This work represents our effort to present the basic concepts of vector and tensor analysis. Volume
I begins with a brief discussion of algebraic structures followed by a rather detailed discussion o . . . . .
This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covere . . . . .
Contents: Introduction; Curves; Gauss Curvature; Surfaces in E3; First Fundamental Form; Second Fundamental Form; The Gauss Curvature in Detail; Geodesics; The Curvature Tensor and the Theorema Egregi . . . . .
This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs.
Why do students take the instruction "prove" . . . . .
Contents: 1. Lorenz Model: an introduction to chaos; 2. The Pendulum: the language of dynamical systems; 3. Nonlinear Oscillators: quasiperiodicity and frequency locking; 4. One Dimensional Maps; 5. T . . . . .
This Electronic Statistics Textbook offers training in the understanding and application of statistics. The material was developed at the StatSoft R&D department based on many years of teaching underg . . . . .
Contents: Introduction; Partial Differentiation; Curves and Surfaces; Line Integrals and Exact Differentials; Multiple Integrals; Vector Differential Operators; The Big Integral Theorems; Orthogonal . . . . .
This is a textbook about prime numbers, congruences, basic public-key cryptography, quadratic reciprocity, continued fractions, elliptic curves, and number theory algorithms. We assume the reader has . . . . .
Contents: Basic Axioms for Z; proof by induction; elementary divisibility properties; The floor and ceiling of a real number; The division algorithm; greatest common divisor; the eucledian algorithm; . . . . .
Contents: Principles of Numerical Calculations; How to Obtain and Estimate Accuracy; Series, Operators and Continued Fractions; Interpolation and Related Subjects; Numerical integration; Scalar Nonlin . . . . .