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)	◎
Elementary Analysis: Introduction to Metric Spaces	◎
Linear Algebra (Ⅰ)		◎
Linear Algebra (Ⅱ)		◎
Computer Programming									◎
Advanced Linear 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 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 Linear Algebra (Ⅱ)		◎
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			◎
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 Statistics						◎
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)			◎
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 (Ⅰ)		◎
Elementary Number Theory (Ⅱ)		◎
SPECIAL PROJECT FOR UNDERGRADUATE(Ⅲ)								◎
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)	◎
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 Analysis(Honor)(Ⅱ)	◎
Introduction to Number Theory(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			◎
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]
Preview of Calculus	◎
Pre-calculus	◎
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)	◎
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]
Measure and Probabilistic models					◎
Precalculus	◎
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)								◎
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 Linear Algebra (Ⅰ)		◎
Introduction to Linear Algebra (II)		◎
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		◎	◎
Algebra(Honor Program)(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]
Algebra(Honor Program)(Ⅱ)		◎
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)		◎
Algebraic 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 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 Geometry (Ⅱ)			◎
Regression Analysis (Ⅰ)						◎
Regression Analysis (Ⅱ)						◎
Topics in Geometry			◎
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 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]
Multivariates Statistical Analysis (Ⅱ)						◎
Number Theory (Ⅰ)		◎
Number Theory (Ⅱ)		◎
Mathematical Statistics (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		◎
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 Curve		◎
Ring Theory (Ⅰ)		◎
Ring Theory (Ⅱ)		◎
Statistical Computing						◎
Commutative Algebra (Ⅰ)		◎
Commutative Algebra (Ⅱ)		◎
Lie Group (Ⅰ)			◎
Lie Group (Ⅱ)			◎
Coding Theory (Ⅰ)		◎
Coding 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]
Calculus of Variation (Ⅰ)	◎
Calculus of Variation (Ⅱ)	◎
Real Analysis (Ⅰ)	◎
Real Analysis (Ⅱ)	◎
Differential Geometry (Ⅰ)			◎
Differential Geometry (Ⅱ)			◎
Financial Mathematics					◎
Differential Topology			◎
Combinatorics (Ⅰ)							◎
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]
Probability Theory (Ⅰ)					◎
Probability Theory (Ⅱ)					◎
Graph Theory (Ⅰ)							◎
Graph Theory (Ⅱ)							◎
Time Series (Ⅰ)					◎
Topics in Partial Differential Equations (Ⅰ)	◎
Algebraic Geometry			◎
Scientific Computing (Ⅰ)				◎
Scientific Computing (Ⅱ)				◎
Introduction to Global Differential 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]
Algebra (Ⅰ)		◎
Algebra (Ⅱ)		◎
Colloquium (Ⅰ)								◎
Colloquium (Ⅱ)								◎
Colloquium (Ⅲ)								◎
Colloquium (Ⅳ)								◎
Quantum Groups		◎
Functional Analysis	◎
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 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 Methods for Forecasting						◎
Regression Analysis						◎
Numerical Partial Differential Equations (Ⅱ)				◎
Stochastic Calculus					◎
Algebraic Graph Theory							◎
Lie Algebra (Ⅰ)		◎
Lie Algebra (Ⅱ)		◎
Graph Algorithms							◎
Fast Algorithms				◎
Introduction to Computational 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]
Computational Finance									◎
Algorithms							◎
Mathematical Software									◎
Game Theory					◎
Introduction to Stochastic Processes					◎
Topics in Cryptography		◎
Elementary Number Theory	◎
Iwasawa Theory		◎
The Arithmetic Theory of Modulat Functions		◎
Rings with Involution (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]
Rings with Involution (Ⅱ)		◎
Introduction to Algebraic Geometry		◎
Generalized Linear Models						◎
Colding Minicozzi		◎
Cryptography		◎
Survival and Recurrent Event Data Analysis						◎
Riemannian Geometry			◎
Combinatorial Optimization (Ⅰ)							◎
Combinatorial Optimization (Ⅱ)							◎
Topics in 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]
The Probability Method							◎
Introduction to Manifolds			◎
Algebraic Combinatorics (Ⅰ)		◎
Algebraic Combinatorics（Ⅱ）		◎
Topology (Ⅰ)			◎
Topology (Ⅲ)			◎
Geometry Flow (Ⅰ)			◎
Geometry Flow (Ⅱ)			◎
Cauchy-riemann Geometry			◎
