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Sequencing of genomes (human and other) has generated a massive quantity of fundamental data that is revolutionizing the life sciences. The focus of this course is on drawing traditional and Bayesian statistical inferences from these data, including: alignment of biopolymer sequences; prediction of their structures, regulatory signals, and compositional characteristics; significances in database searches; phylogeny; and functional genomics. Emphasis is on inferences of the discrete high dimensional objects that are common in this field. Statistical topics: parameter estimation, hypothesis testing and false discovery rates, statistical decision theory, and Bayesian posterior inference. Recommended: APMA 1650 or MATH 1610 or equivalent; BIOL 0200 or equivalent; and experience with Matlab or another programming language. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Prerequisites: Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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. A brief introduction to Matlab is given. Prerequisites: MATH 0520 is recommended, not required. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Fundamental numerical techniques for solving ordinary and partial differential equations. Overview of techniques for approximation and integration of functions. Development of multistep and multistage 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. Introduction to Matlab is given but some programming experience is expected. Prerequisites: APMA 0330, 0340 or 0350, 0360 (AM 33, 34 or 35, 36). APMA 1170 (AM 117) is recommended. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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 or MATH 1610, or equivalent. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Course Attributes: Liberal Learning Prerequisites: Undergraduate level APMA 1650 Minimum Grade of S or Undergraduate level MATH 1610 Minimum Grade of S Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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An introduction to the dynamics of fluid flow and deforming elastic solids for students in the physical or mathematical sciences. Topics in fluid mechanics include statics, simple viscous flows, inviscid flows, potential flow, linear water waves, and acoustics. Topics in solid mechanics include elastic/plastic deformation, strain and stress, simple elastostatics, and elastic waves with reference to seismology. Offered in alternate years. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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See Methods Of Applied Mathematics III, IV (AM0133) for course description. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Overview and introduction to dynamical systems. Local and global theory of maps. Attractors and limit sets. Lyapunov exponents and dimensions. Fractals: definition and examples. Lorentz attractor, Hamiltonian systems, homoclinic orbits and Smale horseshoe orbits. Chaos in finite dimensions and in PDEs. Can be used to fulfill the senior seminar requirement in applied mathematics. Prerequisites: differential equations and linear algebra. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
APMA 1650 begins 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: MATH 0100, MATH 0170, MATH 0180, MATH 0190, MATH 0200, or MATH 0350. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Prerequisites: Undergraduate level MATH 0100 Minimum Grade of S or Undergraduate level MATH 0170 Minimum Grade of S or Undergraduate level MATH 0180 Minimum Grade of S or Undergraduate level MATH 0190 Minimum Grade of S or Undergraduate level MATH 0200 Minimum Grade of S or Undergraduate level MATH 0350 Minimum Grade of S or AP Calculus BC 4 or AP Calculus BC 5 Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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 or equivalent, basic linear algebra. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Prerequisites: Undergraduate level APMA 1650 Minimum Grade of S Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Time series analysis is an important branch of mathematical statistics with many applications to signal processing, econometrics, geology, etc. The course emphasizes methods for analysis in the frequency domain, in particular, estimation of the spectrum of time-series, but time domain methods are also covered. Prerequisites: elementary probability and statistics on the level of AM 165-166. Offered in alternate years. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
A systematic treatment of distribution-free alternatives to classical statistical tests. These nonparametric tests make minimum assumptions about distributions governing the generation of observations, yet are of nearly equal power to the classical alternatives. Prerequisite: APMA 1650 or equivalent. Offered in alternate years. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Prerequisites: Undergraduate level APMA 1650 Minimum Grade of S Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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, probabilistic grammars. Offered in alternate years. 0.000 OR 1.000 Credit Hours 0.000 OR 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Lab, Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The course consists of two parts: the first treats life contingencies, i.e. the construction of models for individual life insurance contracts. The second treats the Collective Theory of Risk, which constructs mathematical models for the insurance company and its portfolio of policies as a whole. Suitable also for students proceeding to the Institute of Actuaries examinations. Prerequisites: Probability Theory to the level of AM 165 or MA 161. Offered in alternate years. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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, capacity, channel coding, source-channel separation, lossy data compression. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Prerequisites: Undergraduate level APMA 1650 Minimum Grade of S or Undergraduate level MATH 1610 Minimum Grade of S Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Canonical forms of orthogonal, Hermitian and normal matrices: Rayleigh quotients. Norms, eigenvalues, matrix equations, generalized inverses. Banded, sparse, non-negative and circulant matrices. Prerequisite: AM 34 or 36, or MA 52 or 54, or permission of the instructor. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
A seminar considering selected topics from two fields: (1) life contingencies-the study of the valuation of life insurance contracts; and (2) collective risk theory, which is concerned with the random process that generates claims for a portfolio of policies. Topics are chosen from Actuarial Mathematics , 2nd ed., by Bowers, Gerber, Hickman, Jones, and Nesbitt. Prerequisite: knowledge of probability theory to the level of AM 165 or MA 161. Particularly appropriate for students planning to take the examinations of the Society of Actuaries. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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, probabilistic grammars. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Information theory is the mathematical study of the fundamental limits of information transmission (or coding) and storage (or compression). This course offers a broad introduction to information theory and its real-world applications. A subset of the following is covered: entropy and information; the asymptotic equipartition property; theoretical limits of lossless data compression and practical algorithms; communication in the presence of noise-channel coding, channel capacity; source-channel separation; Gaussian channels; Lossy data compression. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Mixing and transport are important in several areas of applied science, including fluid mechanics, atmospheric science, chemistry, and particle dynamics. In many cases, mixing seems highly complicated and unpredictable. We use the modern theory of dynamical systems to understand and predict mixing and transport from the differential equations describing the physical process in question. Prerequisites: AM 33,34 or AM 35,36. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Works through the popular book by Henry Stommel entitled A View of the Sea. Introduces the appropriate mathematics to match the physical concepts introduced in the book. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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