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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Service Learning (a)
Service Learning (b)
Calculus (general Mathematics) (a)(1)	◎
Calculus (general Mathematics) (a)(2)	◎
Calculus (General Mathematics) (B)	◎
Linear Algebra (Ⅰ)		◎
Linear Algebra (Ⅱ)		◎
Computer Programming									◎
Advanced Linear Algebra (Ⅰ)		◎
Advanced Linear Algebra (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Advanced Calculus (Ⅰ)	◎
Advanced Calculus (Ⅱ)	◎
Introduction to Algebra (Ⅰ)		◎
Introduction to Algebra (Ⅱ)		◎
Introductory Number Theory		◎
Introduction to Ordinary Differential Equations	◎
Introduction to Partial Differential Equations	◎
Geometry			◎
Introduction to Manifolds			◎
Introduction to Statistics						◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Introduction to Number Theory		◎
Introduction to Mathematical Statistics (Ⅰ)						◎
Introduction to Mathematical Statistics (Ⅱ)						◎
Functions of a Complex Variable	◎
Introduction to Probability Theory					◎
Introduction to Computational Mathematics				◎
Statistics						◎
Elliptic Functions A Classical Approach (Ⅰ)			◎
Elliptic Functions A Classical Approach (Ⅱ)			◎
Elementary Number Theory (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Elementary Number Theory (Ⅱ)		◎
Honors Algebra (Ⅰ)		◎
Honors Algebra (Ⅱ)		◎
Honors Advanced Calculus (Ⅰ)	◎
Honors Advanced Calculus (Ⅱ)	◎
Introduction to Mathematical Analysis(Ⅰ)	◎
Introduction to Mathematical Analysis(Ⅱ)	◎
Introduction to Mathematical Analysis(Honor)(Ⅰ)	◎
Introduction to Mathematical Analysis(Honor)(Ⅱ)	◎
Introduction to Number Theory(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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Introduction to Number Theory(Ⅱ)		◎
Calculus(Ⅰ)	◎
Calculus(Ⅱ)	◎
Linear Algebra (Ⅱ)		◎
Introduction to Algebra(Ⅱ)		◎
Introduction to Mathematical Analysis(Ⅱ)	◎
Introduction to Probability Theory					◎
Introduction to Topology			◎
Preview of Calculus	◎
Pre-calculus	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Basic measure theory and distribution theory	◎	◎
Pre-calculus (I)	◎
Functions of A Complex Variable II	◎
CALCULUS (1)	◎
CALCULUS (2)	◎
CALCULUS (3)	◎
CALCULUS (4)	◎
Calculus 4 (Applications in Economics and Management)	◎
Measure and Probabilistic models					◎
Precalculus	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Mathematical statistics						◎
Functions of A Complex Variable	◎
Thesis (B.A.)	◎
A Modern Approach of Differential Equations and Applications	◎
Introduction to the Foundation of Mathematics	◎	◎
Introduction to Linear Algebra Ⅰ(Ⅰ)		◎
Service Learning (a)								◎
Service Learning (b)								◎
Introduction to Linear Algebra (Ⅰ)		◎
Introduction to Linear Algebra (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Special Topic on Statistical Inferencei						◎
Statistical and Machine Learning						◎
Mathematical Modeling and Analysis of Infectious Diseases		◎						◎
Aspects of Geometric Analysis		◎						◎
Elliptic curves		◎
Advanced Topics in Combinatorics							◎
Teichmüller theory and moduli space of Riemann surfaces		◎	◎
Functional Analysis (Ⅰ)	◎
Functional Analysis (Ⅱ)	◎
Partial Differential Equations (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Partial Differential Equations (Ⅱ)	◎
Algebraic Number Theory (Ⅰ)		◎
Algebraic Number Theory (Ⅱ)		◎
Group Representations (Ⅰ)		◎
Group Representations (Ⅱ)		◎
Algebraic Geometry (Ⅰ)			◎
Algebraic Geometry (Ⅱ)			◎
Regression Analysis (Ⅰ)						◎
Regression Analysis (Ⅱ)						◎
Topics in 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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Nonparametric Regression Models						◎
Differential Topology (Ⅰ)			◎
Differential Topology (Ⅱ)			◎
Algebraic Topology (Ⅰ)			◎
