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Graduate School
Perspectives in Mathematical Sciences III
Nobuo YOSHIDA Professor
Department: Graduate School of Mathematics
Class Time:  2016 Spring Tuesday 
Recommended for:  School of Science 4th year students 
Course Overview
The Purpose of the Course
This course is designed as one of the English courses which the Graduate School of Mathematics provides for the graduate and undergraduate students not only from foreign countries, but also domestic students who wish to study abroad or to communicate with foreign scientists in English. All course activities, including lectures, homework assignments, questions and consultations are in English. The purpose of this course is to introduce and explain various methods in mathematical sciences. This year, the course is organized by three instructors with different coverage of subjects from a variety of fields in mathematics.
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Syllabus
The Plan of the Course
The course is divided into three parts (Part 1 by Yamagami, Part 2 by Yoshida and Part 3 by Ito) and the detail of part division will be announced at the first lecture time of the course. See the part syllabus provided by each instructor for more information.
Keywords
See the syllabus of each instructor.
Required Knowledge
Working knowledge of basic undergraduate mathematics, including calculus and linear algebra, is required.
References
See the syllabus of each instructor.
Attendance
This course is open for all students at Nagoya University as one of the "open subject" of general education.
Additional Advice
See the syllabus of each instructor.
Part 2: Introduction to Percolation
References
[1] Grimmett, G. : "Percolation", Springer Verlag, 2nd Ed. (1999).
[2] Higuchi, Y.: "Percolation" (In Japanese) Yuuseisha, 2nd Ed. (2011)
The Purpose of the Course
The purpose of this course is to provide an introduction to the theory of percolation
The Plan of the Course
Here is a tentative outline:
1. Percolation and random variable.
2. The critical probability.
3. The infinite cluster.
Keywords
ddimensional integer lattice, percolation, critical probability, infinite cluster [Required Knowledge] basic notion in modern probability theory such as probability space, random variables and their independence.
Attendance
This course is open for all students of Nagoya University
Additional Advice
The reference [2] is easy to read. My office hours are Thursday 14:30  15:30.
The Method of Evaluation
Three instructors evaluate their own parts independently in the order S,A,B,C,F,N(=Nonattendance) (see the partwise course designs for further information) and the final grade of the couse is set to be the middle of these three scores (for example, if you get A,C,F as part scores, the course grade is set to be C).
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Class Materials
Lecture Handout
 all of lecture note Percolation (PDF, 10509KB)
 section0 Introdution (PDF, 1014KB)
 section1 The percolation probability (PDF, 2652KB)
 section2 Ergodic theory in the context of percolation (PDF, 2960KB)
 section3 Infinite cluster (PDF, 3825KB)
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Page last updated August 5, 2016
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.