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APMA 1650: Statistical Inference I
1.00 Credits
Brown University
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, 0170, 0180, 0190, 0200, or 0350.
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APMA 1660: Statistical Inference II
1.00 Credits
Brown University
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.
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APMA 1670: Statistical Analysis of Time Series
1.00 Credits
Brown University
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.
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APMA 1670 - Statistical Analysis of Time Series
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APMA 1680: Nonparametric Statistics
1.00 Credits
Brown University
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.
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APMA 1690: Computational Probability and Statistics
0.00 - 1.00 Credits
Brown University
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.
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APMA 1690 - Computational Probability and Statistics
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APMA 1700: The Mathematics of Insurance
1.00 Credits
Brown University
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.
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APMA 1710: Information Theory
1.00 Credits
Brown University
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.
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APMA 1720: Monte Carlo Simulation with Applications to Finance
1.00 Credits
Brown University
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
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APMA 1720 - Monte Carlo Simulation with Applications to Finance
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APMA 1850: Introdution to High Performance Parallel Computing
1.00 Credits
Brown University
No description available.
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APMA 1850 - Introdution to High Performance Parallel Computing
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APMA 1880: Advanced Matrix Theory
1.00 Credits
Brown University
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.
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APMA 1880 - Advanced Matrix Theory
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