Mathematics of Approximation The approximation of a continuous function by either an algebraic polynomial a trigonometric polynomial or a spline is an important issue in application areas like computer aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation and with the prerequisites of only calculus and linear algebra the material is targeted at senior undergraduate level with a treatment that is both rigorous and self contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton Cotes Gauss and Clenshaw Curtis quadrature; the Euler Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation with an extensive treatment of local spline interpolation and its application in quadrature. Exercises are provided at the end of each chapter. Polynomial Interpolation Formulas Error Analysis For Polynomial Interpolation Polynomial Uniform Convergence Best Approximation Approximation Operators Best Uniform Polynomial Approximation Orthogonality Interpolatory Quadrature Approximation of Periodic Functions Spline Approximation.