• Students intersted in scientific computing and numerical analysis might take these courses.
• Students interested in dynamical systems might take these courses.
• Students interested in signal and image processing might take these courses.
• Students interested in mathematical finance might take these courses.
• Students interested in mathematical biology might take these courses.
  
  Note that these are merely examples and each student customizes his or her own course selection. In particular, for all Applied Math students, there are several options regarding first-year algebra and analysis.

Courses in Signal Processing

A student interested in signal and image processing will most likely minor in Electrical and Computer Engineering. The sample course study below assumes and ECE minor. Other relevant choices for a minor include Computer Science and Statistics.

• Year 1, fall semester:
  • Math 4130 or Math 6110,
  • Math 4330 or Math 6710,
  • ECE 4250 (Digital Signal Processing),
  • ECE 4110 (Random signals in communications and signal processing).
• Year 1, spring semester:
  • Math 4140 (or 6120),
  • Math 4340 (or 6720),
  • ECE 5480 (Digital Image Processing).
• Year 2, fall semester:
  • Math 6110 or EE 5620 (Fundamental Information Theory)
  • ECE 5260 (Advanced Signal Processing),
  • ECE 4110 (Random Signals in Communications and Signal Processing) or Math 6710 (Probability Theory) or CS 6210(Matrix Computations)
• Year 2, spring semester:
  • Math 6120 (Complex Analysis),
  • ECE 5660 (Fundamentals of Networks) or Math 6720 (Probability Theory),
  • ECE 5670 (Topics in Digital Communication)
• Year 3, fall semester:
  • Math 6150 (Mathematical Methods in Physics) or OR 6500 (Applied Stochastic Processes) or T&AM 6120 (Methods of Applied Mathematics 3),
  • CS 6210 (Matrix Computations)
  • ECE 5620 (Fundamental Information Theory) or ECE 5640 (Decision Making and Estimation)
• Year 3, spring semester:
  • Math 6150 (Mathematical Methods in Physics) or T&AM 6120- (Methods of Applied Mathematics III) or CS 6220 (Nonlinear equations and optimization)
  • ECE 5210 (linear systems) or other ECE elective
  • elective

• ECE 4670 & 4680 -- Communication Systems
• ECE 4720 -- Digital Control systems
  
  
  

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  Courses in Mathematical Finance

  This sample course of study assumes that the student has had at least one semester of calculus-based probability. If not, Math 4710 (Basic
  Probability) should be taken in the fall semester of the first year.

  • Year 1, Fall: CS 6210 (Matrix Computations), Math 6110/6210 (Real Analysis/Measure Theory), Math 4330 (Linear Algebra)
  • Year 1, Spring: Math 6220 (Applied Functional Analysis), ORIE 6510 (Probability), CS 522 (Computational Methods in Finance)
  • Year 2, Fall: ORIE 5600 (Financial Engineering with Stochastic Calculus), Math 6710 (Probability Theory I)
  • Year 2, Spring: Math 6720 (Probability Theory II), Math 6740 (Mathematical Statistics), ORIE 4712 (Credit Risk: Modeling, Valuation and Management)
  • Year 3, Fall: Math 7770 (Seminar in Stochastic Processes), ORIE 7590 (Selected Topics in Applied Probability)
  • Year 3, Spring: Math 7780 (Seminar in Stochastic Processes), ORIE 7591 (Selected Topics in Applied Probability)

  Other relevant courses:

  Math 6190-6200 (PDEs)
  ORIE 6500 (Applied Stochastic Processes)
  Econ 6090-6100 (Microeconomics)
  NBA 5550 (Fixed-Income Securities)
  NBA 6730-6740 (Intro to Derivatives)
  NCC 5060 (Managerial Finance)

  For more emphasis on numerical methods:

  ORIE 4580 (Simulation Modeling and Analysis)
  CS 6220 (Numerical Optimization)
  CS 6240 (Numerical Solutions of Differential Equations)

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  Courses in Mathematical Biology

  A) Mathematical Modeling & Dynamical Systems Theory Applied to Biological Systems:

  First, please see the example of courses in dynamical systems and review the “Applied Emphasis”. Rather than minor in TAM, you will minor in the biological area of interest. Some typical minor fields are:
  Neurobiology and Behavior
  Ecology and Evolutionary Biology
  Micro-Biology
  Biochemistry, Molecular & Cell Biology

  Modeling and studying biological systems will require an understanding of the mathematical theory, the biology, and the computer methods that enable us to study such complicated systems.

