There is a lot of practical information in the subject handbook entry.
In a nutshell, we will spend the semester exploring the use of computational methods (predominantly of a symbolic, as opposed to numerical, nature) to assist research in mathematics. The main tools at our disposal will be the software package Mathematica (which you can obtain via this webpage, look for Wolfram) and the free open source system SageMath (which can be obtained here).
I will give more information about this in the first lectures, but you can get a head start and attempt to install this software on your own computer/laptop. It will be possible to access and use the software without installing it on your own device, but this will give you more flexibility.
The first assignment is now available! Get the pdf file here.
Lecture and lab notes
I'll try to keep writing up some kind of narrative around the things that I mention in the lectures and labs.
Here is the current version of the lecture notes (last modified Friday 29 May).
Here is the current version of the lab worksheets (last modified Friday 29 May).
Code from labs and lectures is slowly making its way to this GitHub repository.
Here is my code for the function intrel:
def intrel(xlst, A):
n = len(xlst)
mlst = identity_matrix(n).rows()
ylst = [(A*x).floor() for x in xlst]
M = matrix(ZZ, mlst)
MR = M.transpose().LLL().transpose()
You use it as follows:
x1 = RR(arctan(1))
x2 = RR(arctan(1/5))
x3 = RR(arctan(1/239))
intrel([x1, x2, x3], 10^6)
- official webpage
- documentation webpage
- Melbourne Uni server (need to be on-campus or use VPN)
- cocalc server (freemium model)
- Python 3 documentation
- book by Greg Bard
- book by Paul Zimmermann et al
- Q & A forum
- documentation centre
- Q & A forum (stackexchange)
- demonstrations project
- language fundamentals
- book by Jon Borwein and Matthew Skerritt (library link)
- symbolics book by Michael Trott (library link)
- numerics book by Michael Trott (library link)
- programming book by Michael Trott (library link)
Other online resources
- Online Encyclopedia of Integer Sequences
- Wolfram Alpha
- David Bailey's Experimental Mathematics website
- M. Petkovsek, H. Wilf, and D. Zeilberger, A=B
- T. Judson, Abstract Algebra