Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Dissertation (Ph.D.)								◎
Topics in Algebraic Number Theory (Ⅰ)		◎
Functional Analysis (Ⅰ)	◎
Functional Analysis (Ⅱ)	◎
Partial Differential Equations (Ⅰ)	◎
Partial Differential Equations (Ⅱ)	◎
Algebraic Number Theory (Ⅰ)		◎
Algebraic Number Theory (Ⅱ)		◎
Group Representations (Ⅰ)		◎
Group Representations (Ⅱ)		◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Algebraic Geometry (Ⅰ)			◎
Algebraic Geometry (Ⅱ)			◎
Regression Analysis (Ⅰ)						◎
Regression Analysis (Ⅱ)						◎
Nonparametric Regression Models						◎
Differential Topology (Ⅰ)			◎
Differential Topology (Ⅱ)			◎
Algebraic Topology (Ⅰ)			◎
Algebraic Topology (Ⅱ)			◎
Multivariates Statistical Analysis (Ⅰ)						◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Multivariates Statistical Analysis (Ⅱ)						◎
Number Theory (Ⅰ)		◎
Number Theory (Ⅱ)		◎
Mathematical Statistics (Ⅰ)						◎
Mathematical Statistics (Ⅱ)						◎
Advanced Statistical Inference (Ⅰ)						◎
Advanced Statistical Inference (Ⅱ)						◎
Ring Theory (Ⅰ)		◎
Ring Theory (Ⅱ)		◎
Commutative Algebra (Ⅰ)		◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Commutative Algebra (Ⅱ)		◎
Lie Group (Ⅰ)			◎
Lie Group (Ⅱ)			◎
Coding Theory (Ⅰ)		◎
Coding Theory (Ⅱ)		◎
Calculus of Variation (Ⅰ)	◎
Calculus of Variation (Ⅱ)	◎
Real Analysis (Ⅰ)	◎
Real Analysis (Ⅱ)	◎
Differential Geometry (Ⅰ)			◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Differential Geometry (Ⅱ)			◎
Financial Mathematics					◎
Differential Topology			◎
Combinatorics (Ⅰ)							◎
Combinatorics (Ⅱ)							◎
Probability Theory (Ⅰ)					◎
Graph Theory (Ⅰ)							◎
Graph Theory (Ⅱ)							◎
Time Series (Ⅰ)					◎
Algebraic Geometry			◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Introduction to Global Differential Geometry	◎
Algebra (Ⅰ)		◎
Algebra (Ⅱ)		◎
Colloquium (Ⅰ)								◎
Colloquium (Ⅱ)								◎
Colloquium (Ⅲ)								◎
Colloquium (Ⅳ)								◎
Quantum Groups		◎
Financial Mathematics (Ⅰ)					◎
Financial Mathematics (Ⅱ)					◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Statistical Methods for Forecasting						◎
Regression Analysis						◎
Stochastic Calculus					◎
Algebraic Graph Theory							◎
Lie Algebra (Ⅰ)		◎
Lie Algebra (Ⅱ)		◎
Graph Algorithms							◎
Fast Algorithms				◎
Algorithms							◎
Game Theory					◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Introduction to Stochastic Processes					◎
Iwasawa Theory		◎
The Arithmetic Theory of Modulat Functions		◎
Rings with Involution (Ⅰ)		◎
Rings with Involution (Ⅱ)		◎
Cryptography		◎
Riemannian Geometry			◎
Combinatorial Optimization (Ⅰ)							◎
Combinatorial Optimization (Ⅱ)							◎
Algebraic Combinatorics (Ⅰ)		◎
Capabilities \ Core Courses	A. Ability to handle continuity phenomena and approximations. B. Ability to operate with symbols and digits. C. Ability to visualize space, shape, and images. D. Ability of computer to do mathematics. E. Ability to apply stochastic mathematics. F. Ability to handle large amount of data. G. Ability to do mathematics relating to discrete models. H. Ability to do independent researches and to write thesis.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]
Algebraic Combinatorics（Ⅱ）		◎
Topology (Ⅰ)			◎
Topology (Ⅲ)			◎
Geometry Flow (Ⅰ)			◎
Geometry Flow (Ⅱ)			◎
Cauchy-riemann Geometry			◎
Introduction to Geometrical Methods and Thought			◎
Group Representation Theory		◎
Special Topics on the Modular Forms and Theta Functions(Ⅰ)	◎
Special Topics on the Modular Forms and Theta Functions(Ⅱ)	◎
Core Capabilities	A Ability to handle continuity phenomena and approximations.	B Ability to operate with symbols and digits.	C Ability to visualize space, shape, and images.	D Ability of computer to do mathematics.	E Ability to apply stochastic mathematics.	F Ability to handle large amount of data.	G Ability to do mathematics relating to discrete models.	H Ability to do independent researches and to write thesis.
Number of Core Courses （Number of All Courses: 90）	11	26	19	1	8	11	9	5