Cambridge University Press by Paul Taylor - Practical Foundations collects the methods of construction of the objects of twentieth century mathematics, teasing out the logical structure that underpins the informal way in which mathematicians actually do
A GNU-FDL book on algorithmic graph theory by David Joyner, Minh Van Nguyen, and Nathann Cohen. This is an introductory book on algorithmic graph theory. Theory and algorithms are illustrated using the Sage open source mathematics software.
The art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Application to mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations.