Algebra, Data Analysis, Fitting, Computer Aided Mathematics

Tools that can assist with algebra, data analysis, fitting and symbolic math (including calculus and linear algebra).
Algebra with SymPy

A tool that allows you to tell the computer what algebraic steps to perform. This facilitates rapid manual manipulation and simplification of complex equations. When used in a Jupyter environment this tool produces typeset equations at each step in the manipulation. This can also be used to leverage some of the automatic equation solver capabilities in SymPy.

lmfit

Tool for fitting data in a relatively straightforward way using python. Has many standard built-in fits and can be extended.

Pandas

A python tool for handling data sets made of multiple related lists (columns, arrays). Works well with lmfit.

Jupyter Pandas GUI

A GUI tool for manipulating and plotting Pandas DataFrames within Jupyter notebooks.

NumPy

Tools for numerical calculations on lists (arrays) in python. Works well with Pandas.

Plotly Python Tools

Python tools to facilitate generating plotly based plots in Jupyter notebooks.

K3D-Jupyter

Tool for very fast interactive 3-D visualization in Jupyter notebooks.