Curriculum | Mathematics and Physics Unit,"Multiscale Analysis,Modelling and Simulation" Top Global University Project,Waseda University

The Math-Phys Unit started a new course for doctoral students!

Recruitment of SGU course of mathematical and physical sciences will start on February 18, 2022.
Please check the following information.

1. About the SGU course of Mathematical and Physical Sciences

The SGU Unit course is offered by the Faculty of Science and Engineering at Waseda University. The course regards research and education as being ''two sides of a coin", prompting students of the program to connect different fields of science through participation in seminars, workshops, forums, and symposiums．
The course is supported by the Mathematics and Physics unit "Multiscale Analysis and Modelling", our top global university project that promotes research and education in collaboration with prominent researchers and partner universities in Europe and America. As part of graduate education, the course offers a unique curriculum in an attempt to encourage flexible thinking, multiple perspectives, and interaction with different research fields, and to help nurture "multi-disciplinary knowledge". Researchers from each department in Faculty of Science and Engineering are involved in the development of the program.

2. Aim of the SGU course

The program carries out research and education by uncovering the mathematically "essential part" of the underlying structure of various phenomena through cross sectoral cooperation among researchers from multiple disciplines including mathematics, physics, information technology and engineering. The main focuses of the course are:
1)Formulation of mathematical models describing various phenomena
2)Verification and validation of these mathematical models through numerical simulation.
To meet these goals, the program conducts R&D, planning, and support for education for doctoral programs based on our multidisciplinary achievements. The mission of the course is to produce internationally competitive researchers and to produce individuals who create a new, comprehensive "system of intelligence" based on mathematics and physics that constitutes valuable contributions to information science and social science, not only to science and engineering, but acting as a bridge between mathematics, physics and the other branches of science. We offer excellent students financial assistance and support for their research activities to help cultivate such human resources.

3. Admission Requirements & Application Procedure

For admission requirements and application procedure, please see the following documents (Japanese documents).
Please note that the application period for admission in April 2022 is from February 18 to February 28 17:00, 2022.

　- Admission Requirements(Japanese) （PDF）
　- Application Form （WORD）

Lectures of The SGU Course of Mathematical and Physical Sciences

2022(April, 2022 - March, 2023) ▼

For details of these lectures please refer to Syllabus.

2021 (April, 2021 - March, 2022) ▼

For details of these lectures please refer to Syllabus.

2020 (April, 2020 - March, 2021) ▼

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field	Course Title	Instructor	Term	credit
Math	Foundation of Mathematical Analysis 1	Hideo Kozono	Spring semester	2 credits
Math	Foundation of Mathematical Analysis 2	Yoshihiro Shibata	Fall semester	2 credits
Math	Foundation of Geometry 1	Martin Guest	Spring semester	2 credits
Math	Computer Assisted Proof of Nonlinear Equations	Shinichi Oishi	Spring semester	2 credits
A Mech	Foundation of Geometry 2	Hiroaki Yoshimura	Spring semester	2 credits
A Mech	Heat Transfer	Amano Yoshiharu, Kiyoshi Saito, Niccolo Giannetti, Yamaguchi Seiichi, Hifni Mukhtar Ariyadi	Spring semester	2 credits
M Mech	Advanced Topics in Applied Mechanics of Fluid-Structure Interactions	Kenji Takizawa	Fall semester	2 credits
Phys	Mathematical Formulation of Quantum Mechanics	Tohru Ozawa	Spring semester	2 credits
Phys	Mathematical Formulation of Classical Field Theory	Tohru Ozawa	Fall semester	2 credits
Phys	Advanced Theoretical Quantum Physics	Kazuya Yuasa	Spring semester	2 credits
Phys	Quantum Information Theory	Kazuya Yuasa	Spring semester	2 credits	We don't hold in AY2020
Phys	Physics of Non-Equilibrium System A	Yoshihiro Yamazaki	Fall semester	2 credits
Phys	Physics of Non-Equilibrium System B	Yoshihiro Yamazaki	Fall semester	2 credits	We don't hold in AY2020
Phys	Computational Biophysics	Mitsunori Takano	Fall semester	2 credits	We don't hold in AY2020

B) Special Lectures
Field	Course Title	Instructor	Term	credit
Math	Advanced Study of Nonlinear Mechanics	Hiroaki Yoshimura, Guest Martin, Peng Linyu	intensive	4 credits
Math	Special Lecture on Mathematical Fluid Mechanics	Hideo Kozono, Yoshihiro Shibata, Mads Kyed, Shuichi Kawashima	intensive	4 credits
Math	Special Lecture on SPDE	Funaki Tadahisa	intensive	2 credits
M Mech	Fluid Mechanics of Computing	Kenji Takizawa, Tayfun E. Tezduyar	intensive (Spring semester)	2 credits
Phys	Special Lecture on Quantum Physics	Kazuya Yuasa, Hiromichi Nakazato, Ozawa Tohru, Vladimir Simeonov Gueorguiev	intensive	4 credits
Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops. Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.