Algebraic Topology (Ⅱ)			◎
Multivariates Statistical Analysis (Ⅰ)						◎
Multivariates Statistical Analysis (Ⅱ)						◎
Number Theory (Ⅰ)		◎
Number Theory (Ⅱ)		◎
Mathematical Statistics (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Mathematical Statistics (Ⅱ)						◎
Harmonic Analysis (Ⅰ)	◎
Numerical Partial Differential Equations (Ⅰ)	◎			◎
Advanced Statistical Inference (Ⅰ)						◎
Advanced Statistical Inference (Ⅱ)						◎
Lie Group and Lie Algebra		◎
Algebraic Curve		◎
Ring Theory (Ⅰ)		◎
Ring Theory (Ⅱ)		◎
Statistical Computing						◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Commutative Algebra (Ⅰ)		◎
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)	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Differential Geometry (Ⅰ)			◎
Differential Geometry (Ⅱ)			◎
Financial Mathematics					◎
Differential Topology			◎
Combinatorics (Ⅰ)							◎
Combinatorics (Ⅱ)							◎
Probability Theory (Ⅰ)					◎
Probability Theory (Ⅱ)					◎
Graph Theory (Ⅰ)							◎
Graph Theory (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Time Series (Ⅰ)					◎
Topics in Partial Differential Equations (Ⅰ)	◎
Algebraic Geometry			◎
Scientific Computing (Ⅰ)				◎
Scientific Computing (Ⅱ)				◎
Introduction to Global Differential Geometry	◎
Algebra (Ⅰ)		◎
Algebra (Ⅱ)		◎
Colloquium (Ⅰ)								◎
Colloquium (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Colloquium (Ⅲ)								◎
Colloquium (Ⅳ)								◎
Quantum Groups		◎
Functional Analysis	◎
Financial Mathematics (Ⅰ)					◎
Financial Mathematics (Ⅱ)					◎
Statistical Methods for Forecasting						◎
Regression Analysis						◎
Numerical Partial Differential Equations (Ⅱ)				◎
Stochastic Calculus					◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Algebraic Graph Theory							◎
Lie Algebra (Ⅰ)		◎
Lie Algebra (Ⅱ)		◎
Graph Algorithms							◎
Fast Algorithms				◎
Introduction to Computational Mathematics				◎
Computational Finance									◎
Algorithms							◎
Mathematical Software									◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Introduction to Stochastic Processes					◎
Topics in Cryptography		◎
Elementary Number Theory	◎
Iwasawa Theory		◎
The Arithmetic Theory of Modulat Functions		◎
Rings with Involution (Ⅰ)		◎
Rings with Involution (Ⅱ)		◎
Introduction to Algebraic Geometry		◎
Generalized Linear Models						◎
Colding Minicozzi		◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Cryptography		◎
Survival and Recurrent Event Data Analysis						◎
Riemannian Geometry			◎
Combinatorial Optimization (Ⅰ)							◎
Combinatorial Optimization (Ⅱ)							◎
Topics in Geometry Analysis			◎
The Probability Method							◎
Introduction to Manifolds			◎
Algebraic Combinatorics (Ⅰ)		◎
Algebraic Combinatorics（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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Topology (Ⅰ)			◎
Topology (Ⅲ)			◎
Geometry Flow (Ⅰ)			◎
Geometry Flow (Ⅱ)			◎
Cauchy-riemann Geometry			◎
Introduction to Geometrical Methods and Thought			◎
Group Representation Theory		◎
Foundation of Cryptography		◎
Stochastic Processes					◎
Topics in Arithmetic 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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Basic Mathematics			◎
Image Processing				◎
Applied Analysis				◎
Models and Applications of Mathematics in Business and Industries								◎
Introduction to Scientific Computing				◎
Basic Mathematics (Ⅱ)			◎
Numerical Optimization				◎
Equations of Mathematical Physics (Ⅰ)	◎			◎
Introduction to Algebraic Topology		◎
Curvature Flow			◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Morse Theory			◎
Seminar on Group Rings	◎
Quasi-Linear Elliptic Differential Equations	◎
Complex Manifolds			◎
Iwasawa Theory		◎
Special Topics on Computational Eigenvalue Problems				◎
