# Solutions Intermediate Teachers 2nd Edition

We calculated solution consistency and coverage based on the findings. Coverage refers to the degree to which the causal condition explains the outcome in the sample.19 There is no specific cut-off for coverage because a lower coverage may indicate a more uncommon causal pathway. We present both the intermediate and complex solutions of sufficient conditions from the truth table analysis in the table and only the intermediate solutions in the narrative.

## Solutions Intermediate Teachers 2nd Edition

The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.

The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.

200. Research and Teaching in AMS (3 credits). F Basic teaching techniques for teaching assistants, including responsibilities and rights; resource materials; computer skills; leading discussions or lab sessions; presentation techniques; maintaining class records; and grading. Examines research and professional training, including use of library; technical writing; giving talks in seminars and conferences; and ethical issues in science and engineering. Enrollment restricted to graduate students. A. Kottas, The Staff 202. Linear Models in SAS. Case study-based course teaches statistical linear modeling using the SAS software package. Teaches generalized linear models; linear regression; analysis of variance/covariance; analysis of data with random effects and repeated measures. Prerequisite(s): course 156 or 256, or permission of instructor. Enrollment restricted to graduate students. B. Mendes 203. Introduction to Probability Theory. F Introduces probability theory and its applications. Requires a multivariate calculus background, but has no measure theoretic content. Topics include: combinatorial analysis; axioms of probability; random variables (discrete and continuous); joint probability distributions; expectation and higher moments; central limit theorem; law of large numbers; and Markov chains. Students cannot receive credit for this course and course 131 or Computer Engineering 107. Enrollment restricted to graduate students, or by permission of the instructor. R. Prado, B. Sanso, A. Kottas 205B. Intermediate Classical Inference. W Statistical inference from a frequentist point of view. Properties of random samples; convergence concepts applied to point estimators; principles of statistical inference; obtaining and evaluating point estimators with particular attention to maximum likelihood estimates and their properties; obtaining and evaluating interval estimators; and hypothesis testing methods and their properties. (Formerly Statistical Inference.) Prerequisite(s): course 203 or equivalent. Enrollment restricted to graduate students. B. Sanso, R. Guhaniyogi, D. Draper 206. Classical and Bayesian Inference. W Introduction to statistical inference at a calculus-based level: maximum likelihood estimation, sufficient statistics, distribution of estimators, confidence intervals, hypothesis testing, and Bayesian inference. Students cannot receive credit for this course and course 132. (Formerly Bayesian Statistics.) Prerequisite(s): course 203. Enrollment restricted to graduate students; undergraduates may enroll by permission of instructor. H. Lee, D. Draper, A. Kottas, R. Prado 206B. Intermediate Bayesian Inference. W Bayesian statistical methods for inference and prediction including: estimatation; model selection and prediction; exchangability; prior, likelihood, posterior, and predictive distributions; coherence and calibration; conjugate analysis; Markov Chain Monte Carlo methods for simulation-based computation; hierarchical modeling; Bayesian model diagnostics, model selection, and sensitivity analysis. Prerequisite(s): course 203. Enrollment restricted to graduate students; undergraduates may enroll by permission of instructor. R. Prado, A. Rodriguez, J. Lee 207. Intermediate Bayesian Statistical Modeling. S Hierarchical modeling, linear models (regression and analysis of variance) from the Bayesian point of view, intermediate Markov chain Monte Carlo methods, generalized linear models, multivariate models, mixture models, hidden Markov models. Prerequisite(s): courses 206 or 206B; enrollment restricted to graduate students or by permission of instructor. R. Prado, D. Draper, B. Sanso 209. Foundations of Scientific Coputing. F Covers the fundamental aspects of scientific computing for research. Introduces algorithmic development; programming (including the use of compilers, libraries, debugging, optimization, and code publication); computational infrastructure; and data-analysis tools. Students gain hands-on experience through practical assignments. Enrollment is restricted to graduate students. Undergraduates may enroll with the permission of the instructor. D. Lee, N. Brummell 211. Foundations of Applied Mathematics. F Accelerated class reviewing fundamental applied mathematical methods for all sciences. Topics include: multivariate calculus, linear algebra, Fourier series and integral transform methods, complex analysis, and ordinary differential equations. Enrollment restricted to graduate students. N. Brummell, J. Katznelson 212A. Applied Mathematical Methods I. W Focuses on analytical methods for partial differential equations (PDEs), including: the method of characteristics for first-order PDEs; canonical forms of linear second-order PDEs; separation of variables; Sturm-Liouville theory; Green's functions. Illustrates each method using applications taken from examples in physics. Course 211 or equivalent is strongly recommended as preparation. Enrollment restricted to graduate students. Undergraduates are encouraged to take this class with permission of instructor. H. Wang, N. Brummell, P. Garaud 212B. Applied