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PrefacePreface

I have a degree in Physics from many years ago and have recently taken to refreshing my knowledge and bring it up to date with recent developments. This is exactly what Leonard Susskind's is trying to help people like me with his fine set Theoretical Minimum material. Each step of the way I have had to go further and further back into my past studies - almost back to high school! On refreshing my maths knowledge I came across the fantastic series of Linear Algebra lectures given by Gilbert Strang at MIT. These lectures are hosted at MITOPENCOURSEWARE Linear Algebra

My aim is to eventually have refreshed my maths to such an extent that I can get past the first couple of chapters of Quantum Field Theory For the Gifted Amateur. This is not happening very quickly but with all this wonderful material available for free I am slowly getting there!

This notebook is an online repository of some Sage Math techniques I have come across in the above pursuits. It is at a very rudimentary level and is far from organised. Over time it may become more coherent and be useful to others.

Another motivating factor is that my daughter, Anna, has just embarked on a four year Maths and Biology Degree at Edinburgh University. I'm hoping that this manual may provide here with some useful material to make here learning experience more fruitful.

The format of this book is taken from Robert Beezer's wonderful work with MathBook XML.

Sage (sagemath.org) is a free, open source, software system for advanced mathematics, which is ideal for assisting with a study of abstract algebra. Sage can be used either on your own computer, a local server, or on SageMathCloud (https://cloud.sagemath.com).

John A Giannelli
Linlithgow, Scotland 2017