Sage is an open source mathematical software system that is built on many components, such as Python, sympy, numpy, gap and scipy, and also brings along the power of the Python programming language. It greatly augments the Python programming language with a rich set of libraries that enable number theoretic computations, differential and integral calculus, combinatorics, polynomials, matrix operations, cryptographic functions, 2D/3D plotting, etc. to be performed from Sage. Sage also uses iPython, a wonderful interactive shell for Python with features such as saving session history, autocomplete etc. Sage also has a notebook interface(with an authentication system) which enables users to collaborate with each other on Sage projects.

It would be impossible to cover everything about Sage. I will try to cover some applications of Sage which will be useful to a majority of people interested in using Python for mathematical computations.

Below is a broad outline of the various topics I hope to cover. 1. Introduction: Modes, usage, customizing. 2. Arithmetic and built-in functions. 3. Algebra related functions. 4. Graph plotting. 5. Number theory. 6. Matrices. 7. Generating LaTeX representation of Sage code. 8. Calling Sage functions from LaTeX. 9. Writing Sage scripts. 10. Conclusion and further reading.