- 2 new chapters, 25 new sections, 25% longer than Second Edition
- Thorough upgrades throughout the text
- Over 100 completely new routines and upgrades of many more.
- New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector Machines
- New Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres
- New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions
- An expanded treatment of ODEs with completely new routines
- linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory