In addition to being a comprehensive and powerful computational system, Mathematica builds in specialized functionality for many technical areas, from computational biology to wavelet analysis. Every function is tightly integrated with the whole Mathematica system, making it possible to investigate a single area in great detail and explore new ideas at the intersection of different fields.
Statistics and data analysisFrom calculating basic descriptive statistics to developing and visualizing multidimensional nonlinear models, Mathematica streamlines the entire statistical analysis workflow. With hundreds of distributions, automated parameter estimation, hypothesis testing, statistical model analysis, and more, Mathematica provides a comprehensive set of tools for assessing and understanding data.
Social network analysisHigh-level functions for community detection, cohesive groups, and centrality and similarity measures, as well as access to social networks from a variety of sources—including directly from social media sites such as Facebook, LinkedIn, and Twitter—make network analysis easier and more flexible than ever before.
Control systemsDesign and analyze control systems using classical and state-space techniques, develop control solutions for analog and digital systems, and simulate models in open- and closed-loop configurations. Easily create models including time delays and algebraic equations, and automatically create PID controllers to meet your design criteria.
Reliability engineeringAnalyze all common system structures such as series, parallel, k-out-of-n, and consecutive k-out-of-n, as well as general configurations, with symbolic and numeric methods. Mathematica supports warm, cold, and mixed standby systems. Pinpoint the most important subsystems for system reliability with built-in importance measures. Integrated survival analysis capabilities provide component models from censored data.
Parallel computingOn any multicore computer, Mathematica automatically runs multiple parts of a computation concurrently—making parallel computing easy enough for everyday use. Mathematica's parallel infrastructure is set up to allow seamless scaling to networks, clusters, grids, and clouds, while the symbolic character of the Mathematica language provides straightforward support of many programming paradigms and data-sharing models.
GPU programmingMathematica includes built-in support for CUDA and OpenCL environments, making GPU programming broadly accessible for the first time. GPU operations are fully integrated into the Mathematica system, including direct exchange of data between processes and automatic compilation and linking of GPU code.
Spline design and analysisMathematica allows you to create, visualize, and manipulate Bézier curves and B-spline and NURBS curves and surfaces in any number of dimensions. Exact symbolic handling of splines, complete integration with 2D and 3D graphics, and spline interpolation of data allow the immediate application of spline methods to any area.
Image processing and analysisWith dozens of features for real-time image acquisition, filtering, segmentation, shape analysis, feature detection, and more, Mathematica offers a complete environment and interactive workflow for image processing and analysis.
Volumetric and medical imagingMathematica extends its image processing capabilities to 3D datasets, which include pixel operations, local filtering, morphology, and more. Out-of-core processing of large images, including medical images and 3D volumes, is supported. In addition to 3D surface rendering, fast and interactive volume rendering is available. Volumes and 3D vector graphics combine seamlessly.
Signal processingMathematica's powerful signal processing capabilities include digital and analog filter design, filtering, and signal analysis using state-of-the-art algebraic and numerical methods that can be applied to audio, image, or other data.
Wavelet analysisMathematica brings a broad spectrum of wavelet analysis tools to your desktop, including support for many wavelet families, and continuous and discrete wavelet transforms. Wavelet transforms work directly with arrays of any dimension as well as sound and image data, providing a symbolic representation of the transform that can easily be visualized or used for further processing.
Financial engineeringMathematica includes built-in functions for pricing derivatives, including exotic options; for computing bond values and sensitivity measures; and for calculating time value of money. With more than a hundred financial indicators, easy connectivity to databases and web services, high-performance computing with built-in parallel processing, and more, Mathematica has everything you need for computational finance.
Geographical information systemsWith built-in geodesy data and comprehensive support for all standard reference ellipsoids, datums, and projections, Mathematica streamlines the process of importing, visualizing, and computing with geospatial data from varied sources—allowing you to apply high-precision geodetic techniques to your GIS applications.
Computational biologyBuilt-in human genome and protein data, state-of-the-art statistical analysis tools, support for regular expressions, graphs and networks, and high-performance sequence analysis algorithms, together with support for standard file formats, ensure that you have all the tools you need to model and visualize biological systems.