Introduction and Motivation
We introduce the material under the umbrella of uncertainty
quantification. We examine its context from topics such as
verification & validation, aleatory vs. epistemic uncertainty, and methods
for characterizing uncertainties.
We also review some basic concepts in probability and approximation theory.
Assignments
Documents
Links
Probability Text 
An online version of the text used in a former STAT116 course. Chapters 2, 5, and 6 are the most
relevant for our class. 
STAT116 
Old course website for STAT116: Introductory Probabilty. 
AA222 
Course website for Intro to Multidisciplinary Design Optimization  a good reference for reviewing optimization. 
Convex Optimization Book 
Stephen Boyd's book on optimization  another good reference. 
Chebyshev and Fourier Spectral Methods 
John P. Boyd's (no relation to Stephen as far as I know) book on spectral methods. The second chapter gives
an excellent intuitive introduction to the convergence of Fourier/Chebyshev series 
Chebfun and Approximation Theory 
Chebfun is a Matlab suite for computing with functions via their Chebyshev expansions. This guide uses Chebfun
to explore some basic approximation theory. 
Approximation Theory and Approximation Practice 
Lloyd N. Trefethen's upcoming book on approximation theory using Chebfun. 
References

Computer Predictions with Quantified Uncertainty, Part I.
Tinsley Oden, Robert Moser, and Omar Ghattas

Computer Predictions with Quantified Uncertainty, Part II.
Tinsley Oden, Robert Moser, and Omar Ghattas

Error and Uncertainty in Modeling and Simulation.
William L. Oberkampf, Sharon M. DeLand, Brian M. Rutherford, Kathleen V. Diegert, Kenneth F. Alvin

Verification, Validation, and Predictive Capability in
Computational Engineering and Physics.
William L. Oberkampf, Timothy G. Trucano, Charles Hirsch

Conceptual and Computational
Basis for the Quantification of Margins and Uncertainty. Jon C. Helton

An Exploration of Alternative Approaches to the Representation of Uncertainty in Model Predictions.
J. C. Helton, J. D. Johnson, and W. L. Oberkampf.

A comprehensive framework for verification, validation,
and uncertainty quantification in scientific computing.
Christopher J. Roy and William L. Oberkampf.