Columbia University Graduate Engineering Distance Learning

Master of Science in Applied Physics: Applied Mathematics

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Department: Applied Physics/Applied Mathematics
Transcript Designation: Master of Science in Applied Physics: Applied Math
Program Advisor: Questions:

About the Applied Mathematics Program:

Applied mathematics is the language of science, engineering, and fields beyond. Just as English is spoken by more non-native speakers than by native, mathematics is used daily by more non-mathematicians than by mathematicians. A Master's Degree in Applied Mathematics is an ideal career complement to nearly any practicing or aspiring researcher in quantitative domains. This has always included the physical sciences and has in the past decades increasingly included the biological and social sciences, as well. With the advent of commodity high-performance computing, applied mathematics has transcended its traditional analytical style and assumes an even greater importance and vitality in the realm of simulation.

Compared with the pure mathematician, the applied mathematician is more interested in problems driven by external fields. Compared with the engineer or scientist, she is more concerned with the formulation of problems (modeling) and the nature of solutions in the abstract. Compared with the computer scientist, he is more concerned with the tradeoff of accuracy against complexity and the interpretation of results. The work of members of all these groups often overlaps, and applied mathematics is smack in the active middle. As such, it naturally offers a degree with flexible elective requirements.

Admission Requirements:

Degree required for admission: Students admitted to the program must possess an undergraduate degree in engineering, science, mathematics, computer science or other related field (subject to the approval of the Applied Mathematics Program) from an accredited academic institution. Applicants should have a strong undergraduate record to be competitive for admission.

GPA required: Minimum of 3.0

GRE requirements: General test required

Other application requirements: Two recommendation letters, transcripts, resume, and a personal-professional statement are required. TOEFL test scores are required of all students who received their bachelor's degree in a country where English is not the official and spoken language. All application requirements in the Graduate Application must be completed as specified in the application.

Degree Requirements:

Students must complete all core courses (described below) and selected electives (described below) for a total of 30 graduate points of academic work via CVN with an academic average of 2.5 or better. All degree requirements must be completed within 5 years of the beginning of the first course credited toward the degree. This includes courses taken in the non-degree program.

Core Courses:

The core courses provide a student with a foundation in the fundamentals of Applied Mathematics. The core courses contribute 15 points of graduate credit toward the degree. Students must complete at least five of the following ten classes:

APMA E4001: Principles of Applied Mathematics

APMA E4101: Introduction to Nonlinear Dynamical Systems

APMA E4150: Applied Functional Analysis

APMA E4200: Partial Differential Equations

APMA E4204: Functions of a Complex Variable

APMA E4300: Numerical Methods

APMA E4301: Numerical Methods for Partial Differential Equations

AMCS E4302: Introduction to Parallel Scientific Computing

APMA E6301: Analytic Methods for Partial Differential Equations

APMA E6302: Numerical Analysis of Partial Differential Equations

Elective Courses:

A student must select five elective courses from those listed above or below for a total of 15 points of graduate credit. All of the courses shown are currently available through CVN. These courses allow the student to pick subjects from a variety of areas to complement the core program. Additional courses not listed below can be applicable towards the elective requirements, subject to the approval of the faculty advisor.

Applied Mathematics and Applied Physics Elective Courses:

APPH E4210: Geophysical Fluid Dynamics

APMA E4400: Introduction to Biophysical Modeling

Computer Science Elective Courses:

CSOR W4231: Analysis of Algorithms, I

COMS W4236: Introduction to Computational Complexity

COMS W4241: Numerical Algorithms and Complexity

COMS W4252: Computational Learning Theory

COMS W4701: Artificial Intelligence

CBMF W4761: Computational Genomics

COMS W4771: Machine Learning

Industrial Engineering/Operations Research Elective Courses:

IEOR E4003: Industrial Economics

IEOR E4004: Introduction to Operations Research: Deterministic Models

IEOR E4007: Optimization: Models and Methods

IEOR E4106: Introduction to Operations Research: Stochastic Models

IEOR E4403: Advanced Engineering and Corporate Economics

IEOR E4407: Game Theoretic Models of Operations

IEOR E4701: Stochastic Models for Financial Engineering

Other Elective Courses (Mechanical Engineering, Materials Science, Electrical Engineering):

MECE E4100: Mechanics of Fluids

MECE E4302: Advanced Thermodynamics

MECE E4501: Geometrical Modeling

MSAE E4215: Mechanical Behavior of Structural Materials

ELEN E4815: Random Signals and Noise

ELEN E6711: Stochastic Models in Information Systems

EEME E6601: Introduction to Control Theory