Perspectives in Mathematical Sciences III

Nobuo YOSHIDA Professor

Department: Graduate School of Mathematics

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) Yuu-sei-sha, 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

d-dimensional 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(=Non-attendance) (see the part-wise 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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