The Applied Mathematics domain bridges rigorous pure mathematical theory with real-world applications. By developing mathematical models, algorithmic frameworks, and computational data analysis, it addresses complex problems across science, engineering, finance, and industry. In response to rapid advancements in artificial intelligence, big data, and high-performance computing, the department’s applied mathematics curriculum encompasses six key subfields and integrates with the Program of Scientific Computing, preparing students with strong cross-disciplinary problem-solving capabilities and modern computational vision.

Six Specialized Subfields

• Differential Equations: Focuses on the theory, well-posedness, dynamical systems, and asymptotic behavior of ordinary and partial differential equations, forming the backbone of physical and biological modeling.
• Probability: Examines stochastic processes, limit theorems, and probabilistic modeling, providing a solid theoretical foundation for financial mathematics, statistical inference, and machine learning.
• Data Science: Integrates algorithm design, machine learning, and mathematical modeling, focusing on high-dimensional data processing, pattern recognition, and the mathematical foundations of modern AI.
• Combinatorics and Discrete Mathematics: Investigates graph theory, combinatorial structures, cryptography, and discrete optimization, serving as the cornerstone of computer science and algorithm design.
• Optimization Theory: Explores convex analysis, nonlinear programming, and large-scale computational optimization, widely applied in operations research, machine learning, and decision sciences.
• Scientific Computing: Combines numerical analysis, matrix computations, numerical solutions of PDEs, and high-performance computing (HPC) to simulate complex physical and natural systems.

Recommended Courses

• Foundational & Core Courses: Calculus, Linear Algebra, Introduction to Differential Equations, Discrete Mathematics, Introduction to Scientific Computing, Introduction to Probability, Linear Programming.
• Advanced & Elective Courses: Partial Differential Equations, Dynamical Systems, Combinatorics, Topics in Scientific Computing, Matrix Computations, Computational Conformal Geometry, Scientific Computing in Data Science, Optimization.

Statistics

The statistics curriculum in our department covers statistical theory, statistical methods, and data analysis. Beginning with foundational courses in probability and statistics, students progress to statistical inference, model building, and various methods of data analysis. The curriculum emphasizes both theory and practice, focusing not only on the mathematical foundations of statistical methods but also on their application to real-world data. This training also provides a foundation for further study in data science and artificial intelligence.

Main Areas of Study

1. Statistical Theory and Inference

This area focuses on the theoretical foundations of statistical models, parameter estimation, hypothesis testing, and statistical inference. Advanced topics include multivariate analysis and stochastic processes.

2. Statistical Methods and Data Analysis

This area covers statistical methods such as regression analysis, experimental design, categorical data analysis, and survival analysis. Emphasis is placed on selecting appropriate statistical models based on research questions and data characteristics, as well as using statistical computing, simulation, and software tools for data analysis and interpretation of results.

Courses

Undergraduate Courses: Introduction to Probability, Statistics, Applied Statistical Methods.

Courses Offered Jointly to Undergraduate and Graduate Students: Mathematical Statistics, Regression Analysis (IB Course), Design and Analysis of Experiments, Categorical Data Analysis, Survival Analysis, Multivariate Analysis, Stochastic Processes, Statistical Computing.