Computational mathematics

Field of mathematics that uses computational techniques

Overview

The YBC 7289 clay tablet, an ancient Babylonian mathematical artifact.

Computational mathematics is a field of mathematics that involves the use of algorithms, numerical analysis, and computer science to solve mathematical problems. It is an interdisciplinary area that combines elements of applied mathematics, computer science, and engineering.

History

The roots of computational mathematics can be traced back to ancient civilizations, such as the Babylonians, who used clay tablets like the YBC 7289 to perform calculations. Over the centuries, the development of mathematical notation and calculus laid the groundwork for modern computational techniques.

Key Concepts

Algorithms

An algorithm is a step-by-step procedure for solving a problem or performing a computation. In computational mathematics, algorithms are essential for tasks such as numerical integration, optimization, and data analysis.

Numerical Analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is concerned with the accuracy and stability of numerical methods and is a fundamental aspect of computational mathematics.

Computer Science

Computer science provides the tools and techniques for implementing algorithms on computers. It includes the study of data structures, programming languages, and software engineering, all of which are crucial for computational mathematics.

Applications

Computational mathematics is applied in various fields, including:

• Physics: For simulating physical systems and solving differential equations.
• Engineering: In the design and analysis of structures and systems.
• Finance: For modeling financial markets and risk management.
• Biology: In the analysis of biological data and modeling of biological systems.

Related Pages

• Numerical analysis
• Algorithm
• Computer science
• Applied mathematics