AutoAbacus
- An equation solving library that finds solutions to equation sets. A set of equations can be passed in as text, while AutoAbacus attempts to find a solution that satisfies all constraints. [Commercial, trial version]
- http://www.singularsys.com/autoabacus/

Colt
- High performance scientific and technical computing data structures and methods. (Open Source, Attribution)
- http://dsd.lbl.gov/~hoschek/colt/

Mersenne Twister Pseudo Random Number Generator Classes
- Offers multiple replacement implementations for java.util.Random. [Open Source]
- http://www.axlradius.com/freestuff/Free.htm

JMP - Sparse matrix library
- A library for sparse matrix computations. Includes a sparse BLAS, many iterative solvers for different problems, sparse matrix I/O and parallelization. [Open source, GPL]
- http://rs.cipr.uib.no/mtj/

JGraphT
- A class library that provides mathematical graph-theory objects and algorithms. JGraphT supports a rich gallery of graphs and is designed to be powerful, extensible and easy to use. [Open source, LGPL]
- http://jgrapht.sourceforge.net/

Mantissa (Mathematical Algorithms for Numerical Tasks In Space System Applications)
- A class library devoted to simulation, including a comprehensive ODE solving package, as well as least square estimators, solvers, polynomials, basic statistics features. [Open source, BSD-like]
- http://www.spaceroots.org/software/mantissa/index.html

JMathTools
- A mathematical Java toolbox designed to be easily used and modified for scientific software engineering. [Open source, BSD License]
- http://jmathtools.sourceforge.net

Mathematical expression parser library for Java [GPL]
- Library to parse mathematical expressions like x^2+sin(x)-root(1/3*x). The following mathematical operations are supported: + - * / ( ) ^ root log sin cos tan asin acos atan. [Open source, GPL]
- http://oglimmer.de/java/mathematical_expression_parser.php

JEP - Java Mathematical Expression Parser
- Java classes for parsing and evaluating mathematical expressions. Supports multiple variables and user-defined functions. [Open source, GPL or commercial]
- http://www.singularsys.com/jep/

JFormula
- A Java library for evaluating mathematical expression. It is compatible with the JDK 1.1 and later. [Shareware]
- http://www.japisoft.com/

JEPLite
- A light-weighted (re)implementation of the Java Expression Parser (jep.sourceforge.net). The intention is to strip some of its not-so-often-used features, and thus speeding the rest. Includes expression optimizer. [Open source, GPL]
- http://jeplite.sourceforge.net/

Significant Figures
- Handles parsing, rounding, and displaying numbers for scientific applications.
- http://ostermiller.org/utils/SignificantFigures.html

Math Parser
- Package to parse and evaluate mathematical expressions at runtime. [Commercial]
- http://www.bestcode.com/html/jbcparser.html

Java Numerics
- Working group that offers presentation, news, and libraries related to numerical computing.
- http://math.nist.gov/javanumerics/

JeksParser
- Parses and computes expressions or functions primarily for use in spreadsheet applications such as the example provided. [Beta Evaluation]
- http://www.eteks.com/jeks/en/

Decimal Arithmetic for Java
- Improved BigDecimal class from IBM. [Open source]
- http://www2.hursley.ibm.com/decimalj/

JMatLink
- Connects Java and MATLAB. Native methods make it possible to use MATLAB's computational engine inside your own java applications, applets and servlets. [Freeware, source available]
- http://www.held-mueller.de/JMatLink/

ArciMath BigDecimal
- Fast and improved BigDecimal class. [Commercial/Free]
- http://users.belgacombusiness.net/arci/math/