Master of Science in Applied Mathematics

Master of Science in Applied Mathematics

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.

Courses

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

Application Fee

1. A processing fee of $200 is required for first time applicants to a graduate degree program.
2. The Graduate Student Services Office will only process applications which are submitted with an application fee. The processing fee is non-refundable. Please make the check payable to: Columbia Video Network.
3. Applications for more than one degree program cannot be processed simultaneously.

Application Deadline

Please note: Applications are accepted on a rolling basis. Once a completed application has been received it will be processed and given to the Admissions Committee for review. Applications will be considered for the next upcoming semester's admissions cycle. For example, an application received in February will be evaluated for the upcoming Summer semester. Only completed applications will be submitted to the Admissions Committee for review.

Transcripts

1. Official transcripts from each college/university you have attended or are currently attending must be submitted with the application. Transcripts must be in the original, sealed envelope.
2. Credits which appear as transfer credits on any other transcript are not valid; an official transcript from the school where the credits were earned must be submitted.
3. Students who have previously or are currently enrolled at Columbia University must request that copies of their transcripts be sent to CVN at Columbia Video Network, 500 W 120th St, 540 MUDD, MC 4719, New York, NY 10027
4. The Graduate Student Services Office requests that transcripts be submitted with the application. If you foresee a delay in submitting official transcripts, please attach an unofficial set to the application. Your file may be reviewed by the department with a complete set of unofficial documents; however, you will be required to submit official transcripts before you will be formally admitted to a graduate degree program.
5. All materials submitted in support of an application, whether official or unofficial, become the property of Columbia University and will not be returned to the applicant or forwarded to other schools or agencies. Since your documents will not be returned, we suggest that you keep copies of any documents you may need for your personal records.

Required Exam Scores

1. Graduate Record Exam (GRE) general test results are required of all MS applicants. GRE scores are valid for 5 years.
2. TOEFL or IELTS is required of all candidates who have not received their bachelor's degree in a country where English is the official spoken language. TOEFL and IELTS scores are valid for two years.
3. All score reports must be official and sent to Graduate Admissions directly from the Educational Testing Service (ETS).
4. The Columbia Engineering CEEB code is 2111 (not 2162 which belongs to the Graduate School of Arts and Science).

Required Documemts

These application materials are designed to help individuals provide personal and academic information about themselves, which will be used to evaluate their candidacy for admission to graduate study in the Fu Foundation School of Engineering and Applied Science at Columbia University. Applicants can assist the Graduate Admissions office in providing prompt feedback about their application status by not submitting extraneous information which has not been requested such as excessive numbers of recommendation letters, copies of abstracts and theses, videotapes and/or photographs of research work, and secondary school transcripts. The information below indicates what items are required for a complete application.

1. Degree application form (online)
2. Two recommendation letters in sealed envelopes via mail, or directly from the recommender via e-mail to records@cvn.columbia.edu
3. Official GRE general exam results

• All score reports must be official and sent directly from the Educational Testing Service (ETS)
• The Columbia Engineering CEEB code is 2111

Please note: Students that begin their studies at Columbia University under non-matriculated status through CVN must continue to take all of their coursework through CVN. When applying for admission to a degree program, students must submit all of their application materials directly to Columbia Video Network for processing. Applications that are sent directly to the Office of Graduate Student Services or submitted online via the ApplyYourself Application form instead of CVN's forms will result in total forfeiture of all credits taken under non-matriculated status through CVN. All Columbia courses to be used towards a student's program must be completed via CVN. Also note that any student taking courses through the auspices of CVN can take on-campus courses solely under the administrative guidance of CVN with advisor approval.