Introduction to Geometrical Methods and Thought			◎
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]
Group Representation Theory		◎
Foundation of Cryptography		◎
Stochastic Processes					◎
Topics in Arithmetic Geometry			◎
Basic Mathematics			◎
Image Processing				◎
Applied Analysis				◎
Models and Applications of Mathematics in Business and Industries								◎
Introduction to Scientific Computing				◎
Basic 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]
Numerical Optimization				◎
Equations of Mathematical Physics (Ⅰ)	◎			◎
Introduction to Algebraic Topology		◎
Curvature Flow			◎
Morse Theory			◎
Seminar on Group Rings	◎
Quasi-Linear Elliptic Differential Equations	◎
Complex Manifolds			◎
Iwasawa Theory		◎
Special Topics on Computational Eigenvalue 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]
Quasi-Linear Elliptic Differential Equations(Ⅱ)	◎
Algebraic Topology			◎
Lie Groups and Lie Algebras(Ⅰ)		◎
Lie Groups and Lie Algebras(Ⅱ)		◎
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		◎
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]
Homological Algebra		◎
Algebraic Groups		◎
Introduction to Riemann Surfaces			◎
Metric Geometry			◎
Topics in Algebra		◎
Introduction to Cryptography				◎
Mathematical Modeling						◎
Modern Algebra (Ⅰ)		◎
Methods of Applied Mathematics				◎
Multivariates Statistical 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]
Numerical Partial Differential Equations				◎
Data Driven Analysis and Optimization in Computer Experiments				◎
Introduction to Symplectic Geometry			◎
Methemetical Control Theory(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		◎
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(Ⅱ)		◎
Topic in Differential Geometry(Ⅱ)			◎
Introduction to Cohomology Theories		◎
Numerical Inverse Problem				◎
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		◎
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]
Ring Theory		◎
Representation Theory of Compact Groups		◎
Experimental Design						◎
High Dimensional Statistical Analysis and Machine Learning						◎
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		◎
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(Ⅱ)			◎
Introduction to Algebraic K-Theory		◎
Seminar in Algebraic Geometry			◎
Homological Algebra		◎
Introduction to Topology			◎
Algebra(Honor Program)(Ⅰ)		◎
Algebra(Honor Program)(Ⅱ)		◎
Analysis(Honor Program)(Ⅰ)	◎
Analysis(Honor Program)(Ⅱ)	◎
Introduction to Complex 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]
Complex Analysis (Honor Program)	◎
Introduction to Geometry			◎
Modern Algebra (Ⅱ)		◎
General mathematics	◎	◎	◎		◎
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	◎
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]
Analysis on manifolds					◎
Elliptic Curve Cryptography				◎
Mathematical statistics for data science				◎
Statistical computing				◎
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			◎
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]
Perturbative quantum field theory			◎
Geometry of higher dimension algebraic varieties			◎
Variational Methods and their Applications to Nonlinear PDE	◎
Statistical machine learning						◎
Computational Methods and Tools for Data Science						◎
Compressive Sensing						◎
General mathematics (Ⅱ)	◎	◎	◎	◎		◎	◎
Topology			◎
Scientific Computing				◎
Module 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]
Fundamentals of English Writing								◎
Evolutionary Dynamics				◎
Introduction to Gromov-Witten theory		◎
Geometry of Several Complex Variables		◎
Financial Technology Introduction		◎		◎
Big Data Applications and Theories				◎
Statistical Learning						◎
D Modules			◎
Introduction to Group Representations		◎
GENERALIZED LINEAR MODELS 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]
Topics in Ring Theory (II) (Ⅱ)		◎
Introduction to Ricci Flow II		◎
Topics in Gromov-Witten theory		◎
Analysis and Geometry on CR manifolds		◎
An Introduction to Equivariant Cohomology		◎
Additive Combinatorics							◎
Topological methods for graph theory							◎
Special topics of PDE and its applications			◎
Academic Writing in English			◎
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 computational & Data Sciences				◎
High Performance Computing and Deep Learning				◎
Stochastic Calculus					◎
Introduction to Lie groups and algebraic groups		◎	◎
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		◎	◎
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]
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)		◎
