• Home
  • Free Previews
  • Request Additional Information
  • Getting Started
  • Non-Degree Program
• About CVN
  • Accreditation
  • How It Works
  • Student Testimonials & Quotes
  • Press
  • Contact Us
• Academic Programs
  • Academic Calendar
  • Course Listings
  • Fall 2008
  • Summer 2008
  • Spring 2008
  • Degree Programs
  • Certificate Programs
  • Applied Mathematics
  • Business Technology
  • Civil Engineering
  • Computer Science
  • Electrical Engineering
  • Financial Engineering
  • Industrial Engineering Operations Research
  • Materials Science
  • Mechanical Engineering
  • Nanotechnology
  • Application for Degree
• Student Center

Certificate of Professional Achievement in Applied Mathematics

Please note: This page is applicable to students who are seeking acceptance into the Applied Math Certificate program for the Summer 2008 semester and later. For those students admitted into the program prior to the Summer 2008 semester, please refer to the old program requirements.

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. 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/she is more concerned with the formulation of problems and the nature of solutions. Compared with the computer scientist, he/she 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 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

APPH E4100: Quantum Physics of Matter

APPH E4200: Physics of Fluids

APPH E4301: Introduction to Plasma Physics

MSAE E4215: Mechanical Behavior of Structural Materials

Certificate Program Requirements

· 4 Graduate-level classes all earned through CVN, as a non-degree student. 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