Quasi-Linear Elliptic Differential Equations(Ⅱ)	◎
Algebraic Topology			◎
Lie Groups and Lie Algebras(Ⅰ)		◎
Lie Groups and Lie Algebras(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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Introduction to Mathematical Finance					◎
Topics in Topological Field Theory(Ⅰ)			◎
Topics in Topological Field Theory(Ⅱ)			◎
Topics in Galois Representations		◎
Kaehler Ricci Flow			◎
Topics in Automophic Forms		◎
Homological Algebra		◎
Algebraic Groups		◎
Introduction to Riemann Surfaces			◎
Metric 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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Topics in Algebra		◎
Introduction to Cryptography				◎
Mathematical Modeling						◎
Modern Algebra (Ⅰ)		◎
Methods of Applied Mathematics				◎
Multivariates Statistical Analysis						◎
Numerical Partial Differential Equations				◎
Data Driven Analysis and Optimization in Computer Experiments				◎
Introduction to Symplectic Geometry			◎
Methemetical Control Theory(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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Methemetical Control Theory(Ⅱ)				◎
Special Topics on Nonlinear Partial Differential Equations(Ⅰ)	◎
Special Topics on Nonlinear Partial Differential Equations(Ⅱ)	◎
Geomety Analysis			◎
Topic in Differential Geometry			◎
Topics in Algebra		◎
Topics in Algebra(Ⅱ)		◎
Topic in Differential Geometry(Ⅱ)			◎
Introduction to Cohomology Theories		◎
Numerical Inverse Problem				◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Functions of A Complex Variable(Ⅱ)	◎
Dimension Reduction in Statistical Modeling						◎
Seminar in Geometric Analysis(Ⅰ)			◎
Seminar in Geometric Analysis(Ⅱ)			◎
ODE in Complex Form	◎
Algebraic Number Theory		◎
Ring Theory		◎
Representation Theory of Compact Groups		◎
Experimental Design						◎
High Dimensional Statistical Analysis and Machine Learning						◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Topics in Geometric Analysis(Ⅰ)			◎
Topics in Algebraic Geometry		◎
The Mathematical Theory of Fluid Mechanics and Its Applications(Ⅰ)				◎
The Mathematical Theory of Fluid Mechanics and Its Applications(Ⅱ)				◎
Topics in Algebraic Geometry		◎
Class Field Theory		◎
Topics in Geometric Analysis(Ⅱ)			◎
Introduction to Algebraic K-Theory		◎
Seminar in Algebraic Geometry			◎
Homological Algebra		◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Introduction to Topology			◎
Algebra(Honor Program)(Ⅰ)		◎
Algebra(Honor Program)(Ⅱ)		◎
Analysis(Honor Program)(Ⅰ)	◎
Analysis(Honor Program)(Ⅱ)	◎
Introduction to Complex Analysis	◎
Complex Analysis (Honor Program)	◎
Introduction to Geometry			◎
Modern Algebra (Ⅱ)		◎
General mathematics	◎	◎	◎		◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Gange Theory of Meromomorphic Connection on Riemann Surfaces	◎		◎
Theory of Rings and Groups		◎
Module Theory (I)		◎
Basic measure theory and distribution theory	◎
Nonlinear Analysis	◎
Topics in higher codimensional mean curvature flow	◎
Analysis on manifolds					◎
Elliptic Curve Cryptography				◎
Mathematical statistics for data science				◎
Statistical computing				◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Software Development for Computational and Data Science				◎
Number theory		◎
Seminar in Differential Geometry(II)(Ⅱ)			◎
Gange Theory of Meromomorphic Connection on Riemann Surfaces(Ⅱ)		◎	◎
Introduction to geometric analysis	◎		◎
Introduction to Ricci Flow			◎
Perturbative quantum field theory			◎
Geometry of higher dimension algebraic varieties			◎
Variational Methods and their Applications to Nonlinear PDE	◎
Statistical machine learning						◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Computational Methods and Tools for Data Science						◎
Compressive Sensing						◎