Mathematical Methods II. S Covers perturbation methods: asymptotic series, stationary phase and expansion of integrals, matched asymptotic expansions, multiple scales and the WKB method, PadÃ© approximants and improvements of series. (Formerly course 212.) Prerequisite(s): course 212A. H. Wang, N. Brummell, P. Garaud 213. Numerical Solutions of Differential Equations. Teaches basic numerical methods for numerical linear algebra and, thus, the solution of ordinary differential equations (ODEs) and partial differential equations (PDEs). Covers LU, Cholesky, and QR decompositions; eigenvalue search methods (QR algorithm); singular value decomposition; conjugate gradient method; Runge-Kutta methods; error estimation and error control; finite differences for PDEs; stability, consistency, and convergence. Basic knowledge of computer programming is needed. Enrollment restricted to graduate students or permission of instructor. H. Wang, Q. Gong, N. Brummell, P. Garaud 213A. Numerical Linear Algebra. W Focuses on numerical solutions to classic problems of linear algebra. Topics include: LU, Cholesky, and QR factorizations; iterative methods for linear equations; least square, power methods, and QR algorithms for eigenvalue problems; and conditioning and stability of numerical algorithms. Provides hands-on experience in implementing numerical algorithms for solving engineering and scientific problems. Basic knowledge of mathematical linear algebra is assumed. (W) Q. Gong, (W) The Staff 213B. Numerical Methods for the Solution of Differential Equations. S Introduces the numerical solutions of ordinary and partial differential equations (ODEs and PDEs). Focuses on the derivation of discrete solution methods for a variety of differential equations, and their stability and convergence. Also provides hands-on experience in implementing such numerical algorithms for the solution of engineering and scientific problems using MATLAB software. The class consists of lectures and hands-on programming sections. Basic mathematical knowledge of ODEs and PDEs is assumed, and a basic working knowledge of programming in MATLAB is expected. Enrollment is restricted to graduate students. D. Lee 214. Applied Dynamical Systems. W Introduces continuous and discrete dynamical systems. Topics include: fixed points; stability; limit cycles; bifurcations; transition to and characterization of chaos; and fractals. Examples drawn from sciences and engineering; founding papers of the subject are studied. Students cannot receive credit for this course and course 114. Enrollment restricted to graduate students. Enrollment of undergraduates by permission of instructor. Enrollment limited to 15. P. Garaud, D. Milutinovic, Q. Gong 215. Stochastic Modeling in Biology. Application of differential equations and probability and stochastic processes to problems in cell, organismal, and population biology. Topics include: life-history theory, behavioral ecology, and population biology. Students may not receive credit for this course and course 115. Enrollment restricted to graduate students or permission of instructor. The Staff 216. Stochastic Differential Equations. Introduction to stochastic differential equations and diffusion processes with applications to biology, biomolecular engineering, and chemical kinetics. Topics include Brownian motion and white noise, gambler's ruin, backward and forward equations, and the theory of boundary conditions. Enrollment restricted to graduate students or consent of instructor. H. Wang 217. Introduction to Fluid Dynamics. F Covers fundamental topics in fluid dynamics at the graduate level: Euler and Lagrange descriptions of continuum dynamics; conservation laws for inviscid and viscous flows; potential flows; exact solutions of the Navier-Stokes equation; boundary layer theory; gravity waves. Students cannot receive credit for this course and course 107. Enrollment restricted to graduate students. N. Brummell, The Staff 221. Bayesian Decision Theory. S Explores conceptual and theoretical bases of statistical decision making under uncertainty. Focuses on axiomatic foundations of expected utility, elicitation of subjective probabilities and utilities, and the value of information and modern computational methods for decision problems. Prerequisite(s): course 206. Enrollment restricted to graduate students. D. Draper, B. Sanso 223. Time Series Analysis. Graduate level introductory course on time series data and models in the time and frequency domains: descriptive time series methods; the periodogram; basic theory of stationary processes; linear filters; spectral analysis; time series analysis for repeated measurements; ARIMA models; introduction to Bayesian spectral analysis; Bayesian learning, forecasting, and smoothing; introduction to Bayesian Dynamic Linear Models (DLMs); DLM mathematical structure; DLMs for trends and seasonal patterns; and autoregression and time series regression models. Prerequisite(s): course 206B, or by permission of instructor. Enrollment restricted to graduate students. R. Prado 225. Multivariate Statistical Methods. F Introduction to statistical methods for analyzing data sets in which two or more variables play the role of outcome or response. Descriptive methods for multivariate data. Matrix algebra and random vectors. The multivariate normal distribution. Likelihood and Bayesian inferences about multivariate mean vectors. Analysis of covariance structure: principle components, factor analysis. Discriminant, classification and cluster analysis. Prerequisite(s): course 206 or 206B, or by permission of instructor. Enrollment restricted to graduate students. D. Draper, J. Lee 227. Waves and Instabilities in Fluids. W Advanced fluid dynamics course introducing various