C) Independent Studies
Field	Course Title	Instructor	Term	credit
General Studies	Internship	Takashi Ariga	Full year	2 credits

2019 (April, 2019 - March, 2020) ▼

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field	Course Title	Instructor	Term	credit
Math	Foundation of Mathematical Analysis 1	Hideo Kozono	Spring semester	2 credits
Math	Foundation of Mathematical Analysis 2	Yoshihiro Shibata	Fall semester	2 credits
Math	Foundation of Geometry 1	Martin Guest	Spring semester	2 credits
Math	Computer Assisted Proof of Nonlinear Equations	Shinichi Oishi	Spring semester	2 credits
A Mech	Foundation of Geometry 2	Hiroaki Yoshimura	Spring semester	2 credits
A Mech	Heat Transfer	Amano Yoshiharu, Kiyoshi Saito, Niccolo Giannetti, Yamaguchi Seiichi, Yoshida Akira	Spring semester	2 credits
M Mech	Advanced Topics in Applied Mechanics of Fluid-Structure Interactions	Kenji Takizawa	Fall semester	2 credits
Phys	Mathematical Formulation of Quantum Mechanics	Tohru Ozawa	Spring semester	2 credits
Phys	Mathematical Formulation of Classical Field Theory	Tohru Ozawa	Fall semester	2 credits	We don't hold in AY2019
Phys	Advanced Theoretical Quantum Physics	Kazuya Yuasa	Spring semester	2 credits	We don't hold in AY2019
Phys	Quantum Information Theory	Kazuya Yuasa	Spring semester	2 credits
Phys	Physics of Non-Equilibrium System A	Yoshihiro Yamazaki	Fall semester	2 credits	We don't hold in AY2019
Phys	Physics of Non-Equilibrium System B	Yoshihiro Yamazaki	Fall semester	2 credits
Phys	Computational Biophysics	Mitsunori Takano	Fall semester	2 credits

B) Special Lectures
Field	Course Title	Instructor	Term	credit
Math	Advanced Study of Nonlinear Mechanics	Hiroaki Yoshimura, Martin Guest	intensive	4 credits
Math	Special Lecture on Mathematical Fluid Mechanics (Advanced Study of Mathematical Fluid Dynamics)	Hideo Kozono, Yoshihiro Shibata, Masao Yamazaki	intensive	4 credits
M Mech	Fluid Mechanics of Computing	Kenji Takizawa	intensive (Spring semester)	2 credits
Phys	Special Lecture on Quantum Physics	Kazuya Yuasa, Hiromichi Nakazato, Ozawa Tohru	intensive	4 credits
Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops. Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.

C) Independent Studies
Field	Course Title	Instructor	Term	credit
General Studies	Internship	Takashi Ariga	Full year	2 credits

2018 (April, 2018 - March, 2019) ▼

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field	Course Title	Instructor	Term	credit
Math	Foundation of Mathematical Analysis 1	Hideo Kozono	Spring semester	2 credits
Math	Foundation of Mathematical Analysis 2	Yoshihiro Shibata	Fall semester	2 credits
Math	Foundation of Geometry 1	Yasushi Homma	Spring semester	2 credits
Math	Computer Assisted Proof of Nonlinear Equations	Shinichi Oishi	Spring semester	2 credits
A Mech	Foundation of Geometry 2	Hiroaki Yoshimura	Spring semester	2 credits
A Mech	Heat Transfer	Kiyoshi Saito	Spring semester	2 credits
M Mech	Advanced Topics in Applied Mechanics of Fluid-Structure Interactions	Kenji Takizawa	Fall semester	2 credits
Phys	Mathematical Formulation of Quantum Mechanics	Tohru Ozawa	Spring semester	2 credits
Phys	Mathematical Formulation of Classical Field Theory	Tohru Ozawa	Fall semester	2 credits
Phys	Advanced Theoretical Quantum Physics	Kazuya Yuasa	Spring semester	2 credits
Phys	Quantum Information Theory	Kazuya Yuasa	Fall semester	2 credits	We don't hold in AY2018
Phys	Physics of Non-Equilibrium System A	Yoshihiro Yamazaki	Fall semester	2 credits
Phys	Physics of Non-Equilibrium System B	Yoshihiro Yamazaki	Fall semester	2 credits	We don't hold in AY2018
Phys	Computational Biophysics	Mitsunori Takano	Fall semester	2 credits	We don't hold in AY2018

B) Special Lectures
Field	Course Title	Instructor	Term	credit
Math	Advanced Study of Nonlinear Mechanics	Hiroaki Yoshimura, Guest Martin	intensive	4 credits
Math	Special Lecture on Mathematical Fluid Mechanics (Advanced Study of Mathematical Fluid Dynamics)	Hideo Kozono, Yoshihiro Shibata	intensive	4 credits
M Mech	Fluid Mechanics of Computing	Kenji Takizawa	intensive (Spring semester)	2 credits
Phys	Special Lecture on Quantum Physics	Hiromichi Nakazato, Kazuya Yuasa	intensive	4 credits
Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops. Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.

