Admission Requirements & Application Procedure

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Admission Requirements & Application Procedure
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Admission Requirements & Application Procedure

 Recruitment of TGU course of mathematical and physical sciences
 Lectures of the TGU Course of Mathematical and Physical Sciences

Students who wish to take the TGU course of Mathematical and Physical Sciences should apply to the Senior Dean of Faculty of Science and Engineering with the necessary documents attached to the application form. Detailed recruitment information will be announced each time.

Recruitment of TGU course (Enrollment in April 2024)

For detail information about the admission requirements, please see the following documents (Japanese documents).

Schedule

Application period for admission in April 2024: January 10 – February 28 17:00
Interview Date (tentative): March 1

Required documents

Application Form（Please download the following form）
Documents confirming courses taken after the bachelor’s program and their grades

Submission method

Please send an E-mail to [email protected] attached with required documents.

For details of these lectures please refer to Syllabus.

AY2021 (April, 2021 - March, 2022)

For details of these lectures please refer to Syllabus.

AY2020 (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

AY2019 (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

AY2018 (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

AY2017 (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

AY2016 (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

AY2015 (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.

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