Educational program

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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