andreabedini / experimental-mathematics

:notebook_with_decorative_cover: Lecture notes for Experimental Mathematics 2014

Experimental Mathematics

Here you can find lecture notes and other material I have prepared for the subject Experimental Mathematics I taught at The University of Melbourne in 2014. It was the first time teaching that subject and the notes are quite rough.

The notes are written mostly in markdown but with heavy use of latex blocks not only for formulas but also to make use of the tufte latex package.

Part one

1. Introduction
2. Interger relation detection
3. Bifurcation points of the logistic map
4. Gröbner basis
5. The quest for pi
6. More on BBP formulas

Part two

The second part covered automated summation of hypergeometric series and followed the book A=B by Petkovsek, Wilf and Zeilberger.

Mathematica Notebooks

1. Week 1 (Intro)
2. Week 2 (PSLQ)
3. Week 3 (Logistic map)
4. Week 4 (Groebner bases)
5. Week 5 (BBP formulas)

Further readings

Ten problems in Experimental Mathematics by Bailey, Borwein, Kapoor and Weisstein, Amer. Math. Monthly 113, 481-509, 2006. Preprint available here.

Assessment

• Assignment 1
• Assignment 2
• Final Exam

Feedback, contributions, pull-requests and high-fives are very welcome.