General mathematics (Ⅱ)	◎	◎	◎	◎		◎	◎
Topology			◎
Scientific Computing				◎
Module Theory II		◎
Fundamentals of English Writing								◎
Evolutionary Dynamics				◎
Introduction to Gromov-Witten theory		◎
Geometry of Several Complex Variables		◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Financial Technology Introduction		◎		◎
Big Data Applications and Theories				◎
Statistical Learning						◎
D Modules			◎
Introduction to Group Representations		◎
GENERALIZED LINEAR MODELS II						◎
Topics in Ring Theory (II) (Ⅱ)		◎
Introduction to Ricci Flow II		◎
Topics in Gromov-Witten theory		◎
Analysis and Geometry on CR manifolds		◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
An Introduction to Equivariant Cohomology		◎
Additive Combinatorics							◎
Topological methods for graph theory							◎
Special topics of PDE and its applications			◎
Academic Writing in English			◎
Introduction to computational & Data Sciences				◎
High Performance Computing and Deep Learning				◎
Stochastic Calculus					◎
Introduction to Lie groups and algebraic groups		◎	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Modular forms		◎
Basic Math from Advanced View Points (I)(Ⅰ)	◎	◎
Elliptic Curves, Modular Forms, and Galois Representation (I)(Ⅰ)		◎
Introduction to Non-commutative Geometry			◎
Statistical Foundations of Data Science (I)						◎
algebraic methods in index theorems		◎	◎
Mathematics and Career Exploration (I)(Ⅰ)								◎
Special topics of PDE and its applications (Carleman estimates)	◎
Topics in algebraic geometry		◎
Topics in identities of rings (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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Topics in identities of rings (II)(Ⅱ)		◎
Scientific Computing and Machine Learning on Multi- and Manycore Architectures				◎
Kinetic theory and Introduction to shock wave theory				◎
High-Performance Numerical Solvers				◎
Basic Math from Advanced View Points(Ⅱ)			◎
The Relativity thought of Einstein								◎
An introduction to Geometric Measure Theory			◎
Elliptic Curves, Modular Forms, and Galois Representation(Ⅱ)			◎
Statistical Foundations of Data Science				◎
Computation in Data Science				◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Introduction to Scientific Computing				◎
Topics on Frobenius Manifolds			◎
Evolutionary Dynamics				◎
Advanced Linear Algebra (Ⅰ)	◎	◎
Advanced Linear Algebra (Ⅱ)	◎	◎
Topics on division rings satisfying a rational identity(Ⅰ)		◎
Topics on division rings satisfying a rational identity (II)(Ⅱ)		◎
Introduction to Analytic Number Theory		◎
Lecture on algebraic number theory(Ⅰ)		◎
Lecture on algebraic number theory (II)(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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Statistical Machine Learning						◎
Introduction to Analytic Number Theory		◎
Artificial Intelligence for Medical Image Analysis				◎
Introduction to Langlands Program	◎	◎	◎
Introduction to perverse sheaves		◎	◎
Lie Algebra		◎	◎
Topics on Complex Geometric Analysis			◎
Discrete Differential Geometry				◎
Algebraic Surfaces			◎
Mathematics and Music	◎	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Einstein's thought of Relativity								◎
Boltzmann Equations	◎
Modular forms (Ⅱ)		◎
Artificial Intelligence for Clinical Data Analytics				◎
Papers Reading and Reports Presenting		◎
Topics in Geometry			◎
History of Mathematics (1)		◎	◎
Dimension Reduction for data science				◎
Classification of Algebraic Varieties		◎
An introduction to the theory of scheme	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Elliptic curves and modular symbols		◎
Survival analysis						◎
Topics in Random Matrix Theory	◎				◎
ALGEBRAIC GEOMETRY (I)(Ⅰ)		◎
Introduction to number theory		◎
