Here are the slides used for the course Efficient experimental mathematics for combinatorics and number theory, given at the Vienna Summer School of Mathematics in Weissensee, Austria, September 23–27, 2019:

  1. Lecture 1: Context, Motivation, Examples.
  2. Problem session 1.
  3. Lecture 2: Experimental Mathematics for Combinatorics.
  4. Lecture 3: Inside the Experimental Math. Toolbox.
  5. Problem session 2.

Here is some documentation on the gfun package.

And here is some documentation on a guessing package for Mathematica.

And below are some additional references:

  1. Bailey and Borwein (2001): Experimental Mathematics: Recent Developments and Future Outlook.
  2. Wilf (2007): Mathematics: an Experimental Science.
  3. Borwein (2008): Implications of Experimental Mathematics for the Philosophy of Mathematics.
  4. Bailey and Borwein (2011): Exploratory Experimentation and Computation.
  5. Nemes, Petkovsek, Wilf and Zeilberger (1997): How to do Monthly problems with your computer.
  6. Trefethen (2002): A Hundred-dollar, Hundred-digit Challenge.
  7. Borwein (2005): The SIAM 100-Digit challenge- a study in high-accuracy numerical computing.
  8. Bailey, Borwein, Kapoor and Weisstein (2006): Ten Problems in Experimental Mathematics.
  9. Stenger (2017): Experimental Math for Math Monthly Problems.
  10. Polya (1954): Induction in the Theory of Numbers (Chap. IV of Induction and Analogy in Mathematics).
  11. Polya (1954): Euler's Most Extraordinary Law of the Numbers (Chap. VI of Induction and Analogy in Mathematics).
  12. Andrews (1983): Euler's Pentagonal Number Theorem.
  13. Preston (1991): The Mountains of Pi.