Principles of Ultralinear Algebra: an article collection

While developing Mathematics, Physics, Chemistry and Engineering, it was often necessary to introduce some calculus tools outside of the rigorous mathematical frameworks of the time, during which those tools were needed. One of the many classic examples is the differential calculus introduced by Newton and Leibniz and then, only several years later, formalized by Cauchy; and even the differential calculus introduced by Newton and Leibniz was indeed a systematization of a disordered set of useful mathematical technics adopted for many years before the two great scientists. Every time this happened, it has encouraged some mathematical researches, leading to an expansion of the present mathematical framework in order to incorporate the new tools.