This book is a concise presentation of the basic concepts used in evolving numerical methods. Special emphasis is placed on developing computational algorithms for solving problems in algebra and calculus on a computer. The author's approach ensures a conceptual understanding of numerical methods by relying on readers' geometric intuition. It is written for undergraduate science and engineering students who have taken a first course in differential and integral calculus. The book provides coverage of iterative methods for solving algebraic and transcendental equations, direct and iterative methods of solving simultaneous algebraic equations, numerical methods for differentiation and integration, and solution of ordinary differential equations with initial conditions. The formulation of algorithms is illustrated with a number of solved examples; an algorithmic language based on English (and similar to PASCAL) is used to express the logic of the numerical procedures. This approach is different from that used in most books which either use a programming language such as FORTRAN or flow charts to express algorithms. The solutions to selected problems are provided at the end of the book.