PG | Department of Mathematics

Sections

Left Column

Image

Image Caption

Overview
Programs
How to Apply
Financial Support
Courses
Awards
Events
PG Intranet

Right Column

Text Area

Course Information 2024-2025 Fall Semester
MATH 5111 - Advanced Algebra I

Description	Advanced theory of groups, linear algebra, rings, modules, and fields, including Galois theory.
(3 units)
	Course Instructor: Prof MENG, Guowu

MATH 5240 - Algebraic Topology

Description	Fundamental group, covering space, Van Kampen theorem, (relative) homology, exact sequences of homology, Mayer-Vietoris sequence, excision theorem, Betti numbers and Euler characteristic.
(3 units)
	Course Instructor: Prof HO, Quoc

MATH 5251 - Algebraic Geometry I

Description	Projective spaces, algebraic curves, divisors, line bundles, algebraic varieties, coherent sheaves, schemes. Some commumative algebra and homological algebra such as notherian ring, regular ring, valuation ring, kahler differentials.
(3 units)
	Course Instructor: Prof JIANG, Qingyuan

MATH 5285 - Applied Analysis

Description	Contraction mapping theorem, Fourier series, Fourier transforms, Basics of Hilbert Space theory, Operator theory in Hilbert Spaces, Basics of Banach space theory, Convex analysis.
(3 units)
	Course Instructor: Prof ZHANG, Hai

MATH 5311 - Advanced Numerical Methods I

Description	Numerical solution of differential equations, finite difference method, finite element methods, spectral methods and boundary integral methods. Basic theory of convergence, stability and error estimates.
(3 units)
	Course Instructor: Prof PENG, Zhichao

MATH 5350 - Computational Fluid Dynamics for Inviscid Flows

Description	Derivation of the Navier-Strokes equations; the Euler equations; Lagriangian vs. Eulerian methods of description; nonlinear hyperbolic conservation laws; characteristics and Riemann invariants; classification of discontinuity; weak solutions and entropy condition; Riemann problem; CFL condition; Godunov method; artificial dissipation; TVD methods; and random choice method.
(3 units)
	Course Instructor: Prof XU, Kun

MATH 5351 - Mathematical Methods in Science and Engineering I

Description	Modeling and analytical solution methods of nonlinear partial differential equations (PDEs). Topics include: derivation of conservation laws and constitutive equations, well-posedness, traveling wave solutions, method of characteristics, shocks and rarefaction solutions, weak solutions to hyperbolic equations, hyperbolic Systems, linear stability analysis, weakly nonlinear approximation, similarity methods, calculus of variations.
(3 units)
	Course Instructor: Prof XIANG, Yang

MATH 5411 - Advanced Probability Theory I

Description	Probability spaces and random variables, distribution functions, expectations and moments, independence, convergence concepts, law of large numbers and random series.
(3 units)
	Course Instructor: Prof NITZSCHNER, Maximilian Alexander

MATH 5431 - Advanced Mathematical Statistics I

Description	Theory of statistical inference in estimation. Topics include: sufficiency, ancillary statistics, completeness, UMVU estimators, information inequality, efficiency, asymptotic maximum likelihood theory. Other topics may include Bayes estimation and conditional inference.
(3 units)
	Course Instructor: Prof GUO, Xinzhou

MATH 5472 - Computer Age Statistical Inference with Applications

Description	This course is designed for RPg students in applied mathematics, statistics, and engineering who are interested in learning from data. It covers advanced topics in statistical learning and inference, with emphasis on the integration of statistical models and algorithms for statistical inference. This course aims to first make connections among classical topics, and then move forward to modern topics, including statistical view of deep learning. Various applications will be discussed, such as computer vision, human genetics, and text mining.
(3 units)
	Course Instructor: Prof YANG, Can

MATH 6771 - Professional Development Training in Mathematics

Description	This one-credit course aims at providing research postgraduate students basic training in teaching skills, research management, career development in and outside academia, and related professional skills in Mathematics. This course lasts for one semester, and is composed of a number of mini-workshops or tasks. Graded PP, P or F.
(1 unit)
	Course Instructor: Prof JIN, Tianling

MATH 6900A - Mathematics Seminar

Description	This course will expose our PG students to the current mathematical research and development and provide them with opportunities to make mathematical and social contacts with the speakers and with local and international mathematical communities in general. Graded P or F.
(1 unit)
	Course Instructor: Prof JIN, Tianling

MATH 6900B - Mathematics Seminar

Description	This course will expose our PG students to the current mathematical research and development and provide them with opportunities to make mathematical and social contacts with the speakers and with local and international mathematical communities in general. Graded P or F.
(1 unit)
	Course Instructor: Prof JIN, Tianling

