Resources

Recommended Readings

Here is a list of textbooks that I have read or skimmed and they may be useful for doing research.

Mathematical Toolkit

• Mathematics for Computer Science

  • Concrete Mathematics: A Foundation for Computer Science, by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik.
  • Foundations of Data Science, by Avrim Blum, John Hopcroft, and Ravindran Kannan.

• Combinatorics

  • The Probabilistic Method, by Noga Alon and Joel H. Spencer.
  • An Invitation to Analytic Combinatorics, by Stephen Melczer.

• High-Dimensional Probability

  • Probability in High Dimension, by Ramon van Handel.
  • High-Dimensional Probability: An Introduction with Applications in Data Science, by Roman Vershynin.

• Statistics

  • High-Dimensional Statistics: A Non-Asymptotic Viewpoint, by Martin J. Wainwright.

• Functional Analysis

  • Introductory Functional Analysis with Applications, by Erwin Kreyszig.

• Differential Equations

  • Differential Equations, Dynamical Systems, and an Introduction to Chaos, by Morris Hirsch, Robert L. Devaney, and Stephen Smale.

• Analysis of Boolean Functions

  • Analysis of Boolean Functions, by Ryan O’Donnell.

Algorithms and Complexity

• Algorithm Design and Analysis

  • The Design of Approximation Algorithms, by David P. Williamson and David Shmoys.
  • Randomized Algorithms, by Rajeev Motwani and Prabhakar Raghavan.
  • Exact Exponential Algorithms, by Dieter Kratsch and Fedor V. Fomin.
  • Parameterized Algorithms, by Marek Cygan, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh.
  • Online Computation and Competitive Analysis, by Allan Borodin and Ran El-Yaniv.
  • Parallel and Distributed Computation: Numerical Methods, by Dimitri P. Bertsekas and John N. Tsitsiklis.
  • Beyond the Worst-Case Analysis of Algorithms, by Tim Roughgarden.

• Optimization

  • Introduction to Linear Optimization, by Dimitris Bertsimas and John N. Tsitsiklis.
  • Convex Optimization, by Stephen Boyd and Lieven Vandenberghe.
  • Convex Optimization: Algorithms and Complexity, by Sébastien Bubeck.
  • Integer Programming, by Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli.

• Heuristic Algorithms

  • Heuristic Search: Theory and Applications, by Stefan Edelkamp and Stefan Schroedl.
  • Handbook of Satisfiability, by Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh.

• Computational Complexity

  • Computational Complexity: A Modern Approach, by Sanjeev Arora and Boaz Barak.
  • Mathematics and Computation, by Avi Wigderson.
  • Communication Complexity (for Algorithm Designers), by Tim Roughgarden.

Machine Learning

• Learning Theory

  • Foundations of Machine Learning, by Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar.
  • Understanding Machine Learning: From Theory to Algorithms, by Shai Shalev-Shwartz and Shai Ben-David.
  • User-Friendly Introduction to PAC-Bayes Bounds, by Pierre Alquier.
  • Bandit Algorithms, by Tor Lattimore and Csaba Szepesvari.

• Reinforcement Learning

  • Neuro-Dynamic Programming, by Dimitri P. Bertsekas and John N. Tsitsiklis.
  • Reinforcement Learning and Optimal Control, by Dimitri P. Bertsekas.