Certificate of Professional Achievement in Applied Mathematics
Applied mathematics deals with mathematical concepts and techniques used in various fields of science
and engineering. Historically, mathematics was first applied with great success in astronomy and mechanics.
Then it developed into a main tool for physics, other physical sciences and engineering. It is now becoming
important in the biological, geological, economics, business, etc. With the coming of age of the computer,
applied mathematics transcended its traditional style, and now assumes an even greater importance and a
new vitality.
Compared with the pure mathematician, the applied mathematician is more interested in problems coming from
other fields. Compared with the engineer and the physical scientist, he is more concerned with the
formulation of problems and the nature of solutions. Compared with the computer scientist, he is more
concerned with the accuracy of approximations and the interpretation of results. Needless to say, even
in this age of specialization, the work of mathematicians, scientists, and engineers frequently overlaps.
Applied mathematics, by its very nature, has occupied a central position in this interplay, and has
remained a field of fascination and excitement for active minds.
Required Courses
Students must take at least three classes from among those listed below. The fourth course can be another
APMA class or may be drawn from a closely related academic area such as the Department of Industrial
Engineering/Operations Research, Computer Science, or another department subject to the approval of the Academic
Advisor. A list of elective courses is provided below.
APMA E4001: Principles of Applied Mathematics
APMA E4101: Introduction to nonlinear Dynamical Systems
APMA E4200: Partial Differential Equations I
APMA E4204: Functions of a Complex Variable
APMA E4300: Numerical Methods
APMA E4301: Numerical Methods for Partial Differential Equations
Elective Courses
Additional courses
not listed below can be applicable towards the elective requirement, subject to the approval of the faculty
advisor.
APMA E4400: Introduction to Biophysical Modeling
CSOR W4231: Analysis of Algorithms, I
COMS W4236: Introduction to Computational Complexity
COMS W4241: Numerical Algorithms and Complexity
COMS W4252: Computational Learning Theory
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
MECE E4100: Mechanics of Fluids
MSAE E4215: Mechanical Behavior of Structural Materials
EEME E6601: Introduction to Control Theory
Certificate Program Requirements
· 4 Graduate-level classes all earned through CVN, under non-degree (Video Special) student status. Students
currently in any degree program at Columbia University are not eligible for the Certificate Program through CVN.
· Minimum of 12 credit points
· Minimum GPA of 3.0
· Completion of program within two (2) calendar years.
Credits earned to fulfill the requirements of a Certificate Program may be applied toward an MS or PD degree,
subject to the approval of an Academic Advisor. However, students must apply for admission to the University
and meet all admissions requirements. Entry into, and completion of a Certificate Program does not ensure
acceptance into an MS or PD program.
In order to apply for acceptance into the Certificate Programs, please visit the link below:
Certificate Application and Instructions Page