Integrable systems and algebraic geometry		◎	◎
Infinite-dimensional Dynamical Systems				◎
Finite group representation		◎
CR Geometry Analysis			◎
History of 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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
An introduction to the theory of scheme(II)	◎
Gaussian process						◎
ALGEBRAIC GEOMETRY (II)(Ⅱ)		◎
Derived category and sheaves on manifolds			◎
Causal inference						◎
Introduction to the Langlands program		◎
ALGEBRAIC GEOMETRY(Ⅱ)		◎	◎
Abelian varieties		◎	◎
Mathematics and Career Exploration								◎
Discrete Geometry Analysis			◎				◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Delay Differential Equations	◎
Motives and periods		◎	◎
Measure and Probabilistic models					◎
Mathematics in Signal Processing and Machine Learning				◎
Ｈeat Equations and Geometric Applications			◎
KdV equations and related subjects	◎
KdV equations and related subjects	◎
Multiple zeta values and iterated integrals		◎
Seminar on Scientific Computing—Viscoelastic fluid flow					◎
An introduction of mathematics	◎	◎	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
AI for Medical Image Analysis									◎
Motives and periods		◎	◎
Introduction to Algebraic Topology		◎
Continuous-Time Stochastic Processes					◎
Mathematics in Deep Learning				◎
Algebraic Geometry		◎	◎
Introduction to Iwasawa theory		◎
Compact Lie groups and their representations		◎	◎
Algebraic Number Theory and Related Topics		◎
Tensor and Gaussian curvature			◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
An introduction of mathematics	◎	◎	◎
Mathematical foundation toward artificial intelligence in medicine				◎
An introduction to complex geometry			◎
Geometry and Topological Field Theory (Ⅰ)			◎
Automorphic forms on GL(2)		◎
High-dimensional probability					◎
Mathematical statistics						◎
Geometry and Topological Field Theory (II)(Ⅱ)			◎
Linear Algebraic Groups		◎
Fundamental groups and Galois groups		◎	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Fundamental groups and Galois groups		◎	◎
Derived categories of coherent sheaves			◎
The practical implementation of artificial intelligence in medical images				◎				◎
The practical implementation of artificial intelligence in medical images				◎
Special Topics in Medical AI: Largescale Real World Medical Data Analytics				◎
Intersection theory		◎	◎
Complex Analysis II	◎
Introduction to Modular Forms		◎
Algebraic Geometry (III)		◎	◎
An introduction to Singularities in Nonlinear Parabolic Problems	◎
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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Advanced Topics in Combinatorics							◎
Planar Statistical Physics Using Probabilistic Approaches					◎
Teichmüller theory and moduli space of Riemann surfaces		◎	◎
Concavity properties for elliptic and parabolic equations	◎
Arithmetic geometry		◎	◎
Introduction to the Minimal Model Program and Singularities		◎	◎
Introduction to geometric evolution equations			◎
Introduction to mean curvature flow	◎		◎
Selected Topics of Fluid Mechanics				◎
Geometry(II)(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 using 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 studies of mathematics. I. Abilities to use computer as a tool.
	[A]	[B]	[C]	[D]	[E]	[F]	[G]	[H]	[I]
Continuum Mechanics				◎
Topics in Minimal Submanifolds			◎
Advanced Topics in Combinatorics II							◎
Introduction to classifications of manifolds			◎
Lie groups and Lie algebras		◎	◎
Algebraic Geometry (Ⅰ)		◎	◎
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 using 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 studies of mathematics.	I Abilities to use computer as a tool.
Number of Core Courses （Number of All Courses: 446）	85	153	112	53	23	38	17	15	4