应用数学

Multi tool use應用數學(英语:Applied Mathematics)是以應用為目的的明確的數學理論和方法的總稱,研究如何應用數學知識到其他範疇(尤其是科學)的數學分支,可以說是純數學的相反,應用純數學中的結論擴展到物理學等其他科學中,應用數學的發展是以科學為依據,作為科學研究的後盾。包括線性代數、矩陣理論、向量分析、複變分析、微分方程、拉普拉斯變換、傅里葉分析、數值分析、概率论、數理統計、運籌學、博弈論、控制理論、組合數學、資訊理論等許多數學分支,也包括從各種應用領域中提出的數學問題的研究。而大部分應用數學是以作為物理分析的工具。計算數學有時也可視為應用數學的一部分。應用數學大部分的教學範疇都是以物理的模型為基礎進行分析,當中或許搭配了各種數學工具,就為了更貼近物理的系統。
圖論應用在網絡分析,拓撲學應用在電路分析,群論應用在結晶學,微分幾何應用在規範場,自動控制理論應用在計算,黎曼幾何應用於相對論,數理邏輯應用於計算機,最小二乘法應用於飛機起降時自動控制,利用數字合成計算機輔助的X射線斷層成像技術(1979年數學家獲得諾貝爾醫學獎)數論應用在密碼學,博弈論、概率論、統計學應用在經濟學,線性規劃用於生產安排調度,都可見數學在不同範疇的應用。
参看
数学领域
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| 注释:数学的领域也可根据“MSC分类标准”或“中国学科分类国家标准”进行分类。 | | 领域 | - 数理逻辑
- 集合论
- 范畴论
代数
- 数论
分析/微积分学
微分方程/动态系统
- 数学物理
- 数理统计
几何
- 拓扑
- 动力系统
- 组合
- 泛函分析
- 博弈论
- 信息论
- 图论
- 数学教育
- 数理逻辑
- 数学物理
- 数值分析
- 最优化
- 序理论
- 数学哲学
- 娛樂數學
- 计算
- 概率
- 表示
- 统计
- 三角
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