Auction Theory, Second Edition. Symposium in Honor of Herbert Giersch, ed. An Introduction to Auction Theory. An Introduction to Structural Econometrics of Auctions.
The Social Construction of Value. University of California Press. Van Ryzin, and C. Elsevier Science Publishers North- Holland. Industrial Organization, Auctions, and Incentives.
- Sid James: A Biography.
- The Amish Nanny (The Women of Lancaster County).
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Bad luck or bad design? Introduction to dynamical systems and their applications in mathematical modeling. Linear flows, local theory of nonlinear flows, linearization theorems, stable manifold theorem. Structural stability and bifurcations of vector fields. Low dimensional phenomena in discrete dynamics.
Bottom-up approach to mathematical modeling. Cellular automata and agent-based models: Additional topics may include power-law distributions in complex systems, self-organized criticality, phase transitions, and critical exponents. Basic definitions, paths and cycles, connectivity, trees and forests, bipartite graphs, Eulerian graphs; Matchings in bipartite graphs and in general graphs; Planar graphs, Euler's formula and Kuratowski's theorem.
Basic definitions, games, strategies, costs and payoffs, equilibria, cooperative games; Complexity of finding Nash equilibria; Mechanism design; Combinatorial auctions; Profit maximization in mechanism design; Cost sharing; Online mechanisms; Inefficiency of equilibria; Selfish routing; Network formation games; Potential function method; The price of anarchy; Sponsored search auctions.
The basic theory of Hilbert spaces, including the Projection Theorem, the Riesz Representation Theorem and the weak topology; weak derivatives, Sobolev spaces and the Sobolev Imbedding Theorem; the variational formulation of boundary value problems for ordinary and partial differential equations, the Lax-Milgram Lemma and its applications; the finite element method. Topological fixed point theory with applications to dynamical systems and optimization.
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Applications of these landmark results to the solvability and qualitative analysis of dynamical systems as well as convex and non-convex optimization are discussed. An introduction to algebraic aspects of number theory. Topics include the general theory of factorization of ideals in Dedekind domains and number fields, Kummer's theory on lifting of prime ideals in extension fields, factorization of prime ideals in Galois extensions, local fields, the proof of Hensel's lemma, arithmetic of global fields.
Review of linear and nonlinear equations in two variables. Exact solution techniques for 1st and 2nd order linear and nonlinear equations. Analysis of solutions, variational formulations, conservation laws, Noether's theorem. Lagrangian and Hamiltonian mechanics, field theory, differential geometric structures, Lie groups and Lie algebras, G-bundles, manifolds, introduction to algebraic topology. Applications to theoretical physics. Abelian groups, permutation groups, rotation groups.
Representations of discrete and continuous groups by linear transformations matrices.
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General properties and constructions of group representations. Representations of specific groups. Lie groups and Lie algebras.
Applications in various areas of Mathematics, including invariant theory and group algebras, and Theoretical Physics , including crystallography and symmetries in quantum systems. An introduction to point set topology concepts and principles. Metric spaces; topological spaces; continuity, compactness; connectedness; countability and separation axioms; metrizability; completeness; Baire spaces.
Advances in Auctions
Theory of finite population sampling; simple random sampling; sampling proportion; estimation of sample size; Stratified sampling; optimal allocation of sample sizes; ratio estimators; regression estimators; systematic and cluster sampling; multi-stage sampling; error in surveys; computational techniques and computer packages, and related topics. Order statistics; rank tests and statistics; methods based on the binomial distribution; contingency tables; Kolmogorov-Smirnov statistics; nonparametric analysis of variance; nonparametric regression; comparisons with parametric methods.
Classical linear model, generalized inverse matrix, distribution and quadratic forms, regression model, nested classification and classification with interaction, covariance analysis, variance components, binary data, polynomial data, log linear model, linear logit models, generalized linear model, conditional likelihoods, quasi-likelihoods, estimating equations, computational techniques and related topics.
MATH 3P86 or equivalent or permission of the instructor. Time series, trend, seasonality and error, theory of stationary processes, spectral theory, Box-Jenkins methods, theory of prediction, inference and forecasting. ARMA and ARIMA processes, vector time series models, state space models, Markov processes, renewal process, martingales, Brownian motion, diffusion processes, branching processes, queueing theory, stochastic models, computational techniques and related topics.
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To receive VEE credit, candidates will need a grade of 70 or better. Revision of probability theory, convergence of random variables, statistical models, sufficiency and ancillarity, point estimation, likelihood theory, optimal estimation, Bayesian methods, computational methods, minimum variance estimation, interval estimation and hypothesis testing, linear and generalized linear models, goodness-of-fit for discrete and continuous data, robustness, large sample theory, Bayesian inference. Theory of multivariate statistics, matrix algebra and random vector, sample geometry and random sampling, multivariate normal distribution, inference about means, covariance matrix, generalized Hotelling's T-square distribution, sample covariance and sample generalized variance, Wishart distribution, general hypothesis testing, analysis of variance and linear regression model, principle components, factor analysis, covariance analysis, canonical correlation analysis, discrimination and classification, cluster analysis and related topics.
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