Master of Science in Applied Mathematics
Department:
Applied Physics/Applied Mathematics
Transcript Designation:
Master of Science in Applied Mathematics
Program Advisor:
Academic Questions: e-mail advisor@cvn.columbia.edu
About the MS in 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 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 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 Elective Courses:
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
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
SIEO W4150: Introduction to Probability and Statistics
IEOR E4403: Advanced Engineering and Corporate Economics
IEOR E4407: Game Theoretic Models of Operations
SIEO W4606: Elementary Stochastic Processes
IEOR E4700: Introduction to Financial Engineering
Other Elective Courses (Mechanical Engineering, Materials Science, Electrical Engineering):
MECE E4100: Mechanics of Fluids
MSAE E4215: Mechanical Behavior of Structural Materials
EEME E6601: Introduction to Control Theory
Transfer of credit:
Up to 6 credit hours (points) of acceptable graduate-level academic work from an accredited academic institution
earned prior to enrolling at Columbia may be transferred to Columbia, subject to departmental approval. Students
must request the transfer of credit while applying to the MS program. Credit will only be
considered for transfer if the grades earned were at least 3.0 on the 4.0 scale. An official college transcript
and copy of the class syllabus and/or course description from the school's bulletin must accompany the "Transfer
of Credit Request" form. Please note that courses already used towards completion of another degree program cannot
be re-used for transfer credit.