Educational program
From Research management course
Contents
Data Science: A Roadmap for Bachelor, Master, and Doctoral Degrees
Mathematics
- Discrete analysis and graphs ***
- Abstract algebra and group theory **
- Mathematical *** and functional analysis *
- ODE, PDE, and mathematical modeling *
- Linear algebra ***
- Tensor algebra and calculus *
- Theoretical physics *
- Differential geometry and Geometric algebra *
- Scientific computation and numerical methods ***
- Measure and Probability ***
- Multivariate statistics ***
- Bayesian statistics and Graphical models **
- Stochastic processes and SDE *
- Bayesian model selection **
- Diffusion probability and flows **
Computer science
- Programming ***
- Computational differentiation **
- Software architectures **
- System analysis **
- Category theory *
- Parallel and distributed computing **
Optimization and control
- Discrete optimization **
- Convex optimization **
- Mathematical programming ***
- Optimal control**
Core of Data science
- Machine learning and data analysis
- Deep learning
- Bayesian model selection
- Bayesian multi-modeling
- Generative models (practice BS and theory MS)
- Reinforcement and online learning
- Geometric deep learning
- Geometric generative models
Applications
- Signal analysis
- Computer vision
- Audio processing
- Natural language processing
- Topic modeling and Information retrieval
- Recommender systems
- Multimedia and heterogeneous data
- Bioinformatics
- Brain-computer interfaces and metaverse
*** essential, ** recommended, * advanced
Exams
- Ph.D. theoretical minimum for Computer science: AI and machine learning