Columbia University offers an exceptional environment for graduate study in applied mathematics leading Master of Science (M.S.), Master of Philosophy (M.Phil.), Doctor of Philosophy (Ph.D.) and Doctor of Engineering Science (Eng.Sc.D. or DES) degrees. The applied mathematics faculty in the Department of Applied Physics and Applied Mathematics are expert in a wide variety of application areas and perform multidisciplinary research spanning atmospheric, oceanic, and climate science; geophysics and solid-earth dynamics; waves in fluids, optics and quantum systems; imaging & image processing; inverse problems, inference and machine learning; bioinformatics & systems biology. Close collaborations exist with Columbia’s Lamont Doherty Earth Observatory and Columbia’s medical school.

1、Principles of applied mathematics

2、Introduction to dynamical systems

3、Applied functional analysis

4、Partial differential equations

5、Functions of a complex variable

6、Introduction to numerical methods

7、Numerical methods for partial differential equations

8、Analytic methods for partial differential equations

9、Numerical analysis for partial differential equations

10、Analysis of algorithms I

11、Introduction to computational complexity

12、 Numerical algorithms and complexity

13、 Computational learning theory

14、 Industrial economics

1、應(yīng)用數(shù)學(xué)原理

2、動力系統(tǒng)介紹

3、應(yīng)用功能分析

4、偏微分方程

5、復(fù)變函數(shù)

6、數(shù)值方法介紹

7、偏微分方程的數(shù)值方法

8、偏微分方程分析方法

9、偏微分方程的數(shù)值分析

10、算法分析1

11、計算的復(fù)雜性介紹

12、數(shù)值算法和復(fù)雜性

13、計算學(xué)習(xí)理論

14、產(chǎn)業(yè)經(jīng)濟(jì)學(xué)