The MathPhys Unit started a new course for doctoral students!
Master's students can take the Basic Lectures which are conditions for the admittion of this course!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 "multidisciplinary
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 September 2021 is
from June 23 to June 30 17:00, 2021.
Lectures of The SGU Course of Mathematical and Physical Sciences
2021(April, 2021  March, 2022) ▼
For details of these lectures please refer to Syllabus.
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 FluidStructure 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 NonEquilibrium System A  Yoshihiro Yamazaki  Fall semester  2 credits  
Phys  Physics of NonEquilibrium 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 Minicourses 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 
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 FluidStructure 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 NonEquilibrium System A  Yoshihiro Yamazaki  Fall semester  2 credits  We don't hold in AY2019 
Phys  Physics of NonEquilibrium 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 Minicourses 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 
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 FluidStructure 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 NonEquilibrium System A  Yoshihiro Yamazaki  Fall semester  2 credits  
Phys  Physics of NonEquilibrium 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 Minicourses 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 
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 FluidStructure 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 NonEquilibrium 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 NonEquilibrium 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 Minicourses 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 
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 NonEquilibrium 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 NonEquilibrium 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 Minicourses 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 
Course Title  Tnstructor  Course Description  Goals and objectives of the lesson 

Special Lecture on Mathematical Fluid Mechanics 
Hideo KOZONO Yoshihiro SHIBATA Maria SCHONBEK Yukihito SUZUKI Masao YAMAZAKI 
1. Prof. Kozono's Lecture 

Topics in Numerical Analysis B 
Shinichi OISHI Segfried M. RUMP 
We introduce socalled "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. 