then go into another subject: the correspondence between electrical networks and random walks on graphs.
From the information of a random walk on a graph, we can draw an electrical network.
The currents and voltages at vertices of the electric network are given as the probabilities or expectations under the associated random walk.
Finally, I want to apply these relations to establish the criterion for recurrence and transience of random walks on graphs.

Random walks and electric networks, Doyle, P.G. and Snell, J.L.,
The mathematical association of America, 1984
Modern Graph Theory, Bollobas, B., Springer, 1998
Markov Chain, Norris, J.R., Cambridge University Press, 1996
PC or AV used in
(More Details) I will distribute handouts through moodle. 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Read the copies very carefully and solve exercises. 
Grading Method Your grade in the class will be determined by a report. The problem sheets for the report will be provided at the beginning of July and the deadline is the middle of Aug. (tentative)
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
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