types of small-amplitude waves and instabilities that commonly arise in geophysical and astrophysical systems. Topics covered include, but are not limited to: pressure waves, gravity waves, Rossby waves, interfacial instabilities, double-diffuse instabilities, and centrifugal instabilities. Advanced mathematical methods are used to study each topic. Undergraduates are encouraged to take this course with permission of the instructor. Prerequisite(s): courses 212A and 217. P. Garaud 231. Nonlinear Control Theory. S Covers analysis and design of nonlinear control systems using Lyapunov theory and geometric methods. Includes properties of solutions of nonlinear systems, Lyapunov stability analysis, effects of perturbations, controllability, observability, feedback linearization, and nonlinear control design tools for stabilization. Prerequisite(s): basic knowledge of mathematical analysis and ordinary differential equations is assumed. Enrollment restricted to graduate students or permission of instructor. Q. Gong 232. Applied Optimal Control. Introduces optimal control theory and computational optimal control algorithms. Topics include: calculus of variations, minimum principle, dynamic programming, HJB equation, linear-quadratic regulator, direct and indirect computational methods, and engineering application of optimal control. Prerequisite(s): course 114 or 214, or Computer Engineering 240 or 241, or Mathematics 145. Enrollment restricted to graduate students. Q. Gong 236. Motion Coordination of Robotic Networks. Comprehensive introduction to motion coordination algorithms for robotic networks. Emphasis on mathematical tools to model, analyze, and design cooperative strategies for control, robotics, and sensing tasks. Topics include: continuous and discrete-time evolution models, proximity graphs, performance measures, invariance principles, and coordination algorithms for rendezvous, deployment, flocking, and consensus. Techniques and methodologies are introduced through application setups from multi-agent robotic systems, cooperative control, and mobile sensor networks. Enrollment restricted to graduate students. Enrollment limited to 15. The Staff 241. Bayesian Nonparametric Methods. F Theory, methods, and applications of Bayesian nonparametric modeling. Prior probability models for spaces of functions. Dirichlet processes. Polya trees. Nonparametric mixtures. Models for regression, survival analysis, categorical data analysis, and spatial statistics. Examples drawn from social, engineering, and life sciences. Prerequisite(s): course 207. Enrollment restricted to graduate students. A. Rodriguez, A. Kottas 245. Spatial Statistics. Introduction to the analysis of spatial data: theory of correlation structures and variograms; kriging and Gaussian processes; Markov random fields; fitting models to data; computational techniques; frequentist and Bayesian approaches. Prerequisite(s): course 207. Enrollment restricted to graduate students. B. Sanso, H. Lee 250. An Introduction to High Performance Computing. S Designed for STEM students and others.Through hands-on practice, this course introduces high-performance parallel computing, including the concepts of multiprocessor machines and parallel computation, and the hardware and software tools associated with them. Students become familiar with parallel concepts and the use of MPI and OpenMP together with some insight into the use of heterogeneous architectures (CPU, CUDA, OpenCL), and some case-study problems. Enrollment is restricted to graduate students. Undergraduates may enroll with permission of instructor. D. Lee, N. Brummell 256. Linear Statistical Models. S Theory, methods, and applications of linear statistical models. Review of simple correlation and simple linear regression. Multiple and partial correlation and multiple linear regression. Analysis of variance and covariance. Linear model diagnostics and model selection. Case studies drawn from natural, social, and medical sciences. Course 205 strongly recommended as a prerequisite. Undergraduates are encouraged to take this class with permission of instructor. Prerequisite(s): course 205A or 205B or permission of instructor. Enrollment restricted to graduate students. The Staff, R. Prado, A. Rodriguez, B. Sanso, J. Lee 260. Computational Fluid Dynamics. Introduces modern computational approaches to solving the differential equations that arise in fluid dynamics, particularly for problems involving discontinuities and shock waves. Examines the fundamentals of the mathematical foundations and computation methods to obtain solutions. Focuses on writing practical numerical codes and analyzing their results for a full understanding of fluid phenomena. Prerequisite(s): Basic knowledge of computer programming languages is assumed. Enrollment is restricted to graduate students. N. Brummell 261. Probability Theory with Markov Chains. W Introduction to probability theory: probability spaces, expectation as Lebesgue integral, characteristic functions, modes of convergence, conditional probability and expectation, discrete-state Markov chains, stationary distributions, limit theorems, ergodic theorem, continuous-state Markov chains, applications to Markov chain Monte Carlo methods. Prerequisite(s): course 205B or by permission of instructor. Enrollment restricted to graduate students. A. Kottas 263. Stochastic Processes. Includes probabilistic and statistical analysis of random processes, continuous-time Markov chains, hidden Markov models, point processes, Markov random fields, spatial and spatio-temporal processes, and statistical modeling and inference in stochastic processes. Applications to a variety of fields. Prerequisite(s): course 205A, 205B, or 261, or by permission of instructo