For terminology, see the math programming glossary
You will find the software package polymake useful in studying systems of linear inequalities and convex polytopes. If you are on (most of) the FCS Linux machines, you can find a local copy of the documentation at /fcs/software/polymake/doc/. To use polymake on FCS Linux machines, you need to add
/fcs/software/polymake/binto your search path.The package glpk can solve linear and integer-linear programs. You can find a local copy of the documentation on my web page.
Jeff Kantor has written web based MathProg IDE
mathp.org is another similar effort.
COIN-OR is an extensive collection of libraries supporting linear programming, integer programming, and much more.