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								◎
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 Geometric Measure Theory			◎
Elliptic Curves, Modular Forms, and Galois Representation(Ⅱ)			◎
Statistical Foundations of Data Science				◎
Computation in Data Science				◎
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)		◎
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 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)		◎
Statistical Machine Learning						◎
Introduction to Analytic Number Theory		◎
Artificial Intelligence for Medical Image Analysis				◎
Introduction to Langlands Program	◎	◎	◎
Introduction to perverse sheaves		◎	◎
Lie 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]
Topics on Complex Geometric Analysis			◎
Discrete Differential Geometry				◎
Algebraic Surfaces			◎
Mathematics and Music	◎	◎
Einstein's thought of Relativity								◎
Boltzmann Equations	◎
Modular forms (Ⅱ)		◎
Artificial Intelligence for Clinical Data Analytics				◎
Papers Reading and Reports Presenting		◎
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]
History of Mathematics (1)		◎	◎
Dimension Reduction for data science				◎
Classification of Algebraic Varieties		◎
An introduction to the theory of scheme	◎
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		◎	◎
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]
Infinite-dimensional Dynamical Systems				◎
Finite group representation		◎
CR Geometry Analysis			◎
History of Mathematics (II)		◎	◎
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		◎
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 GEOMETRY(Ⅱ)		◎	◎
Abelian varieties		◎	◎
Mathematics and Career Exploration								◎
Discrete Geometry Analysis			◎				◎
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	◎
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]
KdV equations and related subjects	◎
Multiple zeta values and iterated integrals		◎
Seminar on Scientific Computing—Viscoelastic fluid flow					◎
An introduction of mathematics	◎	◎	◎
AI for Medical Image Analysis									◎
Motives and periods		◎	◎
Introduction to Algebraic Topology		◎
Continuous-Time Stochastic Processes					◎
Mathematics in Deep Learning				◎
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 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 Iwasawa theory		◎
Compact Lie groups and their representations		◎	◎
Algebraic Number Theory and Related Topics		◎
Tensor and Gaussian curvature			◎
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					◎
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						◎
Geometry and Topological Field Theory (II)(Ⅱ)			◎
Linear Algebraic Groups		◎
Fundamental groups and Galois groups		◎	◎
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		◎	◎
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]
Complex Analysis II	◎
Introduction to Modular Forms		◎
Algebraic Geometry (III)		◎	◎
An introduction to Singularities in Nonlinear Parabolic Problems	◎
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		◎	◎
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 geometric evolution equations			◎
Introduction to mean curvature flow	◎		◎
Selected Topics of Fluid Mechanics				◎
Geometry(II)(Ⅱ)			◎
Continuum Mechanics				◎
Topics in Minimal Submanifolds			◎
Advanced Topics in Combinatorics II							◎
Introduction to classifications of manifolds			◎
Graph Theory (III)							◎
Advanced Topics in 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 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]
Representation theory of finite groups of Lie type		◎
Topics related to index theorems (Ⅰ)			◎
Singular support and characteristic cycle of an étale sheaf			◎
Lie groups and Lie algebras		◎	◎
Topics in Algebraic Geometry (K-stability and moduli spaces)		◎	◎
Automorphic forms and Weil representations		◎
Introduction to the local Langlands correspondence		◎
Topics in complex analytic geometry	◎		◎
Derived Algebraic Geometry		◎	◎
Derived 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 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]
Generative Artificial Intelligence and Business Applications		◎		◎	◎	◎
Topics related to index theorems II(Ⅱ)			◎
sheaf and category in topology		◎	◎
Algebraic Geometry (Ⅰ)		◎	◎
Coding Theory		◎					◎
Theory of algebraic groups		◎
Convex geometry			◎
An introduction to theory of operator algebras	◎	◎
Linear Model					◎				◎
Rigorous Numerics in Dynamical Systems(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: 470）	88	166	121	55	25	39	20	16	5