Computational mathematics: Difference between revisions

Latest revision as of 11:09, 15 February 2025

Field of mathematics that uses computational techniques

Overview[edit]

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[edit]

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[edit]

Algorithms[edit]

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[edit]

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[edit]

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[edit]

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[edit]

@@ Line 1: / Line 1: @@
-'''Computational mathematics''' involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods with the concept of computation. The field is different from theoretical and applied mathematics.
+{{Short description|Field of mathematics that uses computational techniques}}
+{{Use dmy dates|date=October 2023}}
 == Overview ==
-[[Computational mathematics]] may also refer to the use of computers for mathematics itself. This includes the use of computers for mathematical computations, mathematical research, the study of [[algorithm|algorithms]] and data structures, and the visualization of mathematical results. The field also includes the study of the mathematical properties of computational methods and various aspects of scientific computing.
+[[File:Ybc7289-bw.jpg|thumb|right|The YBC 7289 clay tablet, an ancient Babylonian mathematical artifact.]]
+'''Computational mathematics''' is a field of mathematics that involves the use of [[algorithm]]s, [[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 history of computational mathematics can be traced back to the ancient times. The [[abacus]], a simple counting aid, could be considered the earliest form of computational mathematics. The development of [[calculus]] by [[Isaac Newton]] and [[Gottfried Wilhelm Leibniz]] in the 17th century revolutionized mathematics and is a cornerstone of modern computational mathematics.
+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.
-== Fields of Computational Mathematics ==
+== Key Concepts ==
-Computational mathematics involves several fields, including:
-* [[Computational geometry]]: This field deals with the study of algorithms which can be stated in terms of geometry.
+=== Algorithms ===
-* [[Computational number theory]]: Also known as algorithmic number theory, it involves the design, analysis and implementation of algorithms to solve problems in number theory.
+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]].
-* [[Computational algebra]]: This field involves the use of computers to solve problems in algebra.
-* [[Computational calculus]]: This field involves the use of computers to solve problems in calculus.
+=== Numerical Analysis ===
-* [[Computational statistics]]: This field involves the use of computers to solve problems in statistics.
+[[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 has wide applications in various fields such as [[physics]], [[engineering]], [[economics]], [[biology]], and [[computer science]]. It is used to solve complex mathematical problems, model natural phenomena, and simulate physical systems.
+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.
-== See also ==
+== Related Pages ==
-* [[Mathematical software]]
 * [[Numerical analysis]]
-* [[Scientific computing]]
+* [[Algorithm]]
-* [[Computational science]]
+* [[Computer science]]
+* [[Applied mathematics]]
-== References ==
-<references />
 [[Category:Computational mathematics]]
-[[Category:Mathematics]]
+[[Category:Applied mathematics]]
-[[Category:Computer science]]
+[[Category:Numerical analysis]]
-{{math-stub}}
-{{compsci-stub}}