MATH 6900C - Mathematics Seminar

Description	This course will expose our PG students to the current mathematical research and development and provide them with opportunities to make mathematical and social contacts with the speakers and with local and international mathematical communities in general. Graded P or F.
(1 unit)
	Course Instructor: Prof JIN, Tianling

MATH 6900D - Mathematics Seminar

Description	This course will expose our PG students to the current mathematical research and development and provide them with opportunities to make mathematical and social contacts with the speakers and with local and international mathematical communities in general. Graded P or F.
(1 unit)
	Course Instructor: Prof JIN, Tianling

MATH 6915 - Scientific Computation Seminar

Description	This course will expose PG students to the current research and new development in scientific computation and provide them with opportunities to make social contacts with the speakers from both the local and international academic communities. Graded P or F.
(1 unit)
	Course Instructor: Prof XIANG, Yang

MATH 6915A - Scientific Computation Seminar

Description	This course will expose PG students to the current research and new development in scientific computation and provide them with opportunities to make social contacts with the speakers from both the local and international academic communities. Graded P or F.
(1 unit)
	Course Instructor: Prof XIANG, Yang

MATH 6916 - Student Seminars on Computation Related Research

Description	Seminar presentation on computation related research by students in the Scientific Computation Concentration (SCC) within the first four regular terms of study. Students should notify their major department 2-3 weeks in advance for the presentation. Graded P or F.
(1 unit)
	Course Instructor: Prof XIANG, Yang

MATH 6990 - MPhil Thesis Research

Description	Master's thesis research supervised by a faculty member. A successful defense of the thesis leads to the grade Pass. No course credit is assigned.

MATH 7990 - Doctoral Thesis Research

Description	Original and independent doctoral thesis research. A successful defense of the thesis leads to the grade Pass. No course credit is assigned.

2024-2025 Spring Semester
MATH 5030 - Complex Function Theory

Description	Review of basic properties of analytic functions. Phragmen-Lindelof principle, normal family, Riemann mapping theorem. Weierstrass factorization theorem, Schwarz reflection principle, analytic continuation, harmonic function, entire function, Hadamard factorization theorem, Picard theorem.
(3 units)
	Course Instructor: Prof CHIANG, Yik Man

MATH 5112 - Advanced Algebra II

Description	Advanced topics in algebra: group representations, associative algebras, commutative algebra, homological algebra, algebraic number theory.
(3 units)
	Course Instructor: Prof ZHU, Yongchang

MATH 5261 - Algebraic Geometry II

Description	Derived functors, cohomology of coherent sheaves on schemes, extension groups of sheaves, higher direct image of sheaves, Serre duality, flat morphisms, smooth morphisms, and semi-continuity, basics of curves and surfaces.
(3 units)
	Course Instructor: Prof JIANG, Qingyuan

MATH 5312 - Advanced Numerical Methods II

Description	Direct and iterative methods. Programming techniques and softwares libraries. Sparse solvers, Fast algorithms, multi-grid and domain decomposition techniques.
(3 units)
	Course Instructor: Prof CAI, Jianfeng

MATH 5352 - Mathematical Methods in Science and Engineering II

Description	Asymptotic methods and perturbation theory for obtaining approximate analytical solutions to differential equations. Topics include: local analysis of solutions to differential equations, asymptotic expansion of integrals, global analysis and perturbation methods, WKB theory, multiple-scale analysis, homogenization method.
(3 units)
	Course Instructor: Prof XIANG, Yang

MATH 5432 - Advanced Mathematical Statistics II

Description	Theory of statistical inference in hypothesis testing. Topics include: uniformly most powerful tests, unbiasedness, invariance, minimax principle, large-sample parametric significance tests. Concept of decision theory also covered.
(3 units)
	Course Instructor: Prof TANG, Rong

MATH 5470 - Statistical Machine Learning

Description	This course covers methodology, major software tools and applications in statistical learning. By introducing principal ideas in statistical learning, the course will help students understand conceptual underpinnings of methods in data mining. The topics include regression, logistic regression, feature selection, model selection, basis expansions and regularization, model assessment and selection; additive models; graphical models, decision trees, boosting; support vector machines; clustering.
(3 units)
	Course Instructor: Prof YAO, Yuan

MATH 5473 - Topological and Geometric Data Reduction and Visualization

Description	This course is a mathematical introduction to data analysis and visualization with a perspective of topology and geometry. Topics covered include: classical linear dimensionality reduction, the principal component analysis (PCA) and its dual multidimensional scaling (MDS), as well as extensions to manifold learning, topological data analysis, and sparse models in applied math/high dimensional statistics. Extensive application examples in biology, finance, and information technology are presented along with course projects.
(3 units)
	Course Instructor: Prof YAO, Yuan