C) Independent Studies
Field	Course Title	Instructor	Term	credit
General Studies	Internship	Takashi Ariga	Full year	2 credits

2017 (April, 2017 - March, 2018) ▼

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field	Course Title	Instructor	Term	credit
Math	Foundation of Mathematical Analysis 1	Hideo Kozono	Spring semester	2 credits
Math	Foundation of Mathematical Analysis 2	Yoshihiro Shibata	Fall semester	2 credits
Math	Foundation of Geometry 1	Guest Martin	Spring semester	2 credits
Math	Computer Assisted Proof of Nonlinear Equations	Shinichi Oishi	Spring semester	2 credits
A Mech	Foundation of Geometry 2	Hiroaki Yoshimura	Spring semester	2 credits
M Mech	Advanced Topics in Applied Mechanics of Fluid-Structure Interactions	Kenji Takizawa	Fall semester	2 credits
Phys	Mathematical Formulation of Quantum Mechanics	Tohru Ozawa	Spring semester	2 credits
Phys	Quantum Information Theory	Kazuya Yuasa	Fall semester	2 credits
Phys	Physics of Non-Equilibrium System B	Yoshihiro Yamazaki	Fall semester	2 credits
Phys	Computational Biophysics	Mitsunori Takano	Fall semester	2 credits
We don't hold "Mathematical Formulation of Classical Field Theory"* (Tohru Ozawa/Fall semester/2 credits), "Advanced Theoretical Quantum Physics"(Kazuya Yuasa/Spring semester/2 credits) and "Physics of Non-Equilibrium System A"(Yoshihiro Yamazak/Spring semester/2 credits) in AY2017. A Mech: the Department of Applied Mechanics and Aerospace Engineering M Mech: the Department of Modern Mechanical Engineering

B) Special Lectures
Field	Course Title	Instructor	Term	credit
Math	Advanced Study of Nonlinear Mechanics	Hiroaki Yoshimura, Guest Martin	intensive	4 credits
Math	Special Lecture on Mathematical Fluid Mechanics (Advanced Study of Mathematical Fluid Dynamics)	Hideo Kozono, Yoshihiro Shibata	intensive	4 credits
M Mech	Fluid Mechanics of Computing	Kenji Takizawa	intensive (Spring semester)	2 credits
Phys	Special Lecture on Quantum Physics	Hiromichi Nakazato, Kazuya Yuasa	intensive	4 credits
Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops. Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.

C) Independent Studies
Field	Course Title	Instructor	Term	credit
General Studies	Internship	Takashi Ariga	Full year	2 credits

2016 (April, 2016 - March, 2017) ▼

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field	Course Title	Instructor	Term	credit
Math	Foundation of Mathematical Analysis 1	Yoshihiro Shibata	Spring semester	2 credits
Math	Foundation of Mathematical Analysis 2	Hideo Kozono	Fall semester	2 credits
Math	Foundation of Geometry 1	Guest Martin	Fall semester	2 credits
Math	Computer Assisted Proof of Nonlinear Equations	Shinichi Oishi	Spring semester	2 credits
Mech	Foundation of Geometry 2	Hiroaki Yoshimura	Spring semester	2 credits
Phys	Mathematical Formulation of Quantum Mechanics	Tohru Ozawa	Spring semester	2 credits
Phys	Mathematical Formulation of Classical Field Theory	Tohru Ozawa	Fall semester	2 credits
Phys	Advanced Theoretical Quantum Physics	Kazuya Yuasa	Spring semester	2 credits
Phys	Physics of Non-Equilibrium System A	Yoshihiro Yamazaki	Spring semester	2 credits
* We don't open "Advanced Theoretical Quantum Physics" (Kazuya Yuasa/Spring semester/2 credits) and "Physics of Non-Equilibrium System B" (Yoshihiro Yamazak/Fall semester/2 credits) in 2016.