  • Year 1 - Fall: Analysis &/or Algebra (Math 4330 is strongly recommended here unless you have a strong linear algebra background!), Math 6170*, Math 6520
  • Year 1 - Spring: Biology class, Analysis &/or Algebra, TAM 5780
  • Year 1 - Summer: Biology Lab/Field Work
  • Year 2 - Fall: CS 6210, CIS 6229, Biology Class
  • Year 2 - Spring: CS 6240**, CS 6220***, Biology Class
  • Year 2 - Summer: Biology Lab/Field Work
  • Year 3 - Fall: Math 7170*, (Math 6520)
  • Year 3 - Spring: CS 6510

  Year 3 - Summer: Research!
  
  CIS 6290 – Computational Methods for Nonlinear Systems
  CS 6220*** – Numerical Optimization and Nonlinear Algebraic Equations
  CS 6570– Computational Molecular Biology
  * = every two years, ** = even-numbered years, *** = odd-numbered years
  
  B) Probability and Statistics Applied to Biology

  Recently, there has been a tremendous expansion in the use of probability models in mathematics and in a wide variety of applications. This has created a strong demand for researchers trained in probability to develop new methodologies and to work in an interdisciplinary context. Modeling and studying biological systems will require an understanding of the mathematical theory, the biology, and the computer methods that enable us to study such complicated systems.
  
  Some typical minor fields are: Genetics and Development, Ecology and Evolutionary Biology, Molecular & Cell Biology, Statistics and BSCB (Biological Statistics and Computational Biology). The following example is geared towards applications in genetics, evolutionary biology.

  • Year 1 - Fall – Stochastic Processes (OR 6500 or 5510– more introductory, offered in spring ), Algebra (Math 4330 is highly recommended unless you have a strong linear algebra background!), Analysis (Math 4130 or 6110*) or Measure Theory (Math 6210 – this is a great class!), Biology eg. Population Genetics (BioGD 4810) or Human Genomics (BioGD 4870)
    (If you need undergraduate probability, take Math 4710)
  • Year 1 - Spring - – Probability (Math 6720), Analysis (Math 4140) or Applied Functional Analysis (Math 6220), Algebra (Math 4340 if you haven't done much abstract algebra), Biology eg. BioGD 684 (if you didn't take 4810)
  • Year 1 - Summer: Start thinking about possible research projects, talk to professors
  • Year 2 - Fall: Probability (Math 6710); Stats (OR 6700); Statistical Genomics (BTRY 6820) or Biology class (see year 1 fall)
  • Year 2 - Spring: Probability (Math 6720), Math Stats (Math 4720 or 6740), BioGD 684 (if you didn't take 4810) or BTRY 6940
  • Year 2 - Summer: Start doing some research
  • Year 3 - Fall: Matrix Computations (CS 6210), Special Topics in stochastic processes (Math 7770) or applied prob/stats (OR 7590) Biology class
  • Year 3 - Spring: Special Topics in stochastic processes (Math 7780) or applied prob/stats (OR 7591)
  • Year 3 - Summer: Research!

    Note: Most students take 3-4 courses a semester in their first year, then 2 or 3 a semester until they've fulfilled their requirements. If you're also a TA, do not take more than 3 courses a semester!

    * Only take Math 6110 if you want a challenge! Note that either Math 6210 or 6110 will count towards your requirement, but not both.