Courses for Spring 2019

  • 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 provides a comprehensive introduction to ordinary differential equations and their applications. During the course, we will see how applied mathematicians use ordinary differential equations to solve practical applications, from understanding the underlying problem, creating a differential-equations model, solving the model using analytical, numerical, or qualitative methods, and interpreting the findings in terms of the original problem. We will also learn about the underlying rigorous theoretical foundations of differential equations. Format: lectures and problem-solving workshops.
    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
    Dafermos
  • Applied Partial Differential Equations I

    Course builds on APMA 0350 which covers ordinary differential equations and systems involving a single independent variable. We will look at processes with two or more independent variables formulated as partial differential equations (PDE) using concepts from multivariable calculus. We will see how problems are described quantitatively as PDEs, how seemingly unrelated contexts can result in similar equations; and develop methods for solution using analytical, numerical or qualitative methods. Contexts include first order equations; the second order wave equation and problems involving diffusion processes; steady state balances for systems in two or three dimensions; together with insights from theory.
    APMA 0360 S01
    Primary Instructor
    Maxey
  • 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
    Lawrence
  • Quantitative Models of Biological Systems

    Quantitative dynamic models help understand problems in biology and there has been rapid progress in recent years. The course provides an introduction to the concepts and techniques, with applications to population dynamics, infectious diseases, enzyme kinetics, aspects of cellular biology. Additional topics covered will vary. Mathematical techniques will be discussed as they arise in the context of biological problems. Prerequisites: APMA 0330, 0340 or 0350, 0360, or written permission.
    APMA 1070 S01
    Primary Instructor
    Bienenstock
  • An Introduction to Numerical Optimization

    This course provides a thorough introduction to numerical methods and algorithms for solving non-linear continuous optimization problems. A particular attention will be given to the mathematical underpinnings to understand the theoretical properties of the optimization problems and the algorithms designed to solve them. Topics will include: line search methods, trust-region methods, nonlinear conjugate gradient methods, an introduction to constrained optimization (Karush-Kuhn-Tucker conditions, mini-maximization, saddle-points of Lagrangians). Some applications in signal and image processing will be explored. Basic programming skills at the level of APMA 16 or CSCI 40 are assumed.
    APMA 1160 S01
    Primary Instructor
    Darbon
  • 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
    Matzavinos
  • Applied Dynamical Systems

    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
    Bramburger
  • 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
    Shin
  • 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
    Li
  • Monte Carlo Simulation with Applications to Finance

    The course will cover the basics of Monte Carlo and its applications to financial engineering: generating random variables and simulating stochastic processes; analysis of simulated data; variance reduction techniques; binomial trees and option pricing; Black-Scholes formula; portfolio optimization; interest rate models. The course will use MATLAB as the standard simulation tool. Prerequisites: APMA 1650 or MATH 1610
    APMA 1720 S01
    Primary Instructor
    Mukherjee
  • 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
    Wang
  • 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/foK0fyGxm5Eu2irA2
    APMA 1910 S01
    Primary Instructor
    Sandstede
  • Wavelets and Applications

    The aim of the course is to introduce you to: the relatively new and interdisciplinary area of wavelets; the efficient and elegants algorithms to which they give rise including the wavelet transform; and the mathematical tools that can be used to gain a rigorous understanding of wavelets. We will also cover some of the applications of these tools including the compression of video streams, approximation of solution of partial differential equations, and signal analysis.
    APMA 1940Y S01
    Primary Instructor
    Ainsworth
  • 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
    Darbon
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S10
    Primary Instructor
    Matzavinos
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S11
    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
    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
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S31
    Primary Instructor
    Crawford
    Schedule Code
    I: Independent Study/Research
  • Hilbert Spaces and Their Applications

    A continuation of APMA 2110: metric spaces, Banach spaces, Hilbert spaces, the spectrum of bounded operators on Banach and Hilbert spaces, compact operators, applications to integral and differential equations.
    APMA 2120 S01
    Primary Instructor
    Dong
  • 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
    Mallet-Paret
  • 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
    Shu
  • Computational Fluid Dynamics

    The course will focus primarily on finite difference methods for viscous incompressible flows. Other topics will include multiscale methods, e.g. molecular dynamics, dissipative particle dynamics and lattice Boltzmann methods. We will start with the mathematical nature of the Navier-Stokes equations and their simplified models, learn about high-order explicit and implicit methods, time stepping, and fast solvers. We will then cover advection-diffusion equations and various forms of the Navier-Stokes equations in primitive variables and in vorticity/streamfunction formulations. In addition to the homeworks the students are required to develop a Navier-Stokes solver as a final project.
    APMA 2580A S01
    Primary Instructor
    Karniadakis
  • 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
    Wang
  • Theory of Probability

    Part two of a two semester course that provides an introduction to probability theory based on measure theory. Standard topics covered in the second-semester (APMA 2640) include the following: discrete time martingale theory, weak convergence (also called convergence in distribution) and the central limit theorem, and a study of Brownian motion. Optional topics include the ergodic theorem and large deviation theory. Prerequisites—undergraduate probability and analysis, co-requisite—graduate real analysis.
    APMA 2640 S01
    Primary Instructor
    Harrison
  • Mathematical Statistics II

    The course covers modern nonparametric statistical methods. Topics include: density estimation, multiple regression, adaptive smoothing, cross-validation, bootstrap, classification and regression trees, nonlinear discriminant analysis, projection pursuit, the ACE algorithm for time series prediction, support vector machines, and neural networks. The course will provide the mathematical underpinnings, but it will also touch upon some applications in computer vision/speech recognition, and biological, neural, and cognitive sciences. Prerequisite: APMA 2670.
    APMA 2680 S01
    Primary Instructor
    Gidas
  • Introduction to Parallel Computing on Heterogeneous (CPU+GPU) Systems

    This course we will learn fundamental aspects of parallel computing on heterogeneous systems composed of multi-core CPUs and GPUs. This course will contain lectures and hands-on parts. We will cover the following topics: shared memory and distributed memory programming models, parallelization strategies and nested parallelism. We will also learn techniques for managing memory and data on systems with heterogeneous memories (DDR for CPUs and HBM for GPUs); parallelization strategies using OpenMP and MPI; programming GPUs using OpenMP4.5 directives and CUDA. We will focus on programming strategies and application performance. Grading will be based on home-work assignments, and final project.
  • 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
    Primary Instructor
    Crawford
    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
    Primary Instructor
    Klivans
    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 residency requirement and are continuing research on a full time basis.
    APMA 2990 S01
    Schedule Code
    E: Grad Enrollment Fee/Dist Prep