B) Special Lectures
Field	Course Title	Instructor	Term	credit
Math	Advanced Study of Nonlinear Mechanics	Hiroaki Yoshimura, Guest Martin	intensive	4 credits
Math	Special Lecture on Mathematical Fluid Mechanics (Advanced Study of Mathematical Fluid Dynamics)	Hideo Kozono, Yoshihiro Shibata	intensive	4 credits
Phys	Special Lecture on Quantum Physics	Hiromichi Nakazato, Kazuya Yuasa	intensive	4 credits
*Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops.

C) Independent Studies
Field	Course Title	Instructor	Term	credit
General Studies	Internship	Nozomu Togawa	Full year	2 credits

2015 (April, 2015 - March, 2016) ▼

Course Title	Tnstructor	Course Description	Goals and objectives of the lesson
Special Lecture on Mathematical Fluid Mechanics Intensive course (Fall semester)	Hideo KOZONO Yoshihiro SHIBATA Maria SCHONBEK Yukihito SUZUKI Masao YAMAZAKI	1. Prof. Kozono's Lecture Critical Sobolev inequality in Besov spaces andits application to the Beale-Kato-Majda blow-up criterion Abstract: It is known that the space H^1,n(Rⁿ)is continuously embedded in L_p(Rⁿ) for all p < ∞, but not in L_∞(Rⁿ). More precisely, H^1,n(Rⁿ) is embedded into BMO space. In the lecture, we give alogarithmic L_∞ bound of functions in terms on BMO and H^1,p(Rⁿ)(n < p < ∞). Furthermore, the generalization to the Besov space in B⁰_∞,∞(Rⁿ)is established. As an application, we show such a blow-upcriterion as Beale-Kato-Majda type for local strong solutions to the Euler andthe Navier-Stokes equations. 2. Prof. Shibata's Lecture The Free Boundary Problem for the Navier-Stokes Equations Abstract: In this lecture, we prove the local and global well-posedness of the free boundary problem for the Navier-Stokes equations. The key issues are to prove the maximal regularity and the stability of the semi-group for the linearized problem. The maximalo regularity is proved with the help of the R boundedness of the Stokes operators with free boundary condition. The stability of the semi-gorup is proved by some sharp analysis of the spectrum near the origin.
Topics in Numerical Analysis B (Spring semester)	Shinichi OISHI Segfried M. RUMP	We introduce so-called "Verification methods" in this lecture. These are numerical methodscomputing correct error bound for the true result including a proof ofsolvability and possibly uniqueness. The proof of correctness is withmathematical rigor including in particular discretization and rounding errors.The methods are introduced with INTLAB, the Matlab/Octave toolbox for ReliableComputing.	To understand possible weaknesses of numerical methods, to understand principle of verification methods, and to be able to devise and write new verification methods.

Course Title

Tnstructor

Course Description

Goals and objectives of the lesson

Special Lecture on Mathematical Fluid Mechanics
Intensive course (Fall semester)

Hideo KOZONO

Yoshihiro SHIBATA

Maria SCHONBEK

Yukihito SUZUKI

Masao YAMAZAKI

1. Prof. Kozono's Lecture
Critical Sobolev inequality in Besov spaces andits application to the Beale-Kato-Majda blow-up criterion
Abstract: It is known that the space H^1,n(Rⁿ)is continuously embedded in L_p(Rⁿ) for all p < ∞, but not in L_∞(Rⁿ). More precisely, H^1,n(Rⁿ) is embedded into BMO space. In the lecture, we give alogarithmic L_∞ bound of functions in terms on BMO and H^1,p(Rⁿ)(n < p < ∞). Furthermore, the generalization to the Besov space in B⁰_∞,∞(Rⁿ)is established.
As an application, we show such a blow-upcriterion as Beale-Kato-Majda type for local strong solutions to the Euler andthe Navier-Stokes equations.

2. Prof. Shibata's Lecture
The Free Boundary Problem for the Navier-Stokes Equations Abstract: In this lecture, we prove the local and global well-posedness of the free boundary problem for the Navier-Stokes equations. The key issues are to prove the maximal regularity and the stability of the semi-group for the linearized problem. The maximalo regularity is proved with the help of the R boundedness of the Stokes operators with free boundary condition. The stability of the semi-gorup is proved by some sharp analysis of the spectrum near the origin.

Topics in Numerical Analysis B
(Spring semester)

Shinichi OISHI

Segfried M. RUMP

We introduce so-called "Verification methods" in this lecture. These are numerical methodscomputing correct error bound for the true result including a proof ofsolvability and possibly uniqueness. The proof of correctness is withmathematical rigor including in particular discretization and rounding errors.The methods are introduced with INTLAB, the Matlab/Octave toolbox for ReliableComputing.

To understand possible weaknesses of numerical methods, to understand principle of verification methods, and to be able to devise and write new verification methods.