Courses for Spring 2018

  • Introduction to Scientific Computing

    For students in any discipline that may involve numerical computations. Includes instruction for programming in MATLAB. Applications discussed include solution of linear equations (with vectors and matrices) and nonlinear equations (by bisection, iteration, and Newton's method), interpolation, and curve-fitting, difference equations, iterated maps, numerical differentiation and integration, and differential equations. Prerequisite: MATH 0100 or its equivalent.
    APMA 0160 S01
    Primary Instructor
    Fu
  • Methods of Applied Mathematics I, II

    This course will cover mathematical techniques involving ordinary differential equations used in the analysis of physical, biological, and economic phenomena. The course emphasizes established methods and their applications rather than rigorous foundation. Topics include: first and second order differential equations, an introduction to numerical methods, series solutions, and Laplace transformations.
    APMA 0330 S01
    Primary Instructor
    Akopian
  • Methods of Applied Mathematics I, II

    Mathematical techniques involving differential equations used in the analysis of physical, biological and economic phenomena. Emphasis on the use of established methods, rather than rigorous foundations. I: First and second order differential equations. II: Applications of linear algebra to systems of equations; numerical methods; nonlinear problems and stability; introduction to partial differential equations; introduction to statistics. Prerequisite: MATH 0100, 0170, 0180, 0190, 0200, or 0350, or advanced placement.
    APMA 0340 S01
    Primary Instructor
    Dobrushkin
  • Applied Ordinary Differential Equations

    This course gives a comprehensive introduction to the qualitative and quantitative theory of ordinary differential equations and their applications. Specific topics covered in the course are applications of differential equations in biology, chemistry, economics, and physics; integrating factors and separable equations; techniques for solving linear systems of differential equations; numerical approaches to solving differential equations; phase-plane analysis of planar nonlinear systems; rigorous theoretical foundations of differential equations.

    Format: Six hours of lectures, and two hours of recitation.

    Prerequisites: MATH 0100, MATH 0170, MATH 0180, MATH 0190, MATH 0200, MATH 0350 or advanced placement. MATH 0520 (can be taken concurrently).
    APMA 0350 S01
    Primary Instructor
    Kunsberg
  • Applied Partial Differential Equations I

    Covers the same material as APMA 0340, albeit of greater depth. Intended primarily for students who desire a rigorous development of the mathematical foundations of the methods used, for those students considering one of the applied mathematics concentrations, and for all students in the sciences who will be taking advanced courses in applied mathematics, mathematics, physics, engineering, etc. Three hours lecture and one hour recitation. Prerequisite: MATH 0100, 0170, 0180, 0190, 0200, or 0350, or advanced placement.
    APMA 0360 S01
    Primary Instructor
    Darbon
  • Essential Statistics

    A first course in probability and statistics emphasizing statistical reasoning and basic concepts. Topics include visual and numerical summaries of data, representative and non-representative samples, elementary discrete probability theory, the normal distribution, sampling variability, elementary statistical inference, measures of association. Examples and applications from the popular press and the life, social and physical sciences. No prerequisites.
    APMA 0650 S01
    Primary Instructor
    Kinnaird
  • Operations Research: Probabilistic Models

    Basic probabilistic problems and methods in operations research and management science. Methods of problem formulation and solution. Markov chains, birth-death processes, stochastic service and queueing systems, the theory of sequential decisions under uncertainty, dynamic programming. Applications. Prerequisite: APMA 1650, 1655 or MATH 1610, or equivalent.
    APMA 1200 S01
    Primary Instructor
    Ramanan
  • Topics in Chaotic Dynamics

    This course gives an overview of the theory and applications of dynamical systems modeled by differential equations and maps. We will discuss changes of the dynamics when parameters are varied, investigate periodic and homoclinic solutions that arise in applications, and study the impact of additional structures such as time reversibility and conserved quantities on the dynamics. We will also study systems with complicated "chaotic" dynamics that possess attracting sets which do not have an integer dimension. Applications to chemical reactions, climate, epidemiology, and phase transitions will be discussed.
    APMA 1360 S01
    Primary Instructor
    Mallet-Paret
  • Statistical Inference I

    APMA 1650 is an integrated first course in mathematical statistics. The first half of APMA 1650 covers probability and the last half is statistics, integrated with its probabilistic foundation. Specific topics include probability spaces, discrete and continuous random variables, methods for parameter estimation, confidence intervals, and hypothesis testing.
    Prerequisite: One year of university-level calculus. At Brown, this corresponds to MATH 0100, MATH 0170, MATH 0180, MATH 0190, MATH 0200, or MATH 0350. A score of 4 or 5 on the AP Calculus BC exam is also sufficient.
    APMA 1650 S01
    Primary Instructor
    Sanz-Alonso
  • Statistical Inference II

