Introduction to Computational Mathematics
The goal of this book is to introduce programming and higher mathematics in a combined setting, for the sake of preparing the reader to further their studies in mathematics, scientific computing, or engineering.
While some topics may be reminiscent of a text on numerical analysis, the style is intended to contrast with those efforts by taking a rigorous approach to software engineering, and a less rigorous approach to the underlying mathematics.
The mathematics presented in this book is entirely constructive, and that is by design; the student should be able to program their own mathematical universe piece-by-piece as new algorithms are introduced. The disadvantage of this approach is that continuity will be oversimplified; interested readers will need to pursue a course in analysis.