School of Mathematical Sciences

About the School

The School of Mathematical Sciences at Tianjin Normal University was founded in 1958 as the Department of Mathematics and was among the University's earliest academic units. Over more than six decades, it has developed a strong tradition in mathematics education and research, guided by a commitment to education, student development, mathematical foundations, and innovation. The School has played a central role in mathematics teacher education in Tianjin while steadily expanding its research in pure, applied, and interdisciplinary mathematics.

The School offers undergraduate programs in Mathematics and Applied Mathematics, Information and Computing Science, and Data Computing and Applications. It also offers master's degree programs in Mathematics and the History of Science and Technology. Mathematics is recognized as a key discipline in Tianjin and is included in priority disciplinary development initiatives. Building on this foundation, the School has developed distinctive strengths in pure mathematics, intelligent computing, differential equations and their applications, combinatorics and graph theory, and the history of mathematics and mathematics education.

Institute of Mathematics and Interdisciplinary Sciences

To further strengthen fundamental research and interdisciplinary collaboration, Tianjin Normal University formally established the Institute of Mathematics and Interdisciplinary Sciences in September 2024. The Institute is designed as a platform for original research and academic leadership in mathematics and its interactions with other scientific fields.

Its principal research directions include pure mathematics—particularly algebra, geometry, analysis, topology, combinatorics, and graph theory—together with computational mathematics and interdisciplinary research connecting mathematics with information science, data science, artificial intelligence, computational optics, mathematical medicine, brain science, AI for Science (AI4S), and geoscience. Together, the School and the Institute provide an expanding environment for fundamental research, interdisciplinary collaboration, graduate education, and international academic exchange.

The School welcomes collaboration with researchers and institutions worldwide in pure mathematics and interdisciplinary research.

Research and Interdisciplinary Development

Research at the School spans a broad spectrum of pure and applied mathematics. Current activities cover algebra, geometry, analysis, differential equations, dynamical systems, combinatorics, graph theory, computational mathematics, intelligent computing, mathematical modeling, and interdisciplinary applications. Faculty members lead and participate in projects supported by the National Natural Science Foundation of China and other national, municipal, and university-level programs, and publish regularly in internationally recognized journals in pure and applied mathematics and computational science.

A defining feature of the School's recent development is the strengthening of interactions between pure mathematics and emerging interdisciplinary areas. Mathematical theory and computation are increasingly connected with artificial intelligence, data science, computational optics, geoscience, brain science, bioinformatics, and other scientific domains.

Research Teams

The School currently organizes its mathematical research around five major teams. Together, these groups span pure mathematics, computational research, and interdisciplinary applications, while providing focal points for collaborative research, graduate supervision, academic seminars, and international exchange. The following profiles summarize the principal research directions and distinctive strengths of each team.

1. Intelligent Computing and Interdisciplinary Sciences

The Intelligent Computing and Interdisciplinary Sciences Research Team develops mathematical models, numerical algorithms, and data-driven methods for challenging problems in science and technology. Its research spans inverse problems and image processing, numerical methods for differential equations, optimization, machine learning, artificial intelligence, high-performance computing, and control of distributed-parameter systems. A distinctive feature of the team is its strong interdisciplinary orientation: mathematical and computational methods are applied to medical imaging, inverse scattering, computational optics, groundwater and geoscience modeling, brain imaging, bioinformatics, systems biology, and related areas. The team has established collaborations with researchers in Hong Kong and overseas and has been selected as an Innovation Team of Tianjin Higher Education Institutions. Its members have published in major international journals, including Mathematics of Computation, Journal of Computational Physics, Inverse Problems, and journals published by SIAM and in the IEEE Transactions series.

2. Algebra and Geometry

The Algebra and Geometry Research Team brings together researchers in algebra, geometry, topology, dynamical systems, and mathematical physics. Its principal directions include generalized Fourier analysis, symplectic geometry and Hamiltonian dynamics, nonlinear partial differential equations, finite groups and representation theory, Lie groups and Lie algebras, algebraic topology and homotopy theory, and mathematical aspects of quantum information. The team's work is characterized by close interaction among algebraic, geometric, topological, and analytical methods. Representative themes include generalized Fourier transforms and special-function kernels, vortex and Hamiltonian dynamics, structural questions in finite-group representation theory, homotopy groups of spheres, and quantitative problems in quantum coherence, uncertainty, and entanglement. Members of the team have published in journals including Journal of Functional Analysis, Communications in Mathematical Physics, Journal of Differential Equations, Monatshefte für Mathematik, Linear Algebra and its Applications, and Quantum Information Processing, and have received sustained support from the National Natural Science Foundation of China and other competitive research programs.

3. Analysis

The Analysis Research Team conducts research in operator theory and operator algebras, ordinary differential equations and dynamical systems, stochastic analysis, several complex variables, and discrete geometry. Its work combines techniques from functional analysis, probability, geometry, and nonlinear dynamics, and has produced results in operator semigroups and invariant-subspace theory, bifurcation and limit-cycle problems, stability of stochastic differential equations, and geometric partition questions. The team has also developed research connections between operator-algebraic structures and mathematical physics, between stochastic dynamics and applications in finance and insurance, and between discrete geometry and problems arising in lattice theory and coding. Recent work by team members has appeared in journals such as Bulletin of the London Mathematical Society, Journal of Differential Equations, Mathematische Zeitschrift, Science China Mathematics, and Journal of Mathematical Physics. The team's projects are supported by the National Natural Science Foundation of China, the Tianjin Natural Science Foundation, and other national and municipal research programs.

4. Differential Equations

The Differential Equations Research Team studies qualitative theory, dynamics, control, and optimization for differential-equation models, with particular emphasis on problems arising from neural systems and complex networks. Major directions include delayed and memristive neural networks, neural dynamics and mathematical models of memory, fully nonlinear partial differential equations, Hamiltonian systems, multi-agent distributed optimization, neurodynamic algorithms, stochastic differential equations, and infinite-dimensional dynamical systems. The team has developed distinctive research programs on proportional-delay neural networks and their stability and synchronization, mathematical modeling of synaptic plasticity and memory formation, Monge-Ampère-type and other nonlinear PDEs, distributed optimization based on neural dynamics, and asymptotic behavior of stochastic evolution equations. These topics connect rigorous analysis with artificial intelligence, control, image encryption, biological modeling, and networked systems. Team members have published in journals such as IEEE Transactions on Neural Networks and Learning Systems, IEEE Transactions on Automatic Control, Neural Networks, Information Sciences, Journal of Differential Equations, Nonlinear Dynamics, and Journal of Mathematical Analysis and Applications.

5. Combinatorics and Graph Theory

The Combinatorics and Graph Theory Research Team works in algebraic and enumerative combinatorics, graph theory and graph algorithms, partition theory, and q-series. A central strand of its combinatorics research concerns structural properties of combinatorial polynomials, including unimodality, log-concavity, gamma-positivity, real-rootedness, multivariate stability, and related positivity phenomena. In graph theory, the team studies integer flows and group connectivity, graph coloring, extremal and structural graph theory, cycle structures, spanning trees, Ramsey-type problems, and algorithmic questions. Other active topics include partition ranks and mock theta functions, as well as permutation statistics and refinements of classical results such as Stanley's shuffle theorem. This combination of algebraic, analytic, and graph-theoretic approaches gives the team a broad profile in modern discrete mathematics. Members have published in leading journals including Journal of Combinatorial Theory, Series A and Series B, Journal of Graph Theory, Advances in Applied Mathematics, SIAM Journal on Discrete Mathematics, Proceedings of the American Mathematical Society, and European Journal of Combinatorics.