    APMA 1660 is designed as a sequel to APMA 1650 to form one of the alternative tracks for an integrated year's course in mathematical statistics. The main topic is linear models in statistics. Specific topics include likelihood-ratio tests, nonparametric tests, introduction to statistical computing, matrix approach to simple-linear and multiple regression, analysis of variance, and design of experiments. Prerequisite: APMA 1650, 1655 or equivalent, basic linear algebra.
    APMA 1660 S01
    Primary Instructor
    Gidas
  • Recent Applications of Probability and Statistics

    This course develops the mathematical foundations of modern applications of statistics to the computational, cognitive, engineering, and neural sciences. The course is rigorous, but the emphasis is on application. Topics include: Gibbs ensembles and their relation to maximum entropy, large deviations, exponential models, and information theory; statistical estimation and the generative, discriminative and algorithmic approaches to classification; graphical models, dynamic programming, MCMC computing, parameter estimation, and the EM algorithm. For 2,000-level credit enroll in 2610; for 1,000-level credit enroll in 1740. Rigorous calculus-based statistics, programming experience, and strong mathematical background are essential. For 2610, some graduate level analysis is strongly suggested.
    APMA 1740 S01
    Primary Instructor
    Garcia Trillos
  • Race and Gender in the Scientific Community

    This course examines the (1) disparities in representation in the scientific community, (2) issues facing different groups in the sciences, and (3) paths towards a more inclusive scientific environment. We will delve into the current statistics on racial and gender demographics in the sciences and explore their background through texts dealing with the history, philosophy, and sociology of science. We will also explore the specific problems faced by underrepresented and well-represented racial minorities, women, and LGBTQ community members. The course is reading intensive and discussion based. To be added to the waitlist for this course, please go to https://goo.gl/forms/SrSMZZfFVHWsPkbz2
    APMA 1910 S01
    Primary Instructor
    Sandstede
  • Topics in Information Theory and Coding Theory

    This class builds on APMA 1710, but stresses applications of information and coding theory, rather than its mathematical foundations. The class provided an overview of widely used probabilistic methods and algorithms, such as Markov Chain Monte Carlo (MCMC), hidden Markov models (HMM), dynamic programming, belief propagation, and Bayesian inference. Information theory is used in combination with these algorithms as a framework to study applications such as code-breaking, speech recognition, image analysis and the study of genetic sequences.

    This class is best suited to students looking for topics for senior theses or capstone classes in applied mathematics, computer science and mathematics.
    APMA 1940X S01
    Primary Instructor
    Menon
  • Independent Study

    Section numbers vary by instructor. Please check Banner for the correct section number and CRN to use when registering for this course.
    APMA 1970 S01
    Primary Instructor
    Bienenstock
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S02
    Primary Instructor
    Dafermos
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S03
    Primary Instructor
    Dupuis
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S04
    Primary Instructor
    Rozovsky
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S05
    Primary Instructor
    Ramanan
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S06
    Primary Instructor
    Morrow
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S07
    Primary Instructor
    Geman
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S08
    Primary Instructor
    Gidas
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S09
    Primary Instructor
    Sanz-Alonso
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S10
    Primary Instructor
    Matzavinos
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S11
    Primary Instructor
    Garcia Trillos
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S12
    Primary Instructor
    Karniadakis
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S13
    Primary Instructor
    Lawrence
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S14
    Primary Instructor
    Maxey
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S15
    Primary Instructor
    McClure
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S16
    Primary Instructor
    Shu
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S17
    Primary Instructor
    Klivans
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S18
    Primary Instructor
    Dobrushkin
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S19
    Primary Instructor
    Harrison
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S20
    Primary Instructor
    Kunsberg
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S21
    Primary Instructor
    Wang
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S22
    Primary Instructor
    Garcia Trillos
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S23
    Primary Instructor
    Dong
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S24
    Primary Instructor
    Guo
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S25
    Primary Instructor
    Guzman
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S26
    Primary Instructor
    Mallet-Paret
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S27
    Primary Instructor
    Menon
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S28
    Primary Instructor
    Sandstede
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S29
    Primary Instructor
    Su
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S30
    Primary Instructor
    Garcia Trillos
    Schedule Code
    I: Independent Study/Research
  • Nonlinear Dynamical Systems: Theory and Applications

    Basic theory of ordinary differential equations, flows, and maps. Two-dimensional systems. Linear systems. Hamiltonian and integrable systems. Lyapunov functions and stability. Invariant manifolds, including stable, unstable, and center manifolds. Bifurcation theory and normal forms. Nonlinear oscillations and the method of averaging. Chaotic motion, including horseshoe maps and the Melnikov method. Applications in the physical and biological sciences.
    APMA 2200 S01
    Primary Instructor
    Matzavinos
  • Partial Differential Equations

    The theory of the classical partial differential equations, as well as the method of characteristics and general first order theory. Basic analytic tools include the Fourier transform, the theory of distributions, Sobolev spaces, and techniques of harmonic and functional analysis. More general linear and nonlinear elliptic, hyperbolic, and parabolic equations and properties of their solutions, with examples drawn from physics, differential geometry, and the applied sciences. Generally, semester II of this course concentrates in depth on several special topics chosen by the instructor.
    APMA 2240 S01
    Primary Instructor
    Dong
  • Numerical Solution of Partial Differential Equations II

    An introduction to weighted residual methods, specifically spectral, finite element and spectral element methods. Topics include a review of variational calculus, the Rayleigh-Ritz method, approximation properties of spectral end finite element methods, and solution techniques. Homework will include both theoretical and computational problems.
    APMA 2560 S01
    Primary Instructor
    Karniadakis
  • Computational Fluid Dynamics

    An introduction to computational fluid dynamics with emphasis on compressible flows. We will cover finite difference, finite volume and finite element methods for compressible Euler and Navier-Stokes equations and for general hyperbolic conservation laws. Background material in hyperbolic partial differential equations will also be covered. Algorithm development, analysis, implementation and application issues will be addressed. Prerequisite: APMA 2550 or equivalent knowledge in numerical methods.
    APMA 2580B S01
    Primary Instructor
    Shu
  • Recent Applications of Probability and Statistics

    This course develops the mathematical foundations of modern applications of statistics to the computational, cognitive, engineering, and neural sciences. The course is rigorous, but the emphasis is on application. Topics include: Gibbs ensembles and their relation to maximum entropy, large deviations, exponential models, and information theory; statistical estimation and the generative, discriminative and algorithmic approaches to classification; graphical models, dynamic programming, MCMC computing, parameter estimation, and the EM algorithm. For 2,000-level credit enroll in 2610; for 1,000-level credit enroll in 1740. Rigorous calculus-based statistics, programming experience, and strong mathematical background are essential. For 2610, some graduate level analysis is strongly suggested.
    APMA 2610 S01
    Primary Instructor
    Garcia Trillos
  • Theory of Probability

    A one-semester course in probability that provides an introduction to stochastic processes. The course covers the following subjects: Markov chains, Poisson process, birth and death processes, continuous-time martingales, optional sampling theorem, martingale convergence theorem, Brownian motion, introduction to stochastic calculus and Ito's formula, stochastic differential equations, the Feynman-Kac formula, Girsanov's theorem, the Black-Scholes formula, basics of Gaussian and stationary processes. Prerequisite: AMPA 2630 or equivalent course.
    APMA 2640 S01
    Primary Instructor
    Dupuis
  • High Order Finite Element Methods: Theory and Implementation

    Traditional FEM seeks accuracy through mesh refinement whereas high order FEM seek to achieve accuracy through the use of increasingly high order polynomials. However, computer implementation and analysis of high order methods is considerably more complex than for traditional FEM. We will cover theory and implementation including: rate of convergence for problems with singularities, choice of basis functions, cost of computing element matrices and load vectors, and efficient solution of the resulting matrix equation. I will assume you are familiar with material in APMA2560 and have written your own piecewise linear FEM code.
    APMA 2822A S01
    Primary Instructor
    Ainsworth
  • Research in Applied Mathematics

    Section numbers vary by instructor. Please check Banner for the correct section number and CRN to use when registering for this course.
    APMA 2980 S01
    Primary Instructor
    Bienenstock
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S02
    Primary Instructor
    Dafermos
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S03
    Primary Instructor
    Dupuis
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S04
    Primary Instructor
    Rozovsky
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S05
    Primary Instructor
    Ramanan
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S06
    Primary Instructor
    Matzavinos
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S07
    Primary Instructor
    Geman
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S08
    Primary Instructor
    Gidas
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S09
    Primary Instructor
    Harrison
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S10
    Primary Instructor
    Wang
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S11
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S12
    Primary Instructor
    Karniadakis
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S13
    Primary Instructor
    Lawrence
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S14
    Primary Instructor
    Maxey
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S15
    Primary Instructor
    McClure
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S16
    Primary Instructor
    Shu
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S17
    Primary Instructor
    Darbon
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S18
    Primary Instructor
    Menon
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S19
    Primary Instructor
    Dobrushkin
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S20
    Primary Instructor
    Guo
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S21
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S22
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S23
    Primary Instructor
    Dong
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S24
    Primary Instructor
    Guzman
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S25
    Primary Instructor
    Mallet-Paret
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S26
    Primary Instructor
    Sandstede
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S27
    Primary Instructor
    Su
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S28
    Schedule Code
    I: Independent Study/Research
    APMA 2980 S29
    Primary Instructor
    Ainsworth
    Schedule Code
    I: Independent Study/Research
  • Thesis Preparation

    For graduate students who have met the tuition requirement and are paying the registration fee to continue active enrollment while preparing a thesis.
    APMA 2990 S01
    Schedule Code
    E: Grad Enrollment Fee/Dist Prep