Applied Math Advising FAQ

This FAQ covers academic questions. For real life questions, it is strongly advised to consult with Columbia's health page, e.g., ODS and CPS.

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1. What is Applied Math?
   • Spiegelman's Definition: Applied Math is mathematics applied to solving problems that arise from a wide variety of fields including physics, biology, economics and finance, Earth science, computer science, sociology and pure mathematics…you name it. A central activity in applied mathematics is developing mathematical tools and models to understand natural and human systems.
   • Wiggins's Definition: using mathematics as a tool for thinking clearly about the world.
2. How does the Applied Math Major work?
   • As befits the broad scope of Applied Mathematics, the Columbia undergraduate Applied Math Major is extremely flexible and combines a core set of required courses with a broad selection of technical electives (min 21 points). (see the Appmath Bulletin)
   • Required Courses
     • Linear Algebra
     • Partial Differential Equations
     • Complex Variables
     • 2 courses in Probability and Applied Probability
     • Dynamical Systems
     • Numerical Methods
     • Modern Analysis
     • Junior and Senior Seminar
     • Research
   • Technical Electives: Any 3000/4000 level course (or above) in math, statistics, science, engineering, computer science, and some technical classes in Economics (but not all)
   • Charts / Degree “Tracks” :
     • First and Second Years
     • Third and Fourth Years

1. Can I take X as a tech elective?
   • See the tech faq
2. Can I take Y as a non-tech elective?
   • See the nontech faq
3. Can I substitute Required Class X for Class Y?
   • There is a standard set of substitutions for many of the required classes and are listed in the fine print in the Third/Fourth year table for Applied Math Appmath Bulletin.
     • Linear Algebra can be satistfied by either APMA 3101 or Math V2010
     • PDE's can be satistfied by either APMA 3102, APMA 4200 or Math V3028
     • Complex Variables: APMA 4204 or Math V3007
     • Modern Analysis: Math V4061 or Math V2500
     • Probability and Applied Probability: One course from Group A and one from Group B (see below)
   • Note: While much of the material is the same between substitution courses, the emphasis (pure vs. applied math) may be different and you should consult with the course professor or course descriptions for details.
   • Examples:
4. Does one course of APMA E2101 complete the requirements of ODE and Linear Algebra (APMA E3101) for people majoring in applied mathematics?
   • No. Students majoring in applied math should take a full ODE course and a full Linear Algebra course.
5. What is all this Group A and B business?
   • Students are required to satisfy two courses in the very broad field of probability and applied probability (e.g. statistics). In past years these have officially been Probability (SIEO 4105) and Statistical Inference (STAT 4107), but in reality there have been considerable room for substituion. From Fall 2006 the requirements will officially be a minimum of two courses, one from group A and one from Group B.
     • Group A
       • Probability SIEO 4105 or SIEO 3658
       • Introduction to Probability and Statistics SIEO 3600 or SIEO 4150
       • Probability Theory Math 4155
     • Group B
       • Introduction to Statistics STAT 3105 (formerly W3000) or STAT W4105
       • Statistical Inference STAT 3107 (formerly W3659) or STAT W4107
       • Elementary Stochastic processes SIEO W4606
       • Stochastic models IEOR E3106 or IEOR E4106
       • Monte Carlo simulations IEOR E4703
       • Machine Learning COMS 4771
       • Introduction to Statistical Inference STAT W3107
       • Statistics W4240 DATA MINING
       • Statistics W4335 SAMPLE SURVEYS
   • Other classes (e.g., Stats 4109) may be substituted with advisor approval. (there's information on the stats website as well as the stats website for columbia college courses; note that, according to Anthony Cruz, Administrative Assistant in the Stats dept, “there isn't any difference between the two courses [SIEO4105 and STATS4105]. one course is offered via the IEOR department the other course is offered in the STAT department.”)
   • note that “Economics W3412 econometrics” does not satisfy a stats requirement.
6. Who are the APAM advisors?
   • General AppMath Advisor — Prof. Marc Spiegelman
     • Class of 2010 Advisors — Prof. Marc Spiegelman and Prof. Lorenzo Polvani (note that Professor Spiegelman will likely be on sabbatical in the Spring of 2009)
     • Class of 2011 Advisors — G. Bal (student last name: A-L) and A. Sobel (student last name: M-Z)
   • Columbia Junior/Senior Class Center Dean Andrew Plaa
   • These are the “official advisors” but students should feel free to approach any member of the Appmath faculty for advice, particularly if you are interested in a specific area of expertise.
7. What about for the 1st two years?
   • SEAS has a special page for advising resources in the first two years here
8. When should I speak with my advisor?
   • Early and often. Much of the applied math major depends upon good advising.
9. What should I bring when I meet with my advisor?
   • You should always bring a copy of your DAR (Degree audit report) and an outline of your two-year plan for finishing both the Required courses and Specialization.
10. How do I find a research advisor, e.g., for E3900?
    • It's important to find a subject that you really care about, or a skill you would like to build on. Start there and ask faculty for help connecting with the most appropriate advisor. This tends to work better than approaching a faculty member and asking ``what do you have?” You should come to an agreement with the faculty member before the semester starts. Make sure you and the professor agree on what concrete deliverable will be delivered by a certain date.
    • Things that would be worked out to register for 3900 credit (plan early!)
      • approval by an AM faculty member,
      • clear statement of deliverable,
      • deadline for the deliverable,
      • consent by a scientific advisor that she or he will suggest a letter grade upon delivery of deliverable,
      • agreement among all 3 parties about the amount of work to be done and number of credits to be awarded for that work.
11. Does SEAS offer any financial support for travel related to Senior Projects?
    • While CC seems to have a stated policy of granting $500 to seniors, SEAS does not (yet). However, Dean Galil has been known to reimburse travel for field work on one occasion, in relation to sustainable development. Until SEAS has some offical policy on this, they will have to be addressed (argued) on a case-by-case basis. A good start is drawing up detailed and well written (but short, 1-2 paragraphs) proposal of what you are doing and why you need funding, along with as complete a budget as possible (including the total amount requested).
12. Where can I get forms to add or drop classes? registrar's page

1. What is Matlab? and how do I learn it?
2. Can I transfer into applied mathematics?
3. How do I do study abroad within the AM major?
   • Best to plan early. Start by visiting Dean Lambrech, 510 mudd. You'll need to get and fill out a course-substitution file, based on what courses are available at the place you are going to visit, then get this approved by your advisor (see above).