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:

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

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