The reader finds a lot of other mathematical tools and toolboxes in the Internet. I have basically concentrated on numeric optimization. Further tools I found interesting are given below.
SageMath is an open source mathematical software built out of nearly 100 open-source packages to study elementary and advanced, pure and applied mathematics. This includes a huge range of mathematics, including basic algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra and much more. SageMath can also be linked to most advanced optimization libraries like Gurobi or Cplex.
Scilab is another open source software for numerical computation. It is –like GNU Octave an open-source alternative to MATLAB. It also contains a high-level, numerically oriented programming language.
A very popular open-source environment for developing models is Jupyter Notebook. All mentioned systems in Python or Julia can be neatly be integrated with Jupyter Notebook. But other languages can be used: Go, Scala, Erlang, etc. For teaching math modeling this is an excellent tool. If you like to model with JuMP/Julia, for instance, you only need to install the IJulia package:
using Pkg Pkg.add("IJulia") using IJulia notebook()Now you are ready to use the Notebook to interactively enter the model code.
The R-Project is a open-source tool containing a programming language basically for statistical applications. But it has also interface to optimization tools.
The NEOS Server is an Internet-based client-server application that provides free access to more than 60 libraries of optimization solvers. A model can be submitted in various formats (GAMS, AMPL, and others).
Mathcad Prime was the first to introduce 1986 live editing (WYSIWYG) of typeset mathematical notation in an interactive notebook, combined with automatic computations. A idea copied by many other systems. The current commercial version contains many features in numerical and symbolic mathematics, visualization, etc. It is not as powerful as Maple or Mathematica.
Besides of the already mentioned solver libraries (Gurobi, Cplex, XPress), HiGHS is one of the most advanced open-source linear optimization solver. MOSEK is a commercial solver library and solves LPs, QPs, SOCPs, SDPs and MIPs. It includes interfaces to C, C++, Java, MATLAB, .NET, Python and R. Knitro is one of the most advanced solver for nonlinear optimization.
If you just need a powerful mathematical library containing high performance algorithms and you program everything else yourself, consider the Nag Library.