Numerical Mathematics

Numerical Mathematics is a unique book that presents rudimentary numerical mathematics in conjunction with computational laboratory assignments. No previous knowledge of calculus or linear algebra is presupposed, and thus the book is tailor-made for undergraduate students, as well as prospective mathematics teachers. The material in the book emphasizes algorithmic aspects of mathematics, which are made viable through numerical assignments, in which the traditional "chalk-and-talk" lecturer turns, in part, into a laboratory instructor. It guides the student to create the algorithm required for any given assignment expressed in whichever programming language is used on the basis of the underlying mathematics. The computational assignments cover iterative processes, area approximations, solution of linear systems, acceleration of series summation, interpolative approximations, and construction of computer-library functions. Throughout the book, strong emphasis is put upon vital concepts such as error bounds, precision control, numerical efficiency, computational complexity, as well as round off errors and numerical stability. The book is not a numerical methods book, containing ready-made computational recipes, but it is the authors' belief that the material presented in this book is part and parcel of the mathematical foundations that should be acquired by a student in the microcomputer era.