Courses for Fall 2017

  • What’s the big deal with Data Science?

    This seminar serves as a practical introduction to the interdisciplinary field of data science. Over the course of the semester, students will be exposed to the diversity of questions that data science can address by reading current scholarly works from leading researchers. Through hands-on labs and experiences, students will gain facility with computational and visualization techniques for uncovering meaning from large numerical and text-based data sets. Ultimately, students will gain fluency with data science vocabulary and ideas. There are no prerequisites for this course. FYS WRIT
    APMA 0110 S01
    Primary Instructor
    Kinnaird
  • 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
    Dobrushkin
  • 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
    Guo
  • 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
    Akopian
  • 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
    Maxey
  • 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
  • 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
  • Introduction to Computational Linear Algebra

    Focuses on fundamental algorithms in computational linear algebra with relevance to all science concentrators. Basic linear algebra and matrix decompositions (Cholesky, LU, QR, etc.), round-off errors and numerical analysis of errors and convergence. Iterative methods and conjugate gradient techniques. Computation of eigenvalues and eigenvectors, and an introduction to least squares methods.
    APMA 1170 S01
    Primary Instructor
    Fu
  • Operations Research: Deterministic Models

    An introduction to the basic mathematical ideas and computational methods of optimizing allocation of effort or resources, with or without constraints. Linear programming, network models, dynamic programming, and integer programming.
    APMA 1210 S01
    Primary Instructor
    Rozovsky
  • Applied Partial Differential Equations II

    Mathematical methods based on functions of a complex variable. Fournier series and its applications to the solution of one-dimensional heat conduction equations and vibrating strings. Series solution and special functions. Vibrating membrance. Sturm-Liouville problem and eigenfunction expansions. Fournier transform and wave propagations.
    APMA 1330 S01
    Primary Instructor
    Sanz-Alonso
  • 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
    Kunsberg
  • Statistical Inference I

    Students may opt to enroll in 1655 for more in depth coverage of APMA 1650. Enrollment in 1655 will include an optional recitation section and required additional individual work. Applied Math concentrators are encouraged to take 1655.

    Prerequisite (for either version): MATH 0100, 0170, 0180, 0190, 0200, or 0350.
    APMA 1655 S01
    Primary Instructor
    Wang
  • Computational Probability and Statistics

    Examination of probability theory and mathematical statistics from the perspective of computing. Topics selected from random number generation, Monte Carlo methods, limit theorems, stochastic dependence, Bayesian networks, dimensionality reduction. Prerequistes: A calculus-based course in probability or statistics (e.g. APMA1650 or MATH1610) is required, and some programming experience is strongly recommended. Prerequisite: MATH 0100, 0170, 0180, 0190, 0200, or 0350, or equivalent placement.
    APMA 1690 S01
    Primary Instructor
    Garcia Trillos
  • Information Theory

    Information theory is the study of the fundamental limits of information transmission and storage. This course, intended primarily for advanced undergraduates and beginning graduate students, offers a broad introduction to information theory and its applications: Entropy and information, lossless data compression, communication in the presence of noise, channel capacity, channel coding, source-channel separation, lossy data compression. Prerequisite: one course in probability.
    APMA 1710 S01
    Primary Instructor
    Menon
  • Approximations for Piecewise Smooth Functions

    We will discuss approximation methods for piecewise smooth functions with isolated discontinuities. Such piecewise smooth functions appear often in applications, most notably in computational fluid dynamics of high speed flows. The basic background required is APMA 0330-0340, and some knowledge of programming (e.g. MATLAB or FORTRAN or C). APMA 1170 and/or APMA 1180 are helpful but not required. Students will be asked to participate actively in the class, and perform individual or group projects which may be designed to fit the interest of each student or group.
    APMA 1930S S01
    Primary Instructor
    Shu
  • 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 2190 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 2230 S01
    Primary Instructor
    Dafermos
  • Numerical Solution of Partial Differential Equations I

    Finite difference methods for solving time-dependent initial value problems of partial differential equations. Fundamental concepts of consistency, accuracy, stability and convergence of finite difference methods will be covered. Associated well-posedness theory for linear time-dependent PDEs will also be covered. Some knowledge of computer programming expected.
    APMA 2550 S01
    Primary Instructor
    Karniadakis
  • Numerical Solution of Partial Differential Equations III

    We will cover finite element methods for ordinary differential equations and for elliptic, parabolic and hyperbolic partial differential equations. Algorithm development, analysis, and computer implementation issues will be addressed. In particular, we will discuss in depth the discontinuous Galerkin finite element method. Prerequisite: APMA 2550 or equivalent knowledge in numerical methods.
    APMA 2570B S01
    Primary Instructor
    Ainsworth
  • Theory of Probability

    A one-semester course that provides an introduction to probability theory based on measure theory. The course covers the following topics: probability spaces, random variables and measurable functions, independence and infinite product spaces, expectation and conditional expectation, weak convergence of measures, laws of large numbers and the Central Limit Theorem, discrete time martingale theory and applications.
    APMA 2630 S01
    Primary Instructor
    Ramanan
  • Mathematical Statistics I

    This course presents advanced statistical inference methods. Topics include: foundations of statistical inference and comparison of classical, Bayesian, and minimax approaches, point and set estimation, hypothesis testing, linear regression, linear classification and principal component analysis, MRF, consistency and asymptotic normality of Maximum Likelihood and estimators, statistical inference from noisy or degraded data, and computational methods (E-M Algorithm, Markov Chain Monte Carlo, Bootstrap). Prerequisite: APMA 2630 or equivalent.
    APMA 2670 S01
    Primary Instructor
    Gidas
  • Convex Analysis and Minimization Algorithms

    This course provides a solid mathematical presentation of modern convex analysis and convex optimization algorithms for large scale problems. Topics include: subdifferential calculus, duality and Fenchel-Legendre transform, proximal operators and Moreau's regularization, optimal first-order methods, Augmented Lagrangian methods and alternating direction method of multipliers, network flows. The course will provide the mathematical and algorithmical underpinnings. It will also explore some applications in signal and image processing, optimal control and machine learning.
    APMA 2811W S01
    Primary Instructor
    Darbon
  • Finitite Element Exterior Calculus

    In this course we will cover finite elements for the Hodge Laplacian. We start in three dimensions and discuss the Nedelec finite element spaces for H^1, H(curl) and H(div) and discuss the corresponding de Rham complex. We discuss how they can be applied to the Stokes problem and electro-magnetic problems. We then generalize these spaces to higher dimensions and show how to use them to approximate the Hodge Laplacian. We will mostly follow the review paper: [Finite Element Exterior Calculus: from Hodge Theory to Numerical Stability].
    APMA 2811X S01
    Primary Instructor
    Guzman
  • 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