Courses for Spring 2017

  • Introduction to Scientific Computing

    For student 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
    APMA 0160 S02
    Primary Instructor
    Kilikian
  • 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
    Dafermos
  • 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, 0170, 0180, 0190, 0200, 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
    Kaspar
  • 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
  • Inference in Genomics and Molecular Biology

    Sequencing of genomes has generated a massive quantity of fundamental biological data. Drawing traditional and Bayesian statistical inferences from these data, including; motif finding; hidden Markov models; other probabilistic models, significances in high dimensions; and functional genomics. Emphasis - application of probability theory to inferences on data sequence, the goal of enabling students to construct prob models. Statistical topics: Bayesian inferences, estimation, hypothesis testing and false discovery rates, statistical decision theory. Enroll in 2080 for more in depth coverage of the class. Prerequisite: APMA 1650, 1655 or MATH 1610 or CSCI 1450; BIOL 0200 recommended, programming skills required.
    APMA 1080 S01
    Primary Instructor
    Lawrence
  • 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. Prereq: functions of several variables (MATH 0180) or equivalent of this. Computational Linear Algebra (APMA 1170) or a similar course is recommended.
    APMA 1160 S01
    Primary Instructor
    Darbon
  • Introduction to Numerical Solution of Differential Equations

    Fundamental numerical techniques for solving ordinary and partial differential equations. Overview of techniques for approximation and integration of functions. Development of mult-istep and multi-stage methods, error analysis, step-size control for ordinary differential equations. Solution of two-point boundary value problems, introduction to methods for solving linear partial differential equations. Students will be required to use Matlab (or other computer languages) to implement the mathematical algorithms under consideration: experience with a programming language is therefore strongly recommended. Prerequisites: APMA 0330, 0340 or 0350, 0360.
    APMA 1180 S01
    Primary Instructor
    Guzman
  • 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
  • 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. This course can be used as a senior seminar. WRIT
    APMA 1360 S01
    Primary Instructor
    Sandstede
  • 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. Since 2016 is a presidential election year, examples throughout the course will be drawn from electoral politics.
    Prerequisite: One year of university-level calculus. At Brown, this corresponds to MATH 0100, 0170, 0180, 0190, 0200, or 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
    Garcia Trillos
  • 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
    Harrison
  • 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/5l62uscm1Zmzz5YJ2
    APMA 1910 S01
    Primary Instructor
    Sandstede
    APMA 1910 S02
    Primary Instructor
    Sandstede
  • Topics in Coding Theory

    This class covers two distinct areas: (1) algebraic coding theory; (2) examples of code breaking and design.
    Part (1) stresses cryptography, data compression, error correction and sphere packings.
    Part (2) will involve case studies of code breaking and code design in applications. Depending on student interest these may include decoding scripts (Ventris and Linear B), or design problems in synthetic biology (e.g. RNA folding and DNA self-assembly).
    APMA 1940V S01
    Primary Instructor
    Menon
  • Randomized Algorithms for Counting, Integration and Optimzation

    We consider the construction and analysis of random methods for approximating sums and integrals, and related questions. Example, consider the problem of counting the number of vectors with integer components that satisfy a collection of linear equality and inequality constraints. Depending on the number of constraints, this could be a problem of counting the number of needles in a haystack, and straightforward enumeration is impossible. There are now a variety of randomized methods that can attack this problem and other problems with similar difficult features. We survey some of the methods and the problems to which they apply.
    APMA 1940W S01
    Primary Instructor
    Dupuis
  • 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
    Li
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S10
    Primary Instructor
    Matzavinos
    Schedule Code
    I: Independent Study/Research
    APMA 1970 S11
    Primary Instructor
    Hesthaven
    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
  • Inference in Genomics and Molecular Biology

    Sequencing of genomes has generated a massive quantity of fundamental biological data. We focus on drawing traditional and Bayesian statistical inferences from these data, including: motif finding; hidden Markov models; other probabilistic models, significances in high dimensions; and functional genomics. Emphasis is on the application of probability theory to inferences on data sequence with the goal of enabling students to independently construct probabilistic models in setting novel to them. Statistical topics: Bayesian inference, estimation, hypothesis testing and false discovery rates, statistical decision theory. For 2,000-level credit enroll in 2080; for 1,000-level credit enroll in 1080.
    APMA 2080 S01
    Primary Instructor
    Lawrence
  • 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
  • Fluid Mechanics II

    Introduction to concepts basic to current fluid mechanics research: hydrodynamic stability, the concept of average fluid mechanics, introduction to turbulence and to multiphase flow, wave motion, and topics in inviscid and compressible flow.
    APMA 2420 S01
    Primary Instructor
    Maxey
  • 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
    Ainsworth
  • 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
    Harrison
  • 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
    Wang
  • 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
  • Discontinous Galerkin Methods

    In this seminar course we will cover the algorithm formulation, stability analysis and error estimates, and implementation and applications of discontinuous Galerkin finite element methods for solving hyperbolic conservation laws, convection diffusion equations, dispersive wave equations, and other linear and nonlinear partial differential equations. Prerequisite: APMA 2550.
    APMA 2810Q S01
    Primary Instructor
    Shu
  • Dynamics and Stochastics

    This course provides a synthesis of mathematical problems at the interface between stochastic problems and dynamical systems that arise in systems biology. For instance, in some biological systems some species may be modeled stochastically while other species can be modeled using deterministic dynamics. Topics will include an introduction to biological networks, multiscale analysis, analysis of network structure, among other topics. Prerequisites: probability theory (APMA 2630/2640, concurrent enrollment in APMA 2640 is acceptable).
    APMA 2811O S01
    Primary Instructor
    Ramanan
  • Neural Dynamics: Theory and Modeling

    Our thoughts and actions are mediated by the dynamic activity of the brain’s neurons. This course will use mathematics and computational modeling as a tool to study neural dynamics at the level of signal neurons and in more complicated networks. We will focus on relevance to modern day neuroscience problems with a goal of linking dynamics to function. Topics will include biophysically detailed and reduced representations of neurons, bifurcation and phase plane analysis of neural activity, neural rhythms and coupled oscillator theory. Audience: advanced undergraduate or graduate students. Prerequisite: APMA 0350-0360 and Matlab programming course. Instructor permission required.
    APMA 2821V S01
    Primary Instructor
    Jones
  • 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
    Hesthaven
    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
    Primary Instructor
    Tice
    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