Courses for Fall 2018

  • Introduction to Modelling

    This course provides an introduction to the mathematical modeling of selected biological, chemical, engineering, and physical processes. The goal is to illustrate the typical way in which applied mathematicians approach practical applications, from understanding the underlying problem, creating a model, analyzing the model using mathematical techniques, and interpreting the findings in terms of the original problem. Single-variable calculus is the only requirement; all other techniques from differential equations, linear algebra, and numerical methods, to probability and statistics will be introduced in class. Prerequisites: Math 0100 or equivalent.
    APMA 0200 S01
    Primary Instructor
    Dafermos
  • 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
    Sandstede
  • 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
  • Inference in Genomics and Molecular Biology

    Massive quantities of fundamental biological and geological sequence data have emerged. Goal of APMA1080 is to enable students to construct and apply probabilistic models to draw inferences from sequence data on problems novel to them. Statistical topics: Bayesian inferences; estimation; hypothesis testing and false discovery rates; statistical decision theory; change point algorithm; hidden Markov models; Kalman filters; and significances in high dimensions. Prerequisites: One of following APMA1650, APMA1655, MATH1610, CSCI1450; and one of the following AMPA0160, CSCI0040, CSCI0150, CSCI0170, CSCI0190, CLPS0950, waver for students with substantial computing experience and their acceptance of responsibility for their own computing.
    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
    Guzman
  • 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
    Fu
  • Applied Partial Differential Equations II

    Review of vector calculus and curvilinear coordinates. Partial differential equations. Heat conduction and diffusion equations, the wave equation, Laplace and Poisson equations. Separation of variables, special functions, Fourier series and power series solution of differential equations. Sturm-Liouville problem and eigenfunction expansions.
    APMA 1330 S01
    Primary Instructor
    Matzavinos
  • 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 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
    Klivans
  • 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
    Wang
  • 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
    Harrison
  • Mathematics and Climate

    The study of Earth’s climate involves many scientific components; mathematical tools play an important role in relating these through quantitative models, computational experiments and data analysis. The course aims to introduce students in applied mathematics to several of the conceptual models, the underlying physical principles and some of the ways data is analyzed and incorporated. Students will develop individual projects later in the semester. Prerequisites: APMA 0360, or APMA 0340, or written permission; APMA 1650 is recommended.
    APMA 1930P S01
    Primary Instructor
    Maxey
  • 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
  • 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
  • Real Analysis

    Provides the basis of real analysis which is fundamental to many of the other courses in the program: metric spaces, measure theory, and the theory of integration and differentiation.
    APMA 2110 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 2190 S01
    Primary Instructor
    Mallet-Paret
  • 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 spectral methods for partial differential equations. Algorithm formulation, analysis, and efficient implementation issues will be addressed. Prerequisite: APMA 2550 or equivalent knowledge in numerical methods.
    APMA 2570A S01
    Primary Instructor
    Ainsworth
  • Theory of Probability

    Part one of a two semester course that provides an introduction to probability theory based on measure theory. The first semester (APMA 2630) covers the following topics: countable state Markov chains, review of real analysis and metric spaces, probability spaces, random variables and measurable functions, Borel-Cantelli lemmas, weak and strong laws of large numbers, conditional expectation and beginning of discrete time martingale theory. Prerequisites—undergraduate probability and analysis, co-requisite—graduate real analysis.
    APMA 2630 S01
    Primary Instructor
    Dupuis
  • 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
  • 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
  • Topics in Stochastic Analysis

    The course provides an introduction to the theory of continuous-time stochastic processes, stochastic integration, stochastic calculus and its applications. The course will cover Brownian motion, continuous-time martingales, stochastic integration, Ito's formula, Girsanov's theorem, and a selection of other topics such as excursion theory, reflected processes, stochastic control and stochastic filtering.
    APMA 2811Y S01
    Primary Instructor
